Daily Papers

Real-valued functions on geometric data -- such as node attributes on a graph -- can be optimized using descriptors from persistent homology, allowing the user to incorporate topological terms in the loss function. When optimizing a single real-valued function (the one-parameter setting), there is a canonical choice of descriptor for persistent homology: the barcode. The operation mapping a real-valued function to its barcode is differentiable almost everywhere, and the convergence of gradient descent for losses using barcodes is relatively well understood. When optimizing a vector-valued function (the multiparameter setting), there is no unique choice of descriptor for multiparameter persistent homology, and many distinct descriptors have been proposed. This calls for the development of a general framework for differentiability and optimization that applies to a wide range of multiparameter homological descriptors. In this article, we develop such a framework and show that it encompasses well-known descriptors of different flavors, such as signed barcodes and the multiparameter persistence landscape. We complement the theory with numerical experiments supporting the idea that optimizing multiparameter homological descriptors can lead to improved performances compared to optimizing one-parameter descriptors, even when using the simplest and most efficiently computable multiparameter descriptors.

Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such descriptors is {\em persistent homology}, which encodes the change in shape as a filtration parameter changes; a typical parameter is the feature scale. For many data sets, it is useful to simultaneously vary multiple filtration parameters, for example feature scale and density. While the theoretical properties of single parameter persistent homology are well understood, less is known about the multiparameter case. In particular, a central question is the problem of representing multiparameter persistent homology by elements of a vector space for integration with standard machine learning algorithms. Existing approaches to this problem either ignore most of the multiparameter information to reduce to the one-parameter case or are heuristic and potentially unstable in the face of noise. In this article, we introduce a new general representation framework that leverages recent results on {\em decompositions} of multiparameter persistent homology. This framework is rich in information, fast to compute, and encompasses previous approaches. Moreover, we establish theoretical stability guarantees under this framework as well as efficient algorithms for practical computation, making this framework an applicable and versatile tool for analyzing geometric and point cloud data. We validate our stability results and algorithms with numerical experiments that demonstrate statistical convergence, prediction accuracy, and fast running times on several real data sets.

Interactive world models continually generate video by responding to a user's actions, enabling open-ended generation capabilities. However, existing models typically lack a 3D representation of the environment, meaning 3D consistency must be implicitly learned from data, and spatial memory is restricted to limited temporal context windows. This results in an unrealistic user experience and presents significant obstacles to down-stream tasks such as training agents. To address this, we present PERSIST, a new paradigm of world model which simulates the evolution of a latent 3D scene: environment, camera, and renderer. This allows us to synthesize new frames with persistent spatial memory and consistent geometry. Both quantitative metrics and a qualitative user study show substantial improvements in spatial memory, 3D consistency, and long-horizon stability over existing methods, enabling coherent, evolving 3D worlds. We further demonstrate novel capabilities, including synthesising diverse 3D environments from a single image, as well as enabling fine-grained, geometry-aware control over generated experiences by supporting environment editing and specification directly in 3D space. Project page: https://francelico.github.io/persist.github.io

In this article, we introduce a new parameterized family of topological invariants, taking the form of candidate decompositions, for multi-parameter persistence modules. We prove that our candidate decompositions are controllable approximations: when restricting to modules that can be decomposed into interval summands, we establish theoretical results about the approximation error between our candidate decompositions and the true underlying module in terms of the standard interleaving and bottleneck distances. Moreover, even when the underlying module does not admit such a decomposition, our candidate decompositions are nonetheless stable invariants; small perturbations in the underlying module lead to small perturbations in the candidate decomposition. Then, we introduce MMA (Multipersistence Module Approximation): an algorithm for computing stable instances of such invariants, which is based on fibered barcodes and exact matchings, two constructions that stem from the theory of single-parameter persistence. By design, MMA can handle an arbitrary number of filtrations, and has bounded complexity and running time. Finally, we present empirical evidence validating the generalization capabilities and running time speed-ups of MMA on several data sets.

Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding quality without labels remains an open challenge. In this work, we propose Persistence, a topology-aware metric based on persistent homology that quantifies the geometric structure and topological richness of embedding spaces in a fully unsupervised manner. Unlike metrics that assume linear separability or rely on covariance structure, Persistence captures global and multi-scale organization. Empirical results across diverse domains show that Persistence consistently achieves top-tier correlations with downstream performance, outperforming existing unsupervised metrics and enabling reliable model and hyperparameter selection.

World Models have emerged as a powerful paradigm for learning compact, predictive representations of environment dynamics, enabling agents to reason, plan, and generalize beyond direct experience. Despite recent interest in World Models, most available implementations remain publication-specific, severely limiting their reusability, increasing the risk of bugs, and reducing evaluation standardization. To mitigate these issues, we introduce stable-worldmodel (SWM), a modular, tested, and documented world-model research ecosystem that provides efficient data-collection tools, standardized environments, planning algorithms, and baseline implementations. In addition, each environment in SWM enables controllable factors of variation, including visual and physical properties, to support robustness and continual learning research. Finally, we demonstrate the utility of SWM by using it to study zero-shot robustness in DINO-WM.

Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such notions? How many parameters are really needed? In this paper we attempt to answer this question by training networks not in their native parameter space, but instead in a smaller, randomly oriented subspace. We slowly increase the dimension of this subspace, note at which dimension solutions first appear, and define this to be the intrinsic dimension of the objective landscape. The approach is simple to implement, computationally tractable, and produces several suggestive conclusions. Many problems have smaller intrinsic dimensions than one might suspect, and the intrinsic dimension for a given dataset varies little across a family of models with vastly different sizes. This latter result has the profound implication that once a parameter space is large enough to solve a problem, extra parameters serve directly to increase the dimensionality of the solution manifold. Intrinsic dimension allows some quantitative comparison of problem difficulty across supervised, reinforcement, and other types of learning where we conclude, for example, that solving the inverted pendulum problem is 100 times easier than classifying digits from MNIST, and playing Atari Pong from pixels is about as hard as classifying CIFAR-10. In addition to providing new cartography of the objective landscapes wandered by parameterized models, the method is a simple technique for constructively obtaining an upper bound on the minimum description length of a solution. A byproduct of this construction is a simple approach for compressing networks, in some cases by more than 100 times.

Existing benchmarks measure capability -- whether a model succeeds on a single attempt -- but production deployments require reliability -- consistent success across repeated attempts on tasks of varying duration. We show these properties diverge systematically as task duration grows, and that pass@1 on short tasks is structurally blind to this divergence. We introduce a reliability science framework for long-horizon LLM agents with four metrics: Reliability Decay Curve (RDC), Variance Amplification Factor (VAF), Graceful Degradation Score (GDS), and Meltdown Onset Point (MOP). We evaluate 10 models across 23,392 episodes on a 396-task benchmark spanning four duration buckets and three domains. Key findings: (1) reliability decay is domain-stratified -- SE GDS drops from 0.90 to 0.44 while document processing is nearly flat (0.74 to 0.71); (2) VAF bifurcates by capability tier -- high VAF is a capability signature, not an instability signal; (3) capability and reliability rankings diverge substantially, with multi-rank inversions at long horizons; (4) frontier models have the highest meltdown rates (up to 19%) because they attempt ambitious multi-step strategies that sometimes spiral; and (5) memory scaffolds universally hurt long-horizon performance across all 10 models. These results motivate reliability as a first-class evaluation dimension alongside capability.

Training large neural networks (NNs) requires optimizing high-dimensional data-dependent loss functions. The optimization landscape of these functions is often highly complex and textured, even fractal-like, with many spurious local minima, ill-conditioned valleys, degenerate points, and saddle points. Complicating things further is the fact that these landscape characteristics are a function of the data, meaning that noise in the training data can propagate forward and give rise to unrepresentative small-scale geometry. This poses a difficulty for gradient-based optimization methods, which rely on local geometry to compute updates and are, therefore, vulnerable to being derailed by noisy data. In practice,this translates to a strong dependence of the optimization dynamics on the noise in the data, i.e., poor generalization performance. To remediate this problem, we propose a new optimization procedure: Rolling Ball Optimizer (RBO), that breaks this spatial locality by incorporating information from a larger region of the loss landscape in its updates. We achieve this by simulating the motion of a rigid sphere of finite radius rolling on the loss landscape, a straightforward generalization of Gradient Descent (GD) that simplifies into it in the infinitesimal limit. The radius serves as a hyperparameter that determines the scale at which RBO sees the loss landscape, allowing control over the granularity of its interaction therewith. We are motivated by the intuition that the large-scale geometry of the loss landscape is less data-specific than its fine-grained structure, and that it is easier to optimize. We support this intuition by proving that our algorithm has a smoothing effect on the loss function. Evaluation against SGD, SAM, and Entropy-SGD, on MNIST and CIFAR-10/100 demonstrates promising results in terms of convergence speed, training accuracy, and generalization performance.

The Polymorphic Combinatorial Framework (PCF) leverages Large Language Models (LLMs) and mathematical frameworks to guide the meta-prompt enabled design of solution spaces and adaptive AI agents for complex, dynamic environments. Unlike static agent architectures, PCF enables real-time parameter reconfiguration through mathematically-grounded combinatorial spaces, allowing agents to adapt their core behavioral traits dynamically. Grounded in combinatorial logic, topos theory, and rough fuzzy set theory, PCF defines a multidimensional SPARK parameter space (Skills, Personalities, Approaches, Resources, Knowledge) to capture agent behaviors. This paper demonstrates how LLMs can parameterize complex spaces and estimate likely parameter values/variabilities. Using PCF, we parameterized mock caf\'e domains (five levels of complexity), estimated variables/variabilities, and conducted over 1.25 million Monte Carlo simulations. The results revealed trends in agent adaptability and performance across the five complexity tiers, with diminishing returns at higher complexity levels highlighting thresholds for scalable designs. PCF enables the generation of optimized agent configurations for specific scenarios while maintaining logical consistency. This framework supports scalable, dynamic, explainable, and ethical AI applications in domains like customer service, healthcare, robotics, and collaborative systems, paving the way for adaptable and cooperative next-generation polymorphic agents.

Recent advances in learning rate (LR) scheduling have demonstrated the effectiveness of decay-free approaches that eliminate the traditional decay phase while maintaining competitive performance. Model merging techniques have emerged as particularly promising solutions in this domain. We present Warmup-Stable and Merge (WSM), a general framework that establishes a formal connection between learning rate decay and model merging. WSM provides a unified theoretical foundation for emulating various decay strategies-including cosine decay, linear decay and inverse square root decay-as principled model averaging schemes, while remaining fully compatible with diverse optimization methods. Through extensive experiments, we identify merge duration-the training window for checkpoint aggregation-as the most critical factor influencing model performance, surpassing the importance of both checkpoint interval and merge quantity. Our framework consistently outperforms the widely-adopted Warmup-Stable-Decay (WSD) approach across multiple benchmarks, achieving significant improvements of +3.5% on MATH, +2.9% on HumanEval, and +5.5% on MMLU-Pro. The performance advantages extend to supervised fine-tuning scenarios, highlighting WSM's potential for long-term model refinement.

Persistent homology (PH) provides topological descriptors for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, e.g., relabeling. Most applications of PH focus on the one-parameter case -- where the descriptors summarize the changes in topology of data as it is filtered by a single quantity of interest -- and there is now a wide array of methods enabling the use of one-parameter PH descriptors in data science, which rely on the stable vectorization of these descriptors as elements of a Hilbert space. Although the multiparameter PH (MPH) of data that is filtered by several quantities of interest encodes much richer information than its one-parameter counterpart, the scarceness of stability results for MPH descriptors has so far limited the available options for the stable vectorization of MPH. In this paper, we aim to bring together the best of both worlds by showing how the interpretation of signed barcodes -- a recent family of MPH descriptors -- as signed measures leads to natural extensions of vectorization strategies from one parameter to multiple parameters. The resulting feature vectors are easy to define and to compute, and provably stable. While, as a proof of concept, we focus on simple choices of signed barcodes and vectorizations, we already see notable performance improvements when comparing our feature vectors to state-of-the-art topology-based methods on various types of data.

Building world models that accurately and comprehensively represent the real world is the utmost aspiration for conditional image generative models as it would enable their use as world simulators. For these models to be successful world models, they should not only excel at image quality and prompt-image consistency but also ensure high representation diversity. However, current research in generative models mostly focuses on creative applications that are predominantly concerned with human preferences of image quality and aesthetics. We note that generative models have inference time mechanisms - or knobs - that allow the control of generation consistency, quality, and diversity. In this paper, we use state-of-the-art text-to-image and image-and-text-to-image models and their knobs to draw consistency-diversity-realism Pareto fronts that provide a holistic view on consistency-diversity-realism multi-objective. Our experiments suggest that realism and consistency can both be improved simultaneously; however there exists a clear tradeoff between realism/consistency and diversity. By looking at Pareto optimal points, we note that earlier models are better at representation diversity and worse in consistency/realism, and more recent models excel in consistency/realism while decreasing significantly the representation diversity. By computing Pareto fronts on a geodiverse dataset, we find that the first version of latent diffusion models tends to perform better than more recent models in all axes of evaluation, and there exist pronounced consistency-diversity-realism disparities between geographical regions. Overall, our analysis clearly shows that there is no best model and the choice of model should be determined by the downstream application. With this analysis, we invite the research community to consider Pareto fronts as an analytical tool to measure progress towards world models.

Reliable evaluation is fundamental to the progress of Large Language Models (LLMs), yet the evaluation process during pre-training is plagued by significant instability that obscures true learning dynamics. In this work, we systematically diagnose this instability, attributing it to two distinct sources: Parameter Instability from training stochasticity and Evaluation Instability from noisy measurement protocols. To counteract both sources of noise, we introduce MaP, a dual-pronged framework that synergistically integrates checkpoint Merging and the Pass@k metric. Checkpoint merging smooths the parameter space by averaging recent model weights, while Pass@k provides a robust, low-variance statistical estimate of model capability. Extensive experiments show that MaP yields significantly smoother performance curves, reduces inter-run variance, and ensures more consistent model rankings. Ultimately, MaP provides a more reliable and faithful lens for observing LLM training dynamics, laying a crucial empirical foundation for LLM research.

The integration of Large Language Models (LLMs) into Geographic Information Systems (GIS) marks a paradigm shift toward autonomous spatial analysis. However, evaluating these LLM-based agents remains challenging due to the complex, multi-step nature of geospatial workflows. Existing benchmarks primarily rely on static text or code matching, neglecting dynamic runtime feedback and the multimodal nature of spatial outputs. To address this gap, we introduce GeoAgentBench (GABench), a dynamic and interactive evaluation benchmark tailored for tool-augmented GIS agents. GABench provides a realistic execution sandbox integrating 117 atomic GIS tools, encompassing 53 typical spatial analysis tasks across 6 core GIS domains. Recognizing that precise parameter configuration is the primary determinant of execution success in dynamic GIS environments, we designed the Parameter Execution Accuracy (PEA) metric, which utilizes a "Last-Attempt Alignment" strategy to quantify the fidelity of implicit parameter inference. Complementing this, a Vision-Language Model (VLM) based verification is proposed to assess data-spatial accuracy and cartographic style adherence. Furthermore, to address the frequent task failures caused by parameter misalignments and runtime anomalies, we developed a novel agent architecture, Plan-and-React, that mimics expert cognitive workflows by decoupling global orchestration from step-wise reactive execution. Extensive experiments with seven representative LLMs demonstrate that the Plan-and-React paradigm significantly outperforms traditional frameworks, achieving the optimal balance between logical rigor and execution robustness, particularly in multi-step reasoning and error recovery. Our findings highlight current capability boundaries and establish a robust standard for assessing and advancing the next generation of autonomous GeoAI.

The presence of linear paths in parameter space between two different network solutions in certain cases, i.e., linear mode connectivity (LMC), has garnered interest from both theoretical and practical fronts. There has been significant research that either practically designs algorithms catered for connecting networks by adjusting for the permutation symmetries as well as some others that more theoretically construct paths through which networks can be connected. Yet, the core reasons for the occurrence of LMC, when in fact it does occur, in the highly non-convex loss landscapes of neural networks are far from clear. In this work, we take a step towards understanding it by providing a model of how the loss landscape needs to behave topographically for LMC (or the lack thereof) to manifest. Concretely, we present a `mountainside and ridge' perspective that helps to neatly tie together different geometric features that can be spotted in the loss landscape along the training runs. We also complement this perspective by providing a theoretical analysis of the barrier height, for which we provide empirical support, and which additionally extends as a faithful predictor of layer-wise LMC. We close with a toy example that provides further intuition on how barriers arise in the first place, all in all, showcasing the larger aim of the work -- to provide a working model of the landscape and its topography for the occurrence of LMC.

Most evaluations of LLM agents look like exams: a discrete task, a clean environment, a score in minutes or hours. We argue that this approach is mismatched with the deployment conditions of autonomous systems, where the relevant timescale can be weeks to months, and where the dynamics that matter most, such as behavioral drift, governance in diverse environmental contexts, and cross-influence between agents from different model families, only emerge over time. We introduce Emergence World, a continuously running multi-agent simulation platform designed to make those dynamics measurable. The platform hosts populations of LLM-driven agents in a shared spatial world grounded in live external data (e.g. real-time weather, news APIs, internet access), equips each agent with 120+ specialized tools and three persistent memory systems, and lets them govern themselves through democratic mechanisms with consequential outcomes. The platform is model-agnostic at the reasoning layer and supports heterogeneous populations in which agents from different vendors share the same world. To illustrate the kinds of questions the platform makes tractable, we present a 15-day cross-vendor study with five parallel worlds powered by Claude Sonnet 4.6, Grok 4.1 Fast, Gemini 3 Flash, GPT-5-mini, and a mixed population. Identical roles and starting conditions produced radically different outcomes, ranging from stable deliberative governance to total population collapse. We release the prompts, log data and configurations to support further research on long-horizon multi-agent autonomy.

Persistent memory is a central capability for AI agents, yet the mathematical foundations of memory retrieval, lifecycle management, and consistency remain unexplored. Current systems employ cosine similarity for retrieval, heuristic decay for salience, and provide no formal contradiction detection. We establish information-geometric foundations through three contributions. First, a retrieval metric derived from the Fisher information structure of diagonal Gaussian families, satisfying Riemannian metric axioms, invariant under sufficient statistics, and computable in O(d) time. Second, memory lifecycle formulated as Riemannian Langevin dynamics with proven existence and uniqueness of the stationary distribution via the Fokker-Planck equation, replacing hand-tuned decay with principled convergence guarantees. Third, a cellular sheaf model where non-trivial first cohomology classes correspond precisely to irreconcilable contradictions across memory contexts. On the LoCoMo benchmark, the mathematical layers yield +12.7 percentage points over engineering baselines across six conversations, reaching +19.9 pp on the most challenging dialogues. A four-channel retrieval architecture achieves 75% accuracy without cloud dependency. Cloud-augmented results reach 87.7%. A zero-LLM configuration satisfies EU AI Act data sovereignty requirements by architectural design. To our knowledge, this is the first work establishing information-geometric, sheaf-theoretic, and stochastic-dynamical foundations for AI agent memory systems.

Consistency models (CMs) are a powerful class of diffusion-based generative models optimized for fast sampling. Most existing CMs are trained using discretized timesteps, which introduce additional hyperparameters and are prone to discretization errors. While continuous-time formulations can mitigate these issues, their success has been limited by training instability. To address this, we propose a simplified theoretical framework that unifies previous parameterizations of diffusion models and CMs, identifying the root causes of instability. Based on this analysis, we introduce key improvements in diffusion process parameterization, network architecture, and training objectives. These changes enable us to train continuous-time CMs at an unprecedented scale, reaching 1.5B parameters on ImageNet 512x512. Our proposed training algorithm, using only two sampling steps, achieves FID scores of 2.06 on CIFAR-10, 1.48 on ImageNet 64x64, and 1.88 on ImageNet 512x512, narrowing the gap in FID scores with the best existing diffusion models to within 10%.

Weight-perturbation evolution strategies (ES) can fine-tune billion-parameter language models with surprisingly small populations (e.g., N!approx!30), contradicting classical zeroth-order curse-of-dimensionality intuition. We also observe a second seemingly separate phenomenon: under fixed hyperparameters, the stochastic fine-tuning reward often rises, peaks, and then degrades in both ES and GRPO. We argue that both effects reflect a shared geometric property of fine-tuning landscapes: they are low-dimensional in curvature. A small set of high-curvature dimensions dominates improvement, producing (i) heterogeneous time scales that yield rise-then-decay under fixed stochasticity, as captured by a minimal quadratic stochastic-ascent model, and (ii) degenerate improving updates, where many random perturbations share similar components along these directions. Using ES as a geometric probe on fine-tuning reward landscapes of GSM8K, ARC-C, and WinoGrande across Qwen2.5-Instruct models (0.5B--7B), we show that reward-improving perturbations remain empirically accessible with small populations across scales. Together, these results reconcile ES scalability with non-monotonic training dynamics and suggest that high-dimensional fine-tuning may admit a broader class of viable optimization methods than worst-case theory implies.

Consistency models have been proposed for fast generative modeling, achieving results competitive with diffusion and flow models. However, these methods exhibit inherent instability and limited reproducibility when training from scratch, motivating subsequent work to explain and stabilize these issues. While these efforts have provided valuable insights, the explanations remain fragmented, and the theoretical relationships remain unclear. In this work, we provide a theoretical examination of consistency models by analyzing them from a flow map-based perspective. This joint analysis clarifies how training stability and convergence behavior can give rise to degenerate solutions. Building on these insights, we revisit self-distillation as a practical remedy for certain forms of suboptimal convergence and reformulate it to avoid excessive gradient norms for stable optimization. We further demonstrate that our strategy extends beyond image generation to diffusion-based policy learning, without reliance on a pretrained diffusion model for initialization, thereby illustrating its broader applicability.

RL post-training strategies are dataset-dependent and reveal a recurring empirical pattern: capacity parameters accumulate monotonically across stages, while regularization parameters predominantly oscillate in response to shifting training dynamics. This distinction matters because fixed schedules commit all parameters to fixed trajectories and therefore cannot express the non-stationary exploration-exploitation tradeoffs that regularization must track; the principle provides actionable design rules for multi-stage training. We discover this through LLMZero, a system where LLM agents search over training trajectories via tree search, diagnosing pathologies at each checkpoint and proposing coordinated multi-parameter transitions. Across 4 diverse GRPO tasks, LLMZero discovers strategies that improve over the base model by 9% to 140% relative and over grid search by 6% to 15% relative, consistently outperforming random search and the skill-based agent. The structural principle transfers across tasks, providing an explanation for why discovered strategies take qualitatively different forms yet share similar parameter dynamics.

The Model Context Protocol (MCP) has rapidly established itself as a standard interface for enabling LLM-based agents to interact with external tools and services. As MCP servers are increasingly entrusted with security-sensitive operations, understanding their real-world risks has become critical. In practice, due to the absence of large-scale runtime MCP servers, such understanding largely relies on security scanners applied to a small number of cases, yet the reliability of these assessments remains unclear. In this study, we revisit how MCP security is measured. We present MCPZoo, the largest collection of MCP servers for dynamic analysis to date. MCPZoo is constructed through a multi-agent framework for transforming in-the-wild static repositories into dynamic services. The framework emulates how human experts build, diagnose, and iteratively repair deployment and runtime defects by combining environment inference with feedback-driven refinement. To ensure practical interactivity at runtime, the servers are validated via real protocol interactions. As a result, MCPZoo contains 64,611 unique MCP servers (113,927 in total), with more than 37,288 supporting dynamic analysis. Leveraging MCPZoo, we conduct the first ecosystem-scale measurement of MCP servers and the scanners that analyze them. While existing scanners report that 96.89% of servers are risky, we find that these signals are unreliable. In particular, manual validation shows that less than 50% of sampled alerts are true positives, and scanner outputs exhibit clear inconsistency across scanners. Overall, MCPZoo enables large-scale, reproducible measurement of MCP server security and exposes limitations of current scanning practices. We further release a public query interface to support practical risk assessment of MCP servers.

Several families of continual learning techniques have been proposed to alleviate catastrophic interference in deep neural network training on non-stationary data. However, a comprehensive comparison and analysis of limitations remains largely open due to the inaccessibility to suitable datasets. Empirical examination not only varies immensely between individual works, it further currently relies on contrived composition of benchmarks through subdivision and concatenation of various prevalent static vision datasets. In this work, our goal is to bridge this gap by introducing a computer graphics simulation framework that repeatedly renders only upcoming urban scene fragments in an endless real-time procedural world generation process. At its core lies a modular parametric generative model with adaptable generative factors. The latter can be used to flexibly compose data streams, which significantly facilitates a detailed analysis and allows for effortless investigation of various continual learning schemes.

Training language models currently requires pre-determining a fixed compute budget because the typical cosine learning rate schedule depends on the total number of steps. In contrast, the Warmup-Stable-Decay (WSD) schedule uses a constant learning rate to produce a main branch of iterates that can in principle continue indefinitely without a pre-specified compute budget. Then, given any compute budget, one can branch out from the main branch at a proper time with a rapidly decaying learning rate to produce a strong model. Empirically, WSD generates a non-traditional loss curve: the loss remains elevated during the stable phase but sharply declines during the decay phase. Towards explaining this phenomenon, we conjecture that pretraining loss exhibits a river valley landscape, which resembles a deep valley with a river at its bottom. Under this assumption, we show that during the stable phase, the iterate undergoes large oscillations due to the high learning rate, yet it progresses swiftly along the river. During the decay phase, the rapidly dropping learning rate minimizes the iterate's oscillations, moving it closer to the river and revealing true optimization progress. Therefore, the sustained high learning rate phase and fast decaying phase are responsible for progress in the river and the mountain directions respectively, and are both critical. Our analysis predicts phenomenons consistent with empirical observations and shows that this landscape can emerge from pretraining on a simple bi-gram dataset. Inspired by the theory, we introduce WSD-S, a variant of WSD that reuses previous checkpoints' decay phases and keeps only one main branch, where we resume from a decayed checkpoint. WSD-S empirically outperforms WSD and Cyclic-Cosine in obtaining multiple language model checkpoints across various compute budgets in a single run for parameters scaling from 0.1B to 1.2B.

We characterize the pre-softmax attention matrix QK^top in transformers as an associative memory matrix encoding pairwise associations between input features. By decomposing this matrix into its symmetric and skew-symmetric parts, we interpret the symmetric component as governing the structure of the energy landscape, and the skew-symmetric component as driving circulation on that landscape. Leveraging the energy formulation induced by the symmetric component, we derive Hopfield-style stability measures that quantify the stability of retrieved features. We observe meaningful correlations between Hopfield-style stability measures and the fidelity-diversity trade-offs in generation. Finally, we propose a controllable knob to modulate this trade-off by modifying the circulation of the underlying dynamics. Code is available at our GitHub (https://github.com/hyeon-cho/Attention-Symmetric-Decomposition).

Large-scale land enclosure for speculative mega-development constitutes a non-equilibrium spatial process whose velocity, topology, and irreversibility remain poorly quantified. We study the Pantai Indah Kapuk 2 (PIK2) coastal mega-development north of Jakarta, Indonesia, using eight years (2017--2024) of Sentinel-2 land-use/land-cover (LULC) data at 10-meter resolution. The landscape is projected onto a Marxian probability simplex partitioning terrestrial pixels into Commons, Agrarian, and Capital fractions. Fisher-Rao (FR) geodesic distances on this simplex identify a transformation pulse of 0.405~rad/yr during 2019--2020, coinciding with major construction activity. Absorbing Markov chain analysis yields expected absorption times into the built environment of 46.0~years for cropland and 38.1~years for tree cover, with a pooled built-area self-retention rate of 96.4%. Percolation analysis reveals that a giant connected component containing 89--95% of all built pixels persists at occupation probabilities p in [0.096, 0.162], far below the random percolation threshold p_c approx 0.593, indicating planned rather than stochastic spatial growth. The box-counting fractal dimension of the urban boundary increases from d_f = 1.316 to 1.397, consistent with increasingly irregular frontier expansion. These results suggest that information-geometric and statistical-mechanical tools can characterize the kinematic and topological signatures of capitalist spatial accumulation with quantitative precision.

The ability to engineer novel proteins with higher fitness for a desired property would be revolutionary for biotechnology and medicine. Modeling the combinatorially large space of sequences is infeasible; prior methods often constrain optimization to a small mutational radius, but this drastically limits the design space. Instead of heuristics, we propose smoothing the fitness landscape to facilitate protein optimization. First, we formulate protein fitness as a graph signal then use Tikunov regularization to smooth the fitness landscape. We find optimizing in this smoothed landscape leads to improved performance across multiple methods in the GFP and AAV benchmarks. Second, we achieve state-of-the-art results utilizing discrete energy-based models and MCMC in the smoothed landscape. Our method, called Gibbs sampling with Graph-based Smoothing (GGS), demonstrates a unique ability to achieve 2.5 fold fitness improvement (with in-silico evaluation) over its training set. GGS demonstrates potential to optimize proteins in the limited data regime. Code: https://github.com/kirjner/GGS

Recent growth in reinforcement learning (RL) has surfaced a need for diverse, specialized training environments. Hand-curated environments with fixed task and reward difficulties become ineffective signals as model performance improves, and sparse rewards over long horizons induce mode collapse on specific workflows or tool structures. World models that simulate environment states have matched pure rollout performance, making them promising for scaling diversity on-demand. However, autoregressive (AR) world models suffer from a left-to-right bias preventing conditioning on globally interdependent state anchors such as tool schemas, prior turns, and expected outcomes. We (i) formalize text-based world modeling as a steerable transition-dynamics problem decomposed into initial state, task context, tool schemas, domain rules, and steering directives, and (ii) curate 239,403 grounded state-action trajectories spanning nine open-source environments and twelve frontier model families. We compare AR LMs and masked diffusion language models (MDLMs), showing MDLMs, via bidirectional anchor-aware denoising, achieve better coherence, groundedness, and empirically validated rollout diversity than LLMs over 4x their parameter size, at comparable inference latency. We introduce a plug-and-play GRPO training framework with deterministic state checks, and perform zero-shot transfer ablations on three OOD environments (ScienceWorld, ALFWorld, AppWorld) across three 1.2B-7B agent backbones (LFM2.5, Qwen3, Mistral), achieving up to 47% absolute gains over baselines without environment-specific fine-tuning. We further conduct behavioral analysis of failure modes under adversarial scenarios and human evaluation on realism, outcome correctness, and training utility. We open-source our work to encourage research in this direction.

Long-term forecasting of chaotic systems from short-term observations remains a fundamental and underexplored challenge due to the intrinsic sensitivity to initial conditions and the complex geometry of strange attractors. Existing approaches often rely on long-term training data or focus on short-term sequence correlations, struggling to maintain predictive stability and dynamical coherence over extended horizons. We propose PhyxMamba, a novel framework that integrates a Mamba-based state-space model with physics-informed principles to capture the underlying dynamics of chaotic systems. By reconstructing the attractor manifold from brief observations using time-delay embeddings, PhyxMamba extracts global dynamical features essential for accurate forecasting. Our generative training scheme enables Mamba to replicate the physical process, augmented by multi-token prediction and attractor geometry regularization for physical constraints, enhancing prediction accuracy and preserving key statistical invariants. Extensive evaluations on diverse simulated and real-world chaotic systems demonstrate that PhyxMamba delivers superior long-term forecasting and faithfully captures essential dynamical invariants from short-term data. This framework opens new avenues for reliably predicting chaotic systems under observation-scarce conditions, with broad implications across climate science, neuroscience, epidemiology, and beyond. Our code is open-source at https://github.com/tsinghua-fib-lab/PhyxMamba.

Autoregressive video diffusion models enable streaming generation but often degrade over long rollouts: static scene layouts drift, while mechanisms that improve spatial stability tend to suppress motion, causing natural flows such as water, fire, or smoke to stagnate. We study this stability-motion trade-off in fixed-camera long-horizon nature video generation, where the two failure modes can be more clearly separated than in moving-camera settings. We propose Steady-Forcing, a memory and training framework combining a persistent visual anchor (V-Sink), an exponential moving-average motion memory (EMA-Sink), block-relative temporal encoding, periodic cache purification, and distillation from a Wan2.1-14B teacher with motion-rewarded priors under task-focused configurations. Together, these components are designed to preserve background identity while sustaining visually plausible fluid dynamics over multi-minute autoregressive rollouts. Evaluations across seven baselines show that Steady-Forcing improves long horizon background consistency and imaging quality, while a blind user study indicates stronger perceived stability and motion continuity. The benchmark evaluation further suggest that generic VBench aggregate scores under-penalize fixed-camera artifacts as well as rewarding drift-induced optical flow as Dynamic Degree while not directly penalizing texture hardening or flow stagnation - motivating future task-specific benchmarks for static-camera nature-flow evaluation. Project page: https://minar09.github.io/steadyforcing/

Large language models (LLMs) are increasingly used to evolve programs and multi-agent systems, yet most existing approaches rely on overwrite-based mutations that maintain only a single candidate at a time. Such methods discard useful variants, suffer from destructive edits, and explore a brittle search space prone to structural failure. We introduce EvoLattice, a framework that represents an entire population of candidate programs or agent behaviors within a single directed acyclic graph. Each node stores multiple persistent alternatives, and every valid path through the graph defines a distinct executable candidate, yielding a large combinatorial search space without duplicating structure. EvoLattice enables fine-grained alternative-level evaluation by scoring each alternative across all paths in which it appears, producing statistics that reveal how local design choices affect global performance. These statistics provide a dense, data-driven feedback signal for LLM-guided mutation, recombination, and pruning, while preserving successful components. Structural correctness is guaranteed by a deterministic self-repair mechanism that enforces acyclicity and dependency consistency independently of the LLM. EvoLattice naturally extends to agent evolution by interpreting alternatives as prompt fragments or sub-agent behaviors. Across program synthesis (proxy and optimizer meta-learning), EvoLattice yields more stable evolution, greater expressivity, and stronger improvement trajectories than prior LLM-guided methods. The resulting dynamics resemble quality-diversity optimization, emerging implicitly from EvoLattice's internal multi-alternative representation rather than an explicit external archive.

Forecasting multiple future events within a given time horizon is essential for applications in finance, retail, social networks, and healthcare. Marked Temporal Point Processes (MTPP) provide a principled framework to model both the timing and labels of events. However, most existing research focuses on predicting only the next event, leaving long-horizon forecasting largely underexplored. To address this gap, we introduce HoTPP, the first benchmark specifically designed to rigorously evaluate long-horizon predictions. We identify shortcomings in widely used evaluation metrics, propose a theoretically grounded T-mAP metric, present strong statistical baselines, and offer efficient implementations of popular models. Our empirical results demonstrate that modern MTPP approaches often underperform simple statistical baselines. Furthermore, we analyze the diversity of predicted sequences and find that most methods exhibit mode collapse. Finally, we analyze the impact of autoregression and intensity-based losses on prediction quality, and outline promising directions for future research. The HoTPP source code, hyperparameters, and full evaluation results are available at GitHub.

In this paper, we investigate the long-term memory learning capabilities of state-space models (SSMs) from the perspective of parameterization. We prove that state-space models without any reparameterization exhibit a memory limitation similar to that of traditional RNNs: the target relationships that can be stably approximated by state-space models must have an exponential decaying memory. Our analysis identifies this "curse of memory" as a result of the recurrent weights converging to a stability boundary, suggesting that a reparameterization technique can be effective. To this end, we introduce a class of reparameterization techniques for SSMs that effectively lift its memory limitations. Besides improving approximation capabilities, we further illustrate that a principled choice of reparameterization scheme can also enhance optimization stability. We validate our findings using synthetic datasets and language models.

Reinforcement learning pipelines for Large Language Model (LLM) training often rely on manually redesigned environments between stages, requiring practitioners to heuristically infer which configuration will best improve the current policy. To automate this process, we propose the LLM-as-Environment-Engineer framework in which the current policy model analyzes failure trajectories together with contextual information and proposes modifications to the next-stage training environment configuration. We also introduce MAPF-FrozenLake, a controllable testbed whose generator exposes multi-dimensional environment configurations, making it suitable for studying and benchmarking environment redesign. On this testbed, we condition the environment engineer on structured summaries of policy behavior, failure cases, and environment statistics, from which it produces the configuration for the next training stage. With Qwen3-4B as the backbone, our framework achieves the strongest aggregate performance on our benchmarks, outperforming larger proprietary LLMs (e.g., GPT, Gemini) and fixed-environment training baselines. We further analyze which forms of context are most effective, finding that successful environment updates rely on failure evidence and preserve configurations that already work. Interestingly, the current RL checkpoint serves as a better environment engineer than the original base model, suggesting that policy learning improves the model's ability to diagnose its remaining weaknesses.

Large Language Models (LLMs) excel at single-turn tasks such as instruction following and summarization, yet real-world deployments require sustained multi-turn interactions where user goals and conversational context persist and evolve. A recurring challenge in this setting is context drift: the gradual divergence of a model's outputs from goal-consistent behavior across turns. Unlike single-turn errors, drift unfolds temporally and is poorly captured by static evaluation metrics. In this work, we present a study of context drift in multi-turn interactions and propose a simple dynamical framework to interpret its behavior. We formalize drift as the turn-wise KL divergence between the token-level predictive distributions of the test model and a goal-consistent reference model, and propose a recurrence model that interprets its evolution as a bounded stochastic process with restoring forces and controllable interventions. We instantiate this framework in both synthetic long-horizon rewriting tasks and realistic user-agent simulations such as in tau-Bench, measuring drift for several open-weight LLMs that are used as user simulators. Our experiments consistently reveal stable, noise-limited equilibria rather than runaway degradation, and demonstrate that simple reminder interventions reliably reduce divergence in line with theoretical predictions. Together, these results suggest that multi-turn drift can be understood as a controllable equilibrium phenomenon rather than as inevitable decay, providing a foundation for studying and mitigating context drift in extended interactions.

Conversational assistants are increasingly integrating long-term memory with large language models (LLMs). This persistence of memories, e.g., the user is vegetarian, can enhance personalization in future conversations. However, the same persistence can also introduce safety risks that have been largely overlooked. Hence, we introduce PersistBench to measure the extent of these safety risks. We identify two long-term memory-specific risks: cross-domain leakage, where LLMs inappropriately inject context from the long-term memories; and memory-induced sycophancy, where stored long-term memories insidiously reinforce user biases. We evaluate 18 frontier and open-source LLMs on our benchmark. Our results reveal a surprisingly high failure rate across these LLMs - a median failure rate of 53% on cross-domain samples and 97% on sycophancy samples. To address this, our benchmark encourages the development of more robust and safer long-term memory usage in frontier conversational systems.

Various algorithms for continual learning (CL) have been designed with the goal of effectively alleviating the trade-off between stability and plasticity during the CL process. To achieve this goal, tuning appropriate hyperparameters for each algorithm is essential. As an evaluation protocol, it has been common practice to train a CL algorithm using diverse hyperparameter values on a CL scenario constructed with a benchmark dataset. Subsequently, the best performance attained with the optimal hyperparameter value serves as the criterion for evaluating the CL algorithm. In this paper, we contend that this evaluation protocol is not only impractical but also incapable of effectively assessing the CL capability of a CL algorithm. Returning to the fundamental principles of model evaluation in machine learning, we propose an evaluation protocol that involves Hyperparameter Tuning and Evaluation phases. Those phases consist of different datasets but share the same CL scenario. In the Hyperparameter Tuning phase, each algorithm is iteratively trained with different hyperparameter values to find the optimal hyperparameter values. Subsequently, in the Evaluation phase, the optimal hyperparameter values is directly applied for training each algorithm, and their performance in the Evaluation phase serves as the criterion for evaluating them. Through experiments on CIFAR-100 and ImageNet-100 based on the proposed protocol in class-incremental learning, we not only observed that the existing evaluation method fail to properly assess the CL capability of each algorithm but also observe that some recently proposed state-of-the-art algorithms, which reported superior performance, actually exhibit inferior performance compared to the previous algorithm.

We derive an expression for the variation between parallel trajectories in phenotypic evolution, extending the well known result that predicts the mean evolutionary path in adaptive dynamics or quantitative genetics. We show how this expression gives rise to the notion of fluctuation domains - parts of the fitness landscape where the rate of evolution is very predictable (due to fluctuation dissipation) and parts where it is highly variable (due to fluctuation enhancement). These fluctuation domains are determined by the curvature of the fitness landscape. Regions of the fitness landscape with positive curvature, such as adaptive valleys or branching points, experience enhancement. Regions with negative curvature, such as adaptive peaks, experience dissipation. We explore these dynamics in the ecological scenarios of implicit and explicit competition for a limiting resource.

Large Language Models (LLMs) have emerged as powerful operators for evolutionary search, yet the design of efficient search scaffolds remains ad hoc. While promising, current LLM-in-the-loop systems lack a systematic approach to managing the evolutionary process. We identify three distinct failure modes: Context Pollution, where experiment history biases future candidate generation; Mode Collapse, where agents stagnate in local minima due to poor exploration-exploitation balance; and Weak Collaboration, where rigid crossover strategies fail to leverage parallel search trajectories effectively. We introduce Progress-Aware Consistent Evolution (PACEvolve), a framework designed to robustly govern the agent's context and search dynamics, to address these challenges. PACEvolve combines hierarchical context management (HCM) with pruning to address context pollution; momentum-based backtracking (MBB) to escape local minima; and a self-adaptive sampling policy that unifies backtracking and crossover for dynamic search coordination (CE), allowing agents to balance internal refinement with cross-trajectory collaboration. We demonstrate that PACEvolve provides a systematic path to consistent, long-horizon self-improvement, achieving state-of-the-art results on LLM-SR and KernelBench, while discovering solutions surpassing the record on Modded NanoGPT.

Multimodal foundation models serve numerous applications at the intersection of vision and language. Still, despite being pretrained on extensive data, they become outdated over time. To keep models updated, research into continual pretraining mainly explores scenarios with either (1) infrequent, indiscriminate updates on large-scale new data, or (2) frequent, sample-level updates. However, practical model deployment often operates in the gap between these two limit cases, as real-world applications often demand adaptation to specific subdomains, tasks or concepts -- spread over the entire, varying life cycle of a model. In this work, we complement current perspectives on continual pretraining through a research test bed as well as provide comprehensive guidance for effective continual model updates in such scenarios. We first introduce FoMo-in-Flux, a continual multimodal pretraining benchmark with realistic compute constraints and practical deployment requirements, constructed over 63 datasets with diverse visual and semantic coverage. Using FoMo-in-Flux, we explore the complex landscape of practical continual pretraining through multiple perspectives: (1) A data-centric investigation of data mixtures and stream orderings that emulate real-world deployment situations, (2) a method-centric investigation ranging from simple fine-tuning and traditional continual learning strategies to parameter-efficient updates and model merging, (3) meta learning rate schedules and mechanistic design choices, and (4) the influence of model and compute scaling. Together, our insights provide a practitioner's guide to continual multimodal pretraining for real-world deployment. Our benchmark and code is here: https://github.com/ExplainableML/fomo_in_flux.

Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality. For example, extending the inference process with auxiliary variables leads to improved sample quality. While there are many such multivariate diffusions to explore, each new one requires significant model-specific analysis, hindering rapid prototyping and evaluation. In this work, we study Multivariate Diffusion Models (MDMs). For any number of auxiliary variables, we provide a recipe for maximizing a lower-bound on the MDMs likelihood without requiring any model-specific analysis. We then demonstrate how to parameterize the diffusion for a specified target noise distribution; these two points together enable optimizing the inference diffusion process. Optimizing the diffusion expands easy experimentation from just a few well-known processes to an automatic search over all linear diffusions. To demonstrate these ideas, we introduce two new specific diffusions as well as learn a diffusion process on the MNIST, CIFAR10, and ImageNet32 datasets. We show learned MDMs match or surpass bits-per-dims (BPDs) relative to fixed choices of diffusions for a given dataset and model architecture.

Remote sensing offers an unparalleled vantage point for observing the Earth's long-term surface evolution, yet it demands that a model not only perceive land cover at isolated moments, but also track changes, memorize evolution histories, and reason across time and space. However, existing studies lack a systematic evaluation that dissects these distinct competencies. To fill this gap, we introduce ChronoBench, a multidimensional benchmark that decomposes this task into four progressive cognitive levels (i.e., Land Cover Perception, Temporal Recognition, Long-Term Memory, and Spatio-Temporal Reasoning). The ChronoBench comprises 12 sub-tasks and 17,689 rigorously validated QA (Question-Answer) pairs. Extensive evaluations reveal that mainstream MLLMs fall drastically behind human experts, with Long-Term Memory emerging as the most critical bottleneck. Motivated by this finding, we further propose GeoChrono, an MLLM with enhanced capabilities for tracing, memorizing, and reasoning about long-term geographic evolution. Leveraging the physical prior that geographic parcels remain spatially fixed while their semantics evolve, we design a Temporal Trajectory Encoder~(TempEnc) that constructs per-location temporal trajectories for dedicated land cover evolution modeling, and we introduce a Coarse-to-Fine Token Compressor~(C2FComp) that adaptively preserves dynamic regions while compressing the static background. To support training, we also construct ChronoInstruct, a 104K-sample instruction-tuning dataset spanning all competency levels for training. GeoChrono achieves state-of-the-art performance on ChronoBench, surpassing the leading commercial MLLMs by over 20%, while C2FComp reduces visual tokens by over 56% while retaining GeoChrono's 94.6% performance. The code and data will be available at https://github.com/IntelliSensing/GeoChrono

We introduce the concept of programmable feature engineering for time series modeling and propose a feature programming framework. This framework generates large amounts of predictive features for noisy multivariate time series while allowing users to incorporate their inductive bias with minimal effort. The key motivation of our framework is to view any multivariate time series as a cumulative sum of fine-grained trajectory increments, with each increment governed by a novel spin-gas dynamical Ising model. This fine-grained perspective motivates the development of a parsimonious set of operators that summarize multivariate time series in an abstract fashion, serving as the foundation for large-scale automated feature engineering. Numerically, we validate the efficacy of our method on several synthetic and real-world noisy time series datasets.

World models enable planning in imagined future predicted space, offering a promising framework for embodied navigation. However, existing navigation world models often lack action-conditioned consistency, so visually plausible predictions can still drift under multi-step rollout and degrade planning. Moreover, efficient deployment requires few-step diffusion inference, but existing distillation methods do not explicitly preserve rollout consistency, creating a training-inference mismatch. To address these challenges, we propose MWM, a mobile world model for planning-based image-goal navigation. Specifically, we introduce a two-stage training framework that combines structure pretraining with Action-Conditioned Consistency (ACC) post-training to improve action-conditioned rollout consistency. We further introduce Inference-Consistent State Distillation (ICSD) for few-step diffusion distillation with improved rollout consistency. Our experiments on benchmark and real-world tasks demonstrate consistent gains in visual fidelity, trajectory accuracy, planning success, and inference efficiency. Code: https://github.com/AIGeeksGroup/MWM. Website: https://aigeeksgroup.github.io/MWM.

On a global level, ecological communities are being perturbed at an unprecedented rate by human activities and environmental instabilities. Yet, we understand little about what factors facilitate or impede long-term persistence of these communities. While observational studies indicate that increased biodiversity must, somehow, be driving stability, theoretical studies have argued the exact opposite viewpoint instead. This encouraged many researchers to participate in the ongoing diversity-stability debate. Within this context, however, there has been a severe lack of studies that consider spatial features explicitly, even though nearly all habitats are spatially embedded. To this end, we study here the linear stability of meta-ecosystems on networks that describe how discrete patches are connected by dispersal between them. By combining results from random-matrix theory and network theory, we are able to show that there are three distinct features that underlie stability: edge density, tendency to triadic closure, and isolation or fragmentation. Our results appear to further indicate that network sparsity does not necessarily reduce stability, and that connections between patches are just as, if not more, important to consider when studying the stability of large ecological systems.

Continual learning, the ability of AI systems to improve through sequential experience, has attracted substantial interest, but no high-quality benchmark exists to evaluate it. We introduce Continual Learning Bench (CL-Bench), the first difficult, expert-validated benchmark designed to measure whether LLM-based systems genuinely improve with experience. CL-Bench spans six diverse domains (software engineering, signal processing, disease outbreak forecasting, database querying, strategic game-playing, and demand forecasting), each validated by domain experts and designed so that tasks share a learnable latent structure (codebase layout, disease outbreak dynamics, opponent strategies) that a stateful system can discover online but a stateless one cannot. We evaluate frontier models across several agent architectures, from naive in-context learning (ICL) to dedicated memory systems, introducing a gain metric to isolate learning from prior capabilities. We find that these systems leave headroom for improved continual learning: agents frequently overfit to immediate observations or fail to reuse knowledge across instances, and dedicated memory systems do not fix this -- in fact, naive ICL outperforms systems dedicated to memory management. CL-Bench is the first benchmark to evaluate continual learning across diverse real-world domains with expert-validated tasks and isolate online learning from underlying model capability, showing a need for better continual learning systems.

As digital environments (data distribution) are in flux, with new GUI data arriving over time-introducing new domains or resolutions-agents trained on static environments deteriorate in performance. In this work, we introduce Continual GUI Agents, a new task that requires GUI agents to perform continual learning under shifted domains and resolutions. We find existing methods fail to maintain stable grounding as GUI distributions shift over time, due to the diversity of UI interaction points and regions in fluxing scenarios. To address this, we introduce GUI-Anchoring in Flux (GUI-AiF), a new reinforcement fine-tuning framework that stabilizes continual learning through two novel rewards: Anchoring Point Reward in Flux (APR-iF) and Anchoring Region Reward in Flux (ARR-iF). These rewards guide the agents to align with shifting interaction points and regions, mitigating the tendency of existing reward strategies to over-adapt to static grounding cues (e.g., fixed coordinates or element scales). Extensive experiments show GUI-AiF surpasses state-of-the-art baselines. Our work establishes the first continual learning framework for GUI agents, revealing the untapped potential of reinforcement fine-tuning for continual GUI Agents.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

We introduce a new generative model that combines latent diffusion with persistent homology to create 3D shapes with high diversity, with a special emphasis on their topological characteristics. Our method involves representing 3D shapes as implicit fields, then employing persistent homology to extract topological features, including Betti numbers and persistence diagrams. The shape generation process consists of two steps. Initially, we employ a transformer-based autoencoding module to embed the implicit representation of each 3D shape into a set of latent vectors. Subsequently, we navigate through the learned latent space via a diffusion model. By strategically incorporating topological features into the diffusion process, our generative module is able to produce a richer variety of 3D shapes with different topological structures. Furthermore, our framework is flexible, supporting generation tasks constrained by a variety of inputs, including sparse and partial point clouds, as well as sketches. By modifying the persistence diagrams, we can alter the topology of the shapes generated from these input modalities.

We study the variance of stochastic policy gradients (SPGs) with many action samples per state. We derive a many-actions optimality condition, which determines when many-actions SPG yields lower variance as compared to a single-action agent with proportionally extended trajectory. We propose Model-Based Many-Actions (MBMA), an approach leveraging dynamics models for many-actions sampling in the context of SPG. MBMA addresses issues associated with existing implementations of many-actions SPG and yields lower bias and comparable variance to SPG estimated from states in model-simulated rollouts. We find that MBMA bias and variance structure matches that predicted by theory. As a result, MBMA achieves improved sample efficiency and higher returns on a range of continuous action environments as compared to model-free, many-actions, and model-based on-policy SPG baselines.

The quest for Continual Learning (CL) seeks to empower neural networks with the ability to learn and adapt incrementally. Central to this pursuit is addressing the stability-plasticity dilemma, which involves striking a balance between two conflicting objectives: preserving previously learned knowledge and acquiring new knowledge. While numerous CL methods aim to achieve this trade-off, they often overlook the impact of network architecture on stability and plasticity, restricting the trade-off to the parameter level. In this paper, we delve into the conflict between stability and plasticity at the architectural level. We reveal that under an equal parameter constraint, deeper networks exhibit better plasticity, while wider networks are characterized by superior stability. To address this architectural-level dilemma, we introduce a novel framework denoted Dual-Arch, which serves as a plug-in component for CL. This framework leverages the complementary strengths of two distinct and independent networks: one dedicated to plasticity and the other to stability. Each network is designed with a specialized and lightweight architecture, tailored to its respective objective. Extensive experiments demonstrate that Dual-Arch enhances the performance of existing CL methods while being up to 87% more compact in terms of parameters.

The modeling of probability distributions, specifically generative modeling and density estimation, has become an immensely popular subject in recent years by virtue of its outstanding performance on sophisticated data such as images and texts. Nevertheless, a theoretical understanding of its success is still incomplete. One mystery is the paradox between memorization and generalization: In theory, the model is trained to be exactly the same as the empirical distribution of the finite samples, whereas in practice, the trained model can generate new samples or estimate the likelihood of unseen samples. Likewise, the overwhelming diversity of distribution learning models calls for a unified perspective on this subject. This paper provides a mathematical framework such that all the well-known models can be derived based on simple principles. To demonstrate its efficacy, we present a survey of our results on the approximation error, training error and generalization error of these models, which can all be established based on this framework. In particular, the aforementioned paradox is resolved by proving that these models enjoy implicit regularization during training, so that the generalization error at early-stopping avoids the curse of dimensionality. Furthermore, we provide some new results on landscape analysis and the mode collapse phenomenon.

Recent advances in video generative models have promoted rapid progress in controllable world models. However, maintaining fine-grained spatio-temporal consistency under long-horizon reasoning remains a key challenge. In this work, we move beyond explicit 3D memory and coarse frame-level implicit modeling, and propose a fine-grained, learnable, and scalable memory for consistent world generation. We first identify two fundamental limitations of naïve learnable memory architectures in long-horizon extrapolation, namely computational inefficiency and attention dispersion. Through a systematic analysis of attention dispersion, we propose DecMem, a decoupled memory architecture that employs Sparse Global Memory for efficient fine-grained access to global history and Anchored Local Memory for stable and high-quality extrapolation. Extensive experiments demonstrate that DecMem significantly outperforms current state-of-the-art methods. By ensuring precise and efficient long-term memory and achieving superior extrapolation capabilities, DecMem enables minute-level controllable long video generation with high fidelity and consistency.

The optimization of multilayer neural networks typically leads to a solution with zero training error, yet the landscape can exhibit spurious local minima and the minima can be disconnected. In this paper, we shed light on this phenomenon: we show that the combination of stochastic gradient descent (SGD) and over-parameterization makes the landscape of multilayer neural networks approximately connected and thus more favorable to optimization. More specifically, we prove that SGD solutions are connected via a piecewise linear path, and the increase in loss along this path vanishes as the number of neurons grows large. This result is a consequence of the fact that the parameters found by SGD are increasingly dropout stable as the network becomes wider. We show that, if we remove part of the neurons (and suitably rescale the remaining ones), the change in loss is independent of the total number of neurons, and it depends only on how many neurons are left. Our results exhibit a mild dependence on the input dimension: they are dimension-free for two-layer networks and depend linearly on the dimension for multilayer networks. We validate our theoretical findings with numerical experiments for different architectures and classification tasks.

We study the properties of common loss surfaces through their Hessian matrix. In particular, in the context of deep learning, we empirically show that the spectrum of the Hessian is composed of two parts: (1) the bulk centered near zero, (2) and outliers away from the bulk. We present numerical evidence and mathematical justifications to the following conjectures laid out by Sagun et al. (2016): Fixing data, increasing the number of parameters merely scales the bulk of the spectrum; fixing the dimension and changing the data (for instance adding more clusters or making the data less separable) only affects the outliers. We believe that our observations have striking implications for non-convex optimization in high dimensions. First, the flatness of such landscapes (which can be measured by the singularity of the Hessian) implies that classical notions of basins of attraction may be quite misleading. And that the discussion of wide/narrow basins may be in need of a new perspective around over-parametrization and redundancy that are able to create large connected components at the bottom of the landscape. Second, the dependence of small number of large eigenvalues to the data distribution can be linked to the spectrum of the covariance matrix of gradients of model outputs. With this in mind, we may reevaluate the connections within the data-architecture-algorithm framework of a model, hoping that it would shed light into the geometry of high-dimensional and non-convex spaces in modern applications. In particular, we present a case that links the two observations: small and large batch gradient descent appear to converge to different basins of attraction but we show that they are in fact connected through their flat region and so belong to the same basin.

We propose MVDream, a multi-view diffusion model that is able to generate geometrically consistent multi-view images from a given text prompt. By leveraging image diffusion models pre-trained on large-scale web datasets and a multi-view dataset rendered from 3D assets, the resulting multi-view diffusion model can achieve both the generalizability of 2D diffusion and the consistency of 3D data. Such a model can thus be applied as a multi-view prior for 3D generation via Score Distillation Sampling, where it greatly improves the stability of existing 2D-lifting methods by solving the 3D consistency problem. Finally, we show that the multi-view diffusion model can also be fine-tuned under a few shot setting for personalized 3D generation, i.e. DreamBooth3D application, where the consistency can be maintained after learning the subject identity.

General continual learning (GCL) challenges intelligent systems to learn from single-pass, non-stationary data streams without clear task boundaries. While recent advances in continual parameter-efficient tuning (PET) of pretrained models show promise, they typically rely on multiple training epochs and explicit task cues, limiting their effectiveness in GCL scenarios. Moreover, existing methods often lack targeted design and fail to address two fundamental challenges in continual PET: how to allocate expert parameters to evolving data distributions, and how to improve their representational capacity under limited supervision. Inspired by the fruit fly's hierarchical memory system characterized by sparse expansion and modular ensembles, we propose FlyPrompt, a brain-inspired framework that decomposes GCL into two subproblems: expert routing and expert competence improvement. FlyPrompt introduces a randomly expanded analytic router for instance-level expert activation and a temporal ensemble of output heads to dynamically adapt decision boundaries over time. Extensive theoretical and empirical evaluations demonstrate FlyPrompt's superior performance, achieving up to 11.23%, 12.43%, and 7.62% gains over state-of-the-art baselines on CIFAR-100, ImageNet-R, and CUB-200, respectively. Our source code is available at https://github.com/AnAppleCore/FlyGCL.

Offline reinforcement learning enables agents to leverage large pre-collected datasets of environment transitions to learn control policies, circumventing the need for potentially expensive or unsafe online data collection. Significant progress has been made recently in offline model-based reinforcement learning, approaches which leverage a learned dynamics model. This typically involves constructing a probabilistic model, and using the model uncertainty to penalize rewards where there is insufficient data, solving for a pessimistic MDP that lower bounds the true MDP. Existing methods, however, exhibit a breakdown between theory and practice, whereby pessimistic return ought to be bounded by the total variation distance of the model from the true dynamics, but is instead implemented through a penalty based on estimated model uncertainty. This has spawned a variety of uncertainty heuristics, with little to no comparison between differing approaches. In this paper, we compare these heuristics, and design novel protocols to investigate their interaction with other hyperparameters, such as the number of models, or imaginary rollout horizon. Using these insights, we show that selecting these key hyperparameters using Bayesian Optimization produces superior configurations that are vastly different to those currently used in existing hand-tuned state-of-the-art methods, and result in drastically stronger performance.

In continual learning (CL), an AI agent (e.g., autonomous vehicles or robotics) learns from non-stationary data streams under dynamic environments. For the practical deployment of such applications, it is important to guarantee robustness to unseen environments while maintaining past experiences. In this paper, a novel CL framework is proposed to achieve robust generalization to dynamic environments while retaining past knowledge. The considered CL agent uses a capacity-limited memory to save previously observed environmental information to mitigate forgetting issues. Then, data points are sampled from the memory to estimate the distribution of risks over environmental change so as to obtain predictors that are robust with unseen changes. The generalization and memorization performance of the proposed framework are theoretically analyzed. This analysis showcases the tradeoff between memorization and generalization with the memory size. Experiments show that the proposed algorithm outperforms memory-based CL baselines across all environments while significantly improving the generalization performance on unseen target environments.

Long-term persona agents must remain identifiable while adapting to new events, relationships, evidence, and social conditions. We identify self-locking as a runtime failure mode in continuing persona-life loops: locally plausible events keep appearing while the generated life collapses toward familiar environments, weak relationships, suspended decisions, and stale life stages. We trace this failure to model-level convergence toward high-probability behavioral channels and system-level context gravity from State, memory, history, and environment summaries. We introduce AutoPersonas, a multi-timescale life-environment engine for bounded persona-level recursive self-evolution. It separates environment-side Occurrences, accumulated Observations, and persona State. Its OSO loop admits divergent future-facing material while requiring evidence-governed absorption before State or reachability changes. A three-year compressed simulation exposed environment watermark shells, occurrence-hardening gaps, slow-change accumulation failures, recursive indecision, and weak relationship persistence. An eight-model 40-day stress test generated 1,600 events and found mean rolling 5-day action-category repetition of 95.2%-97.6%, with all models crossing 90% by day 11. Semantic re-keeping found 79.0%-88.0% macro-theme repetition across all direct-loop runs. In a same-runtime 40-day A/B, context-slice masking plus per-sample divergence targeting reduced macro-theme repetition from 61.8% to 36.3% and roughly doubled cumulative theme count. A juvenile-goblin fictional-world run reproduced the anti-fixation regime without hard real-world intrusions. These results support a bounded claim: separating controlled divergence from evidence-governed absorption can reduce persona-environment self-locking while preserving identity continuity.

Progress in computer-aided synthesis planning (CASP) is obscured by the lack of standardized evaluation infrastructure and the reliance on metrics that prioritize topological completion over chemical validity. We introduce RetroCast, a unified evaluation suite that standardizes heterogeneous model outputs into a common schema to enable statistically rigorous, apples-to-apples comparison. The framework includes a reproducible benchmarking pipeline with stratified sampling and bootstrapped confidence intervals, accompanied by SynthArena, an interactive platform for qualitative route inspection. We utilize this infrastructure to evaluate leading search-based and sequence-based algorithms on a new suite of standardized benchmarks. Our analysis reveals a divergence between "solvability" (stock-termination rate) and route quality; high solvability scores often mask chemical invalidity or fail to correlate with the reproduction of experimental ground truths. Furthermore, we identify a "complexity cliff" in which search-based methods, despite high solvability rates, exhibit a sharp performance decay in reconstructing long-range synthetic plans compared to sequence-based approaches. We release the full framework, benchmark definitions, and a standardized database of model predictions to support transparent and reproducible development in the field.

The rapid emergence of multi-agent AI systems (MAS), including LangChain, CrewAI, and AutoGen, has shaped how large language model (LLM) applications are developed and orchestrated. However, little is known about how these systems evolve and are maintained in practice. This paper presents the first large-scale empirical study of open-source MAS, analyzing over 42K unique commits and over 4.7K resolved issues across eight leading systems. Our analysis identifies three distinct development profiles: sustained, steady, and burst-driven. These profiles reflect substantial variation in ecosystem maturity. Perfective commits constitute 40.8% of all changes, suggesting that feature enhancement is prioritized over corrective maintenance (27.4%) and adaptive updates (24.3%). Data about issues shows that the most frequent concerns involve bugs (22%), infrastructure (14%), and agent coordination challenges (10%). Issue reporting also increased sharply across all frameworks starting in 2023. Median resolution times range from under one day to about two weeks, with distributions skewed toward fast responses but a minority of issues requiring extended attention. These results highlight both the momentum and the fragility of the current ecosystem, emphasizing the need for improved testing infrastructure, documentation quality, and maintenance practices to ensure long-term reliability and sustainability.

For decades, procedural worlds have been built on procedural noise functions such as Perlin noise, which are fast and infinite, yet fundamentally limited in realism and large-scale coherence. We introduce Terrain Diffusion, an AI-era successor to Perlin noise that bridges the fidelity of diffusion models with the properties that made procedural noise indispensable: seamless infinite extent, seed-consistency, and constant-time random access. At its core is InfiniteDiffusion, a novel algorithm for infinite generation, enabling seamless, real-time synthesis of boundless landscapes. A hierarchical stack of diffusion models couples planetary context with local detail, while a compact Laplacian encoding stabilizes outputs across Earth-scale dynamic ranges. An open-source infinite-tensor framework supports constant-memory manipulation of unbounded tensors, and few-step consistency distillation enables efficient generation. Together, these components establish diffusion models as a practical foundation for procedural world generation, capable of synthesizing entire planets coherently, controllably, and without limits.

World models aim to endow AI systems with the ability to represent, generate, and interact with dynamic environments in a coherent and temporally consistent manner. While recent video generation models have demonstrated impressive visual quality, they remain limited in real-time interaction, long-horizon consistency, and persistent memory of dynamic scenes, hindering their evolution into practical world models. In this report, we present TeleWorld, a real-time multimodal 4D world modeling framework that unifies video generation, dynamic scene reconstruction, and long-term world memory within a closed-loop system. TeleWorld introduces a novel generation-reconstruction-guidance paradigm, where generated video streams are continuously reconstructed into a dynamic 4D spatio-temporal representation, which in turn guides subsequent generation to maintain spatial, temporal, and physical consistency. To support long-horizon generation with low latency, we employ an autoregressive diffusion-based video model enhanced with Macro-from-Micro Planning (MMPL)--a hierarchical planning method that reduces error accumulation from frame-level to segment-level-alongside efficient Distribution Matching Distillation (DMD), enabling real-time synthesis under practical computational budgets. Our approach achieves seamless integration of dynamic object modeling and static scene representation within a unified 4D framework, advancing world models toward practical, interactive, and computationally accessible systems. Extensive experiments demonstrate that TeleWorld achieves strong performance in both static and dynamic world understanding, long-term consistency, and real-time generation efficiency, positioning it as a practical step toward interactive, memory-enabled world models for multimodal generation and embodied intelligence.

Tool-augmented LLMs are increasingly deployed as agents that interleave natural-language reasoning with executable Python actions, as in CodeAct-style frameworks. In deployment, these agents rely on runtime state that persists across steps. By contrast, common training pipelines treat agent traces as token sequences, with execution semantics left implicit. This raises a data-centric question: Is state persistence merely an inference-time scaffold, or can models learn to exploit it when training data exposes the corresponding execution semantics? We isolate state persistence as a training-time variable. We introduce Opaque Knapsack, a procedurally generated family of partially observable optimization tasks designed to prevent one-shot solutions. Item attributes and constraints are hidden behind budgeted tool calls, forcing multi-turn control flow and iterative state revision. Holding task instances, prompts, tools, model, and supervision fixed, we generate paired trajectories differing only in whether interpreter state persists across steps or resets after each action. We then fine-tune identical base models (Qwen3-8B) on each trace variant and evaluate all four train-runtime combinations. Our 2x2 cross-evaluation shows that execution semantics primarily affect how agents reach solutions, not whether they do: solution quality is statistically indistinguishable across conditions, but token cost and stability differ substantially. A persistent-trained model in a stateless runtime triggers missing-variable errors in roughly 80% of episodes; a stateless-trained model in a persistent runtime redundantly re-derives retained state, using roughly 3.5x more tokens. Interpreter persistence should be treated as a first-class semantic of agent traces. Aligning fine-tuning data with deployment runtimes improves efficiency and reduces brittle train-runtime mismatches.

We present AlphaApollo, a self-evolving agentic reasoning system that aims to address two bottlenecks in foundation model (FM) reasoning-limited model-intrinsic capacity and unreliable test-time iteration. AlphaApollo orchestrates multiple models with professional tools to enable deliberate, verifiable reasoning. It couples (i) a computation tool (Python with numerical and symbolic libraries) and (ii) a retrieval tool (task-relevant external information) to execute exact calculations and ground decisions. The system further supports multi-round, multi-model solution evolution via a shared state map that records candidates, executable checks, and feedback for iterative refinement. In evaluations on AIME 2024/2025 across multiple models, AlphaApollo delivers consistent gains: +5.15% Average@32 and +23.34% Pass@32 for Qwen2.5-14B-Instruct, and +8.91% Average@32 with +26.67% Pass@32 for Llama-3.3-70B-Instruct. Tool-use analysis shows that more than 80% of tool calls are successfully executed, with consistent outperformance of non-tool baselines, thereby lifting the capability ceiling of FMs. More empirical results and implementation details will be updated at https://github.com/tmlr-group/AlphaApollo.

Current LLM unlearning methods face a critical security vulnerability that undermines their fundamental purpose: while they appear to successfully remove sensitive or harmful knowledge, this ``forgotten" information remains precariously recoverable through relearning attacks. We identify that the root cause is that conventional methods optimizing the forgetting loss at individual data points will drive model parameters toward sharp minima in the loss landscape. In these unstable regions, even minimal parameter perturbations can drastically alter the model's behaviors. Consequently, relearning attacks exploit this vulnerability by using just a few fine-tuning samples to navigate the steep gradients surrounding these unstable regions, thereby rapidly recovering knowledge that was supposedly erased. This exposes a critical robustness gap between apparent unlearning and actual knowledge removal. To address this issue, we propose StableUN, a bi-level feedback-guided optimization framework that explicitly seeks more stable parameter regions via neighborhood-aware optimization. It integrates forgetting feedback, which uses adversarial perturbations to probe parameter neighborhoods, with remembering feedback to preserve model utility, aligning the two objectives through gradient projection. Experiments on WMDP and MUSE benchmarks demonstrate that our method is significantly more robust against both relearning and jailbreaking attacks while maintaining competitive utility performance.

In recent years, persistent homology (PH) has been successfully applied to real-world data in many different settings. Despite significant computational advances, PH algorithms do not yet scale to large datasets preventing interesting applications. One approach to address computational issues posed by PH is to select a set of landmarks by subsampling from the data. Currently, these landmark points are chosen either at random or using the maxmin algorithm. Neither is ideal as random selection tends to favour dense areas of the data while the maxmin algorithm is very sensitive to noise. Here, we propose a novel approach to select landmarks specifically for PH that preserves coarse topological information of the original dataset. Our method is motivated by the Mayer-Vietoris sequence and requires only local PH computation thus enabling efficient computation. We test our landmarks on artificial datasets which contain different levels of noise and compare them to standard landmark selection techniques. We demonstrate that our landmark selection outperforms standard methods as well as a subsampling technique based on an outlier-robust version of the k--means algorithm for low sampling densities in noisy data with respect to robustness to outliers.

Neural models are usually adapted through changes in parameters shared among model components via fine-tuning, alignment-based training, and reinforcement learning. These changes have been found effective in short-term optimization. However, they result in long-term alterations in the model's base behavior. In this study, we introduce the concept of structural irreversibility as a characteristic of shared-parameter model adaptation. This concept refers to the intertwining of task-specific objectives with the representational identity of the model. We show that when parameters are directly mutated, the resulting model behaves divergently from the original model. This divergence cannot be reversed deterministically without an explicit parameter snapshot. We introduce reversible behavioral learning, in which model behaviors are structurally dissociated from identity parameters and can be deterministically unloaded through an explicit unload process. We also introduce the Recoverability Factor as a normalized measure of behavioral recoverability and provide additional diagnostics based on model divergence. Experiments show that reversible model adaptation achieves rollback within numerical precision, whereas shared-parameter mutation exhibits persistent post-reset divergence.

Parameter-efficient fine-tuning (PEFT) is usually treated as a cheaper alternative to full fine-tuning. We study a broader role: small trainable adapters as persistent local state on top of strong shared foundation models. In this framing, the base model provides shared competence while adapters carry instance-specific behavior such as preferences, skills, tool habits, and memory-like updates. We organize the problem around three scaling axes: Scale Up, where stronger shared priors make small local updates more useful; Scale Down, where we study how small adapters can be while remaining reliable; and Scale Out, where many persistent adapted instances coexist. MinT provides one infrastructure example for managing adapter identity, revision, provenance, evaluation, and serving residency. Together, the results suggest that PEFT can be a compact substrate for persistent personal models rather than only a budget substitute for full fine-tuning.

Symbolic world modeling requires inferring and representing an environment's transitional dynamics as an executable program. Prior work has focused on largely deterministic environments with abundant interaction data, simple mechanics, and human guidance. We address a more realistic and challenging setting, learning in a complex, stochastic environment where the agent has only "one life" to explore a hostile environment without human guidance. We introduce OneLife, a framework that models world dynamics through conditionally-activated programmatic laws within a probabilistic programming framework. Each law operates through a precondition-effect structure, activating in relevant world states. This creates a dynamic computation graph that routes inference and optimization only through relevant laws, avoiding scaling challenges when all laws contribute to predictions about a complex, hierarchical state, and enabling the learning of stochastic dynamics even with sparse rule activation. To evaluate our approach under these demanding constraints, we introduce a new evaluation protocol that measures (a) state ranking, the ability to distinguish plausible future states from implausible ones, and (b) state fidelity, the ability to generate future states that closely resemble reality. We develop and evaluate our framework on Crafter-OO, our reimplementation of the Crafter environment that exposes a structured, object-oriented symbolic state and a pure transition function that operates on that state alone. OneLife can successfully learn key environment dynamics from minimal, unguided interaction, outperforming a strong baseline on 16 out of 23 scenarios tested. We also test OneLife's planning ability, with simulated rollouts successfully identifying superior strategies. Our work establishes a foundation for autonomously constructing programmatic world models of unknown, complex environments.

We present Manifold Diffusion Fields (MDF), an approach to learn generative models of continuous functions defined over Riemannian manifolds. Leveraging insights from spectral geometry analysis, we define an intrinsic coordinate system on the manifold via the eigen-functions of the Laplace-Beltrami Operator. MDF represents functions using an explicit parametrization formed by a set of multiple input-output pairs. Our approach allows to sample continuous functions on manifolds and is invariant with respect to rigid and isometric transformations of the manifold. Empirical results on several datasets and manifolds show that MDF can capture distributions of such functions with better diversity and fidelity than previous approaches.

Generative foundation models are increasingly scaled in both width and depth, posing significant challenges for stable feature learning and reliable hyperparameter (HP) transfer across model sizes. While maximal update parameterization (μP) has provided a principled solution to both problems for width scaling, existing extensions to the joint width-depth scaling regime remain fragmented, architecture- and optimizer-specific, and often rely on technically involved theories. In this work, we develop a simple and unified spectral framework for μP under joint width-depth scaling. Considering residual networks of varying block depths, we first introduce a spectral μP condition that precisely characterizes how the norms of weights and their per-step updates should scale with width and depth, unifying previously disparate μP formulations as special cases. Building on this condition, we then derive a general recipe for implementing μP across a broad class of optimizers by mapping the spectral constraints to concrete HP parameterizations. This approach not only recovers existing μP formulations (e.g., for SGD and AdamW) but also naturally extends to a wider range of optimizers. Finally, experiments on GPT-2 style language models demonstrate that the proposed spectral μP condition preserves stable feature learning and enables robust HP transfer under width-depth scaling.

The objective of this study is to evaluate the potential for History Matching (HM) to tune a climate system with multi-scale dynamics. By considering a toy climate model, namely, the two-scale Lorenz96 model and producing experiments in perfect-model setting, we explore in detail how several built-in choices need to be carefully tested. We also demonstrate the importance of introducing physical expertise in the range of parameters, a priori to running HM. Finally we revisit a classical procedure in climate model tuning, that consists of tuning the slow and fast components separately. By doing so in the Lorenz96 model, we illustrate the non-uniqueness of plausible parameters and highlight the specificity of metrics emerging from the coupling. This paper contributes also to bridging the communities of uncertainty quantification, machine learning and climate modeling, by making connections between the terms used by each community for the same concept and presenting promising collaboration avenues that would benefit climate modeling research.

Understanding the loss landscape is an important problem in machine learning. One key feature of the loss function, common to many neural network architectures, is the presence of exponentially many low lying local minima. Physical systems with similar energy landscapes may provide useful insights. In this work, we point out that black holes naturally give rise to such landscapes, owing to the existence of black hole entropy. For definiteness, we consider 1/8 BPS black holes in N = 8 string theory. These provide an infinite family of potential landscapes arising in the microscopic descriptions of corresponding black holes. The counting of minima amounts to black hole microstate counting. Moreover, the exact numbers of the minima for these landscapes are a priori known from dualities in string theory. Some of the minima are connected by paths of low loss values, resembling mode connectivity. We estimate the number of runs needed to find all the solutions. Initial explorations suggest that Stochastic Gradient Descent can find a significant fraction of the minima.

Parameter generation has struggled to scale up for a long time, significantly limiting its range of applications. In this study, we introduce Recurrent diffusion for large-scale Parameter Generation, called RPG. We first divide the trained parameters into non-overlapping parts, after which a recurrent model is proposed to learn their relationships. The recurrent model's outputs, as conditions, are then fed into a diffusion model to generate the neural network parameters. Using only a single GPU, recurrent diffusion enables us to generate popular vision and language models such as ConvNeXt-L and LoRA parameters of LLaMA-7B. Meanwhile, across various architectures and tasks, the generated parameters consistently perform comparable results over trained networks. Notably, our approach also shows the potential to generate models for handling unseen tasks, which largely increases the practicality of parameter generation. Our code is available https://github.com/NUS-HPC-AI-Lab/Recurrent-Parameter-Generation{here}.

Autoregressive video diffusion models have proved effective for world modeling and interactive scene generation, with Minecraft gameplay as a representative application. To faithfully simulate play, a model must generate natural content while exploring new scenes and preserve spatial consistency when revisiting explored areas. Under limited computation budgets, it must compress and exploit historical cues within a finite context window, which exposes a trade-off: Temporal-only memory lacks long-term spatial consistency, whereas adding spatial memory strengthens consistency but may degrade new scene generation quality when the model over-relies on insufficient spatial context. We present Memory Forcing, a learning framework that pairs training protocols with a geometry-indexed spatial memory. Hybrid Training exposes distinct gameplay regimes, guiding the model to rely on temporal memory during exploration and incorporate spatial memory for revisits. Chained Forward Training extends autoregressive training with model rollouts, where chained predictions create larger pose variations and encourage reliance on spatial memory for maintaining consistency. Point-to-Frame Retrieval efficiently retrieves history by mapping currently visible points to their source frames, while Incremental 3D Reconstruction maintains and updates an explicit 3D cache. Extensive experiments demonstrate that Memory Forcing achieves superior long-term spatial consistency and generative quality across diverse environments, while maintaining computational efficiency for extended sequences.

Predictive world models that simulate future observations under explicit camera control are fundamental to interactive AI. Despite rapid advances, current systems lack spatial persistence: they fail to maintain stable scene structures over long trajectories, frequently hallucinating details when cameras revisit previously observed locations. We identify that this geometric drift stems from reliance on screen-space positional embeddings, which conflict with the projective geometry required for 3D consistency. We introduce ViewRope, a geometry-aware encoding that injects camera-ray directions directly into video transformer self-attention layers. By parameterizing attention with relative ray geometry rather than pixel locality, ViewRope provides a model-native inductive bias for retrieving 3D-consistent content across temporal gaps. We further propose Geometry-Aware Frame-Sparse Attention, which exploits these geometric cues to selectively attend to relevant historical frames, improving efficiency without sacrificing memory consistency. We also present ViewBench, a diagnostic suite measuring loop-closure fidelity and geometric drift. Our results demonstrate that ViewRope substantially improves long-term consistency while reducing computational costs.

While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data. Measures for characterizing and monitoring structural properties, however, have not been developed. In this work, we propose neural persistence, a complexity measure for neural network architectures based on topological data analysis on weighted stratified graphs. To demonstrate the usefulness of our approach, we show that neural persistence reflects best practices developed in the deep learning community such as dropout and batch normalization. Moreover, we derive a neural persistence-based stopping criterion that shortens the training process while achieving comparable accuracies as early stopping based on validation loss.

Safety alignment of Large Language Models (LLMs) is extremely fragile, as fine-tuning on a small number of benign samples can erase safety behaviors learned from millions of preference examples. Existing studies attempt to explain this phenomenon by comparing parameters and hidden states before and after fine-tuning, but overlook their dynamic evolution during fine-tuning. In this paper, we uncover a critical mechanism underlying safety degradation by analyzing parameter dynamics, where benign fine-tuning causes parameters to cumulatively drift toward danger-aligned directions, progressively undermining the model's safety. This finding suggests that samples contributing more to this drift has greater fine-tuning risks. Based on this insight, we propose a method of Sample-Level Quantification of Safety Degradation (SQSD), which quantifies the influence of each training sample on safety degradation. Specifically, SQSD computes continuous risk scores to samples by measuring their induced parameter updates' projection difference between danger and safety directions. Extensive experiments across multiple models and datasets demonstrate that SQSD effectively quantifies sample-level fine-tuning risks and exhibits strong transferability across model architectures, parameter scales, and parameter-efficient methods.

Recent generative video world models aim to simulate visual environment evolution, allowing an observer to interactively explore the scene via camera control. However, they implicitly assume that the world only evolves within the observer's field of view. Once an object leaves the observer's view, its state is "frozen" in memory, and revisiting the same region later often fails to reflect events that should have occurred in the meantime. In this work, we identify and formalize this overlooked limitation as the "out-of-sight dynamics" problem, which impedes video world models from representing a continuously evolving world. To address this issue, we propose LiveWorld, a novel framework that extends video world models to support persistent world evolution. Instead of treating the world as static observational memory, LiveWorld models a persistent global state composed of a static 3D background and dynamic entities that continue evolving even when unobserved. To maintain these unseen dynamics, LiveWorld introduces a monitor-based mechanism that autonomously simulates the temporal progression of active entities and synchronizes their evolved states upon revisiting, ensuring spatially coherent rendering. For evaluation, we further introduce LiveBench, a dedicated benchmark for the task of maintaining out-of-sight dynamics. Extensive experiments show that LiveWorld enables persistent event evolution and long-term scene consistency, bridging the gap between existing 2D observation-based memory and true 4D dynamic world simulation. The baseline and benchmark will be publicly available at https://zichengduan.github.io/LiveWorld/index.html.

Self-evolving LLM agents update their internal state across sessions, often by writing and reusing long-term memory. This design improves performance on long-horizon tasks but creates a security risk: untrusted external content observed during a benign session can be stored as memory and later treated as instruction. We study this risk and formalize a persistent attack we call a Zombie Agent, where an attacker covertly implants a payload that survives across sessions, effectively turning the agent into a puppet of the attacker. We present a black-box attack framework that uses only indirect exposure through attacker-controlled web content. The attack has two phases. During infection, the agent reads a poisoned source while completing a benign task and writes the payload into long-term memory through its normal update process. During trigger, the payload is retrieved or carried forward and causes unauthorized tool behavior. We design mechanism-specific persistence strategies for common memory implementations, including sliding-window and retrieval-augmented memory, to resist truncation and relevance filtering. We evaluate the attack on representative agent setups and tasks, measuring both persistence over time and the ability to induce unauthorized actions while preserving benign task quality. Our results show that memory evolution can convert one-time indirect injection into persistent compromise, which suggests that defenses focused only on per-session prompt filtering are not sufficient for self-evolving agents.

Neural world models coupled with model predictive control (MPC) replan at every environment step to bound accumulated prediction error, but this incurs substantial computational overhead. Reusing a cached plan reduces this overhead, yet its effectiveness depends on how prediction mismatch propagates through the local dynamics. We analyze this trade-off with a perturbation-based dynamic-regret framework and show that stale-plan penalties scale with the reuse tolerance, the accumulated mismatch since the last replanning step, and the local dynamics sensitivity. Based on this structure, we propose AdaReP, a training-free wrapper that adapts the replanning tolerance online using the current deviation from the cached rollout and a local sensitivity estimate, without modifying the learned world model or planner. Across image-space planning, latent-space control, and real-world robotic manipulation, AdaReP substantially reduces planner-side computation while maintaining comparable task performance, including over 80% fewer queries on a 50-trial physical robot study.

Continual learning in visual understanding aims to deal with catastrophic forgetting in Multimodal Large Language Models (MLLMs). MLLMs deployed on devices have to continuously adapt to dynamic scenarios in downstream tasks, such as variations in background and perspective, to effectively perform complex visual tasks. To this end, we construct a multimodal visual understanding dataset (MSVQA) encompassing four different scenarios and perspectives including high altitude, underwater, low altitude and indoor, to investigate the catastrophic forgetting in MLLMs under the dynamics of scenario shifts in real-world data streams. Furthermore, we propose mUltimodal coNtInual learning with MLLMs From multi-scenarIo pERspectives (UNIFIER) to address visual discrepancies while learning different scenarios. Specifically, it decouples the visual information from different scenarios into distinct branches within each vision block and projects them into the same feature space. A consistency constraint is imposed on the features of each branch to maintain the stability of visual representations across scenarios. Extensive experiments on the MSVQA dataset demonstrate that UNIFIER effectively alleviates forgetting of cross-scenario tasks and achieves knowledge accumulation within the same scenario.

Model-based reinforcement learning (RL) can be effectively supported at scale through the use of world models. However, in practice, scaling such approaches remains fundamentally limited. A commonly recognized challenge is model bias and error compounding, which degrade long-horizon predictions. Beyond these issues, we identify a more critical yet underexplored bottleneck: a structural misalignment between search and value learning in existing world model approaches. In particular, policy improvement often relies on value functions induced by a separate, non-search policy, resulting in training inconsistency and ultimately suboptimal learning. To address this limitation, we propose Model-Based Diffusion Policy Optimization (MBDPO) in world models, a framework that unifies search and policy optimization through diffusion policy representations, thereby unlocking the potential of world models for scalable policy learning. Instead of constructing an explicit planner over a learned world model, we reformulate policy optimization as a diffusion process over searched trajectories in latent world models. In this view, we extract an implicit energy function from the collected dataset that anchors the policy, enabling MBDPO to refine the score field for policy optimization while mitigating misalignment. We evaluate MBDPO across a wide range of settings, including multi-task offline pretraining, online learning, and offline-to-online fine-tuning. In the offline regime, we further investigate its scaling behavior by pretraining on large-scale datasets, observing consistent and monotonic performance gains with increasing model capacity.

Loss landscape is a useful tool to characterize and compare neural network models. The main challenge for analysis of loss landscape for the deep neural networks is that they are generally highly non-convex in very high dimensional space. In this paper, we develop "the roughness"concept for understanding such landscapes in high dimensions and apply this technique to study two neural network models arising from solving differential equations. Our main innovation is the proposal of a well-defined and easy-to-compute roughness index (RI) which is based on the mean and variance of the (normalized) total variation for one-dimensional functions projected on randomly sampled directions. A large RI at the local minimizer hints an oscillatory landscape profile and indicates a severe challenge for the first-order optimization method. Particularly, we observe the increasing-then-decreasing pattern for RI along the gradient descent path in most models. We apply our method to two types of loss functions used to solve partial differential equations (PDEs) when the solution of PDE is parametrized by neural networks. Our empirical results on these PDE problems reveal important and consistent observations that the landscapes from the deep Galerkin method around its local minimizers are less rough than the deep Ritz method.

Diffusion language models (DLMs) are an attractive alternative to autoregressive models because they promise sublinear-time, parallel generation, yet practical gains remain elusive as high-quality samples still demand hundreds of refinement steps. In continuous domains, consistency training along the probability-flow ODE is a popular recipe to accelerate diffusion. For discrete diffusion, no analogous sample-space ODE exists, making direct adaptation ill-defined. We argue that the natural discrete substitute is not a deterministic trajectory but its stochastic counterpart: the exact posterior bridge, available in closed form for broad corruption families including masked and uniform diffusion. Building on this observation, we introduce Multi-Path Discrete Consistency (MPDC), a new principle that trains a denoiser to be path-invariant in expectation across these stochastic bridges, and instantiate it as the Consistent Diffusion Language Model (CDLM), a single-stage, teacher-free training framework. A single CDLM objective unifies masked diffusion, continuous consistency models, and progressive/discrete distillation as analytic limits or empirical approximations of one common view. Empirically, CDLM establishes a new state of the art on both conditional and unconditional text-generation, consistently outperforming strong base discrete diffusion models and often even multi-stage distilled baselines across sampling budgets, with the largest gains in the few-step regime. Together, these results position CDLM as a principled and scalable foundation for the next generation of fast, high-fidelity discrete generative modeling.

Sequential learning paradigms pose challenges for gradient-based deep learning due to difficulties incorporating new data and retaining prior knowledge. While Gaussian processes elegantly tackle these problems, they struggle with scalability and handling rich inputs, such as images. To address these issues, we introduce a technique that converts neural networks from weight space to function space, through a dual parameterization. Our parameterization offers: (i) a way to scale function-space methods to large data sets via sparsification, (ii) retention of prior knowledge when access to past data is limited, and (iii) a mechanism to incorporate new data without retraining. Our experiments demonstrate that we can retain knowledge in continual learning and incorporate new data efficiently. We further show its strengths in uncertainty quantification and guiding exploration in model-based RL. Further information and code is available on the project website.

Terrain modeling has traditionally relied on procedural techniques, which often require extensive domain expertise and handcrafted rules. In this paper, we present MESA - a novel data-centric alternative by training a diffusion model on global remote sensing data. This approach leverages large-scale geospatial information to generate high-quality terrain samples from text descriptions, showcasing a flexible and scalable solution for terrain generation. The model's capabilities are demonstrated through extensive experiments, highlighting its ability to generate realistic and diverse terrain landscapes. The dataset produced to support this work, the Major TOM Core-DEM extension dataset, is released openly as a comprehensive resource for global terrain data. The results suggest that data-driven models, trained on remote sensing data, can provide a powerful tool for realistic terrain modeling and generation.

Continual learning systems are increasingly deployed in environments where retraining or reset is infeasible, yet many approaches emphasize task performance rather than the evolution of internal representations over time. In this work, we study a minimal continual learning agent designed to isolate representational dynamics from architectural complexity and optimization objectives. The agent maintains a persistent state vector across executions and incrementally updates it as new textual data is introduced. We quantify representational change using cosine similarity between successive normalized state vectors and define a stability metric over time intervals. Longitudinal experiments across eight executions reveal a transition from an initial plastic regime to a stable representational regime under consistent input. A deliberately introduced semantic perturbation produces a bounded decrease in similarity, followed by recovery and restabilization under subsequent coherent input. These results demonstrate that meaningful stability plasticity tradeoffs can emerge in a minimal, stateful learning system without explicit regularization, replay, or architectural complexity. The work establishes a transparent empirical baseline for studying representational accumulation and adaptation in continual learning systems.

We address the challenge of adapting pre-trained Large Language Models (LLMs) for multivariate time-series analysis, where their deployment is often hindered by prohibitive computational and memory demands. Our solution, One-for-All, introduces Gaussian Rank-Stabilized Low-Rank Adapters (rsLoRA) to enable parameter-efficient fine-tuning of frozen LLMs. While inspired by LoRA, rsLoRA introduces a mathematically grounded rank-stabilization mechanism that enables provable gradient stability at low ranks a novel contribution absent in prior PEFT methods. Our framework injects trainable rank decomposition matrices (rank 16) into positional embeddings and output layers, while keeping self-attention weights fixed. This design reduces trainable parameters by 6.8times (vs. TimesNet), 21times (vs. GPT4TS), and 11.8times (vs. TIME-LLM), while achieving a 168-1,776times smaller memory footprint (2.2MiB vs. 340MiB-4.18GiB in SOTA models). Rigorous evaluation across six time-series tasks demonstrates that One-for-All achieves state-of-the-art efficiency-accuracy trade-offs: 5.5times higher parameter efficiency (MSE=5.50) than TimesNet and 21times better than GPT4TS, while matching their forecasting accuracy (MSE=0.33). The framework's stability is validated through consistent performance across diverse horizons (96-720 steps) and datasets (ETT, Weather, M3, M4), with 98.3% fewer parameters than conventional transformers. These advances enable deployment on edge devices for healthcare, finance, and environmental monitoring without compromising performance.

We present a memory system for AI agents that treats stored information as continuous fields governed by partial differential equations rather than discrete entries in a database. The approach draws from classical field theory: memories diffuse through semantic space, decay thermodynamically based on importance, and interact through field coupling in multi-agent scenarios. We evaluate the system on two established long-context benchmarks: LoCoMo (ACL 2024) with 300-turn conversations across 35 sessions, and LongMemEval (ICLR 2025) testing multi-session reasoning over 500+ turns. On LongMemEval, the field-theoretic approach achieves significant improvements: +116% F1 on multi-session reasoning (p<0.01, d= 3.06), +43.8% on temporal reasoning (p<0.001, d= 9.21), and +27.8% retrieval recall on knowledge updates (p<0.001, d= 5.00). Multi-agent experiments show near-perfect collective intelligence (>99.8%) through field coupling. Code is available at github.com/rotalabs/rotalabs-fieldmem.

Machine-learning-based parameterizations (i.e. representation of sub-grid processes) of global climate models or turbulent simulations have recently been proposed as a powerful alternative to physical, but empirical, representations, offering a lower computational cost and higher accuracy. Yet, those approaches still suffer from a lack of generalization and extrapolation beyond the training data, which is however critical to projecting climate change or unobserved regimes of turbulence. Here we show that a multi-fidelity approach, which integrates datasets of different accuracy and abundance, can provide the best of both worlds: the capacity to extrapolate leveraging the physically-based parameterization and a higher accuracy using the machine-learning-based parameterizations. In an application to climate modeling, the multi-fidelity framework yields more accurate climate projections without requiring major increase in computational resources. Our multi-fidelity randomized prior networks (MF-RPNs) combine physical parameterization data as low-fidelity and storm-resolving historical run's data as high-fidelity. To extrapolate beyond the training data, the MF-RPNs are tested on high-fidelity warming scenarios, +4K, data. We show the MF-RPN's capacity to return much more skillful predictions compared to either low- or high-fidelity (historical data) simulations trained only on one regime while providing trustworthy uncertainty quantification across a wide range of scenarios. Our approach paves the way for the use of machine-learning based methods that can optimally leverage historical observations or high-fidelity simulations and extrapolate to unseen regimes such as climate change.

Extracting insight from the enormous quantity of data generated from molecular simulations requires the identification of a small number of collective variables whose corresponding low-dimensional free-energy landscape retains the essential features of the underlying system. Data-driven techniques provide a systematic route to constructing this landscape, without the need for extensive a priori intuition into the relevant driving forces. In particular, autoencoders are powerful tools for dimensionality reduction, as they naturally force an information bottleneck and, thereby, a low-dimensional embedding of the essential features. While variational autoencoders ensure continuity of the embedding by assuming a unimodal Gaussian prior, this is at odds with the multi-basin free-energy landscapes that typically arise from the identification of meaningful collective variables. In this work, we incorporate this physical intuition into the prior by employing a Gaussian mixture variational autoencoder (GMVAE), which encourages the separation of metastable states within the embedding. The GMVAE performs dimensionality reduction and clustering within a single unified framework, and is capable of identifying the inherent dimensionality of the input data, in terms of the number of Gaussians required to categorize the data. We illustrate our approach on two toy models, alanine dipeptide, and a challenging disordered peptide ensemble, demonstrating the enhanced clustering effect of the GMVAE prior compared to standard VAEs. The resulting embeddings appear to be promising representations for constructing Markov state models, highlighting the transferability of the dimensionality reduction from static equilibrium properties to dynamics.

Given a set of K probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals. The structure of this joint distribution should identify multi-way correspondences among the prescribed marginals. We formalize an approach to this task within a generalization of the stochastic interpolant framework, leading to efficient learning algorithms built upon dynamical transport of measure. Our generative models are defined by velocity and score fields that can be characterized as the minimizers of simple quadratic objectives, and they are defined on a simplex that generalizes the time variable in the usual dynamical transport framework. The resulting transport on the simplex is influenced by all marginals, and we show that multi-way correspondences can be extracted. The identification of such correspondences has applications to style transfer, algorithmic fairness, and data decorruption. In addition, the multimarginal perspective enables an efficient algorithm for reducing the dynamical transport cost in the ordinary two-marginal setting. We demonstrate these capacities with several numerical examples.

Irregular multivariate time series impose a trade-off for long-horizon forecasting: discrete methods can distort temporal structure via re-gridding, while continuous-time models often require sequential solvers prone to drift. To bridge this gap, we present Latent Laplace Diffusion (LLapDiff), a generative framework that models the target as a low-dimensional latent trajectory, enabling horizon-wide generation without step-by-step integration over physical time. We guide the reverse process utilizing a stable modal parameterization motivated by stochastic port-Hamiltonian dynamics, and parameterize its mean evolution in the Laplace domain via learnable complex-conjugate poles, enabling direct evaluation over irregular timestamps. We also link continuous dynamics to irregular observations through renewal-averaging analysis, which maps sampling gaps to effective event-domain poles and motivates a gap-aware history summarizer. Extensive experiments show that LLapDiff improves over baselines in long-horizon forecasting, and its continuous-time generative nature supports missing-value imputation by querying the same model at historical timestamps. Code is available at https://github.com/pixelhero98/LLapDiffusion.

Selective state space models (SSM), such as Mamba, have gained prominence for their effectiveness in modeling sequential data. Despite their outstanding empirical performance, a comprehensive theoretical understanding of deep selective SSM remains elusive, hindering their further development and adoption for applications that need high fidelity. In this paper, we investigate the dynamical properties of tokens in a pre-trained Mamba model. In particular, we derive the dynamical system governing the continuous-time limit of the Mamba model and characterize the asymptotic behavior of its solutions. In the one-dimensional case, we prove that only one of the following two scenarios happens: either all tokens converge to zero, or all tokens diverge to infinity. We provide criteria based on model parameters to determine when each scenario occurs. For the convergent scenario, we empirically verify that this scenario negatively impacts the model's performance. For the divergent scenario, we prove that different tokens will diverge to infinity at different rates, thereby contributing unequally to the updates during model training. Based on these investigations, we propose two refinements for the model: excluding the convergent scenario and reordering tokens based on their importance scores, both aimed at improving practical performance. Our experimental results validate these refinements, offering insights into enhancing Mamba's effectiveness in real-world applications.

The Model Context Protocol (MCP) has unified the interface between Large Language Models (LLMs) and external tools, yet a fundamental gap remains in how agents conceptualize the environments within which they operate. Current paradigms are bifurcated: Task-level planning often ignores execution-time dynamics, while reactive execution lacks long-horizon foresight. We present MCP-Cosmos, a framework that infuses generative World Models (WM) into the MCP ecosystem to enable predictive task automation. By unifying three disparate technologies, namely MCP, World Model, and Agent, we demonstrate that a "Bring Your Own World Model" (BYOWM) strategy allows agents to simulate state transitions and refine plans in a latent space before execution. We conducted experiments using two strategies, namely ReAct and SPIRAL with 2 planning models and 3 representative world models over 20+ MCP-Bench tasks. We observed improvements in Agent's environment interaction KPI such as tool success rate and tool parameter accuracy. The framework also offers new metrics such as Execution Quality to generate new insights about the effectiveness of world models compared to baseline.

Current Large Language Models (LLMs) exhibit a critical modal disconnect: they possess vast semantic knowledge but lack the procedural grounding to respect the immutable laws of the physical world. Consequently, while these agents implicitly function as world models, their simulations often suffer from physical hallucinations-generating plans that are logically sound but physically unexecutable. Existing alignment strategies predominantly rely on resource-intensive training or fine-tuning, which attempt to compress dynamic environmental rules into static model parameters. However, such parametric encapsulation is inherently rigid, struggling to adapt to the open-ended variability of physical dynamics without continuous, costly retraining. To bridge this gap, we introduce WorldMind, a framework that autonomously constructs a symbolic World Knowledge Repository by synthesizing environmental feedback. Specifically, it unifies Process Experience to enforce physical feasibility via prediction errors and Goal Experience to guide task optimality through successful trajectories. Experiments on EB-ALFRED and EB-Habitat demonstrate that WorldMind achieves superior performance compared to baselines with remarkable cross-model and cross-environment transferability.

Despite the success of reinforcement learning for large language models, a common failure mode is reduced sampling diversity, where the policy repeatedly generates similar erroneous behaviors. Classical entropy regularization encourages randomness under the current policy, but does not explicitly discourage recurrent failure patterns across rollouts. We propose MEDS, a Memory-Enhanced Dynamic reward Shaping framework that incorporates historical behavioral signals into reward design. By storing and leveraging intermediate model representations, we capture features of past rollouts and use density-based clustering to identify frequently recurring error patterns. Rollouts assigned to more prevalent error clusters are penalized more heavily, encouraging broader exploration while reducing repeated mistakes. Across five datasets and three base models, MEDS consistently improves average performance over existing baselines, achieving gains of up to 4.13 pass@1 points and 4.37 pass@128 points. Additional analyses using both LLM-based annotations and quantitative diversity metrics show that MEDS increases behavioral diversity during sampling.

Multi-turn, multi-agent LLM game evaluations often exhibit substantial run-to-run variance. In long-horizon interactions, small early deviations compound across turns and are amplified by multi-agent coupling. This biases win rate estimates and makes rankings unreliable across repeated tournaments. Prompt choice worsens this further by producing different effective policies. We address both instability and underperformance with MEMO (Memory-augmented MOdel context optimization), a self-play framework that optimizes inference-time context by coupling retention and exploration. Retention maintains a persistent memory bank that stores structured insights from self-play trajectories and injects them as priors during later play. Exploration runs tournament-style prompt evolution with uncertainty-aware selection via TrueSkill, and uses prioritized replay to revisit rare and decisive states. Across five text-based games, MEMO raises mean win rate from 25.1% to 49.5% for GPT-4o-mini and from 20.9% to 44.3% for Qwen-2.5-7B-Instruct, using 2,000 self-play games per task. Run-to-run variance also drops, giving more stable rankings across prompt variations. These results suggest that multi-agent LLM game performance and robustness have substantial room for improvement through context optimization. MEMO achieves the largest gains in negotiation and imperfect-information games, while RL remains more effective in perfect-information settings.

Amid mounting concern about the reliability and credibility of machine learning research, we present a principled framework for making robust and generalizable claims: the multiverse analysis. Our framework builds upon the multiverse analysis (Steegen et al., 2016) introduced in response to psychology's own reproducibility crisis. To efficiently explore high-dimensional and often continuous ML search spaces, we model the multiverse with a Gaussian Process surrogate and apply Bayesian experimental design. Our framework is designed to facilitate drawing robust scientific conclusions about model performance, and thus our approach focuses on exploration rather than conventional optimization. In the first of two case studies, we investigate disputed claims about the relative merit of adaptive optimizers. Second, we synthesize conflicting research on the effect of learning rate on the large batch training generalization gap. For the machine learning community, the multiverse analysis is a simple and effective technique for identifying robust claims, for increasing transparency, and a step toward improved reproducibility.

With the advancement of interactive video generation, diffusion models have increasingly demonstrated their potential as world models. However, existing approaches still struggle to simultaneously achieve memory-enabled long-term temporal consistency and high-resolution real-time generation, limiting their applicability in real-world scenarios. To address this, we present Matrix-Game 3.0, a memory-augmented interactive world model designed for 720p real-time longform video generation. Building upon Matrix-Game 2.0, we introduce systematic improvements across data, model, and inference. First, we develop an upgraded industrial-scale infinite data engine that integrates Unreal Engine-based synthetic data, large-scale automated collection from AAA games, and real-world video augmentation to produce high-quality Video-Pose-Action-Prompt quadruplet data at scale. Second, we propose a training framework for long-horizon consistency: by modeling prediction residuals and re-injecting imperfect generated frames during training, the base model learns self-correction; meanwhile, camera-aware memory retrieval and injection enable the base model to achieve long horizon spatiotemporal consistency. Third, we design a multi-segment autoregressive distillation strategy based on Distribution Matching Distillation (DMD), combined with model quantization and VAE decoder pruning, to achieve efficient real-time inference. Experimental results show that Matrix-Game 3.0 achieves up to 40 FPS real-time generation at 720p resolution with a 5B model, while maintaining stable memory consistency over minute-long sequences. Scaling up to a 2x14B model further improves generation quality, dynamics, and generalization. Our approach provides a practical pathway toward industrial-scale deployable world models.

Diffusion models operate in a reflexive System 1 mode, constrained by a fixed, content-agnostic sampling schedule. This rigidity arises from the curse of state dimensionality, where the combinatorial explosion of possible states in the high-dimensional noise manifold renders explicit trajectory planning intractable and leads to systematic computational misallocation. To address this, we introduce Chain-of-Trajectories (CoTj), a train-free framework enabling System 2 deliberative planning. Central to CoTj is Diffusion DNA, a low-dimensional signature that quantifies per-stage denoising difficulty and serves as a proxy for the high-dimensional state space, allowing us to reformulate sampling as graph planning on a directed acyclic graph. Through a Predict-Plan-Execute paradigm, CoTj dynamically allocates computational effort to the most challenging generative phases. Experiments across multiple generative models demonstrate that CoTj discovers context-aware trajectories, improving output quality and stability while reducing redundant computation. This work establishes a new foundation for resource-aware, planning-based diffusion modeling. The code is available at https://github.com/UnicomAI/CoTj.

The cost of hyperparameter tuning in deep learning has been rising with model sizes, prompting practitioners to find new tuning methods using a proxy of smaller networks. One such proposal uses muP parameterized networks, where the optimal hyperparameters for small width networks transfer to networks with arbitrarily large width. However, in this scheme, hyperparameters do not transfer across depths. As a remedy, we study residual networks with a residual branch scale of 1/text{depth} in combination with the muP parameterization. We provide experiments demonstrating that residual architectures including convolutional ResNets and Vision Transformers trained with this parameterization exhibit transfer of optimal hyperparameters across width and depth on CIFAR-10 and ImageNet. Furthermore, our empirical findings are supported and motivated by theory. Using recent developments in the dynamical mean field theory (DMFT) description of neural network learning dynamics, we show that this parameterization of ResNets admits a well-defined feature learning joint infinite-width and infinite-depth limit and show convergence of finite-size network dynamics towards this limit.

Large language models (LLMs) underpin applications in code generation, mathematical reasoning, and agent-based workflows. In practice, systems access LLMs via commercial APIs or open-source deployments, and the model landscape (e.g., GPT, Claude, Llama) evolves rapidly. This rapid evolution forces frequent model switches driven by capability, cost, deployment constraints, and privacy. Yet prompts are highly model-sensitive: reusing a prompt engineered for one model on another often yields substantially worse performance than a prompt optimized for the target model. We term this phenomenon Model Drifting. Through extensive empirical analysis across diverse LLM configurations, we show that model drifting is both common and severe. To address this challenge, we introduce PromptBridge, a training-free framework that preserves prompt effectiveness under model switches, enabling cross-model prompt transfer without costly per-task or per-model re-optimization. PromptBridge requires only a small set of alignment tasks for calibration. It first applies Model-Adaptive Reflective Prompt Evolution (MAP-RPE) to obtain task- and model-specific optimal prompts via iterative reflective refinement and quantitative evaluation. Using the resulting calibrated prompt pairs for the source and target models, PromptBridge learns a cross-model prompt mapping. At test time, i.e., for an unseen task, given a source-model prompt, this mapping directly produces an optimized prompt for the target model. Experiments in single-agent and multi-agent settings show that PromptBridge consistently improves downstream accuracy while reducing migration effort. The code will be available soon.

Humans possess a remarkable ability to mentally explore and replay 3D environments they have previously experienced. Inspired by this mental process, we present EvoWorld: a world model that bridges panoramic video generation with evolving 3D memory to enable spatially consistent long-horizon exploration. Given a single panoramic image as input, EvoWorld first generates future video frames by leveraging a video generator with fine-grained view control, then evolves the scene's 3D reconstruction using a feedforward plug-and-play transformer, and finally synthesizes futures by conditioning on geometric reprojections from this evolving explicit 3D memory. Unlike prior state-of-the-arts that synthesize videos only, our key insight lies in exploiting this evolving 3D reconstruction as explicit spatial guidance for the video generation process, projecting the reconstructed geometry onto target viewpoints to provide rich spatial cues that significantly enhance both visual realism and geometric consistency. To evaluate long-range exploration capabilities, we introduce the first comprehensive benchmark spanning synthetic outdoor environments, Habitat indoor scenes, and challenging real-world scenarios, with particular emphasis on loop-closure detection and spatial coherence over extended trajectories. Extensive experiments demonstrate that our evolving 3D memory substantially improves visual fidelity and maintains spatial scene coherence compared to existing approaches, representing a significant advance toward long-horizon spatially consistent world modeling.

A central challenge in sequence modeling is efficiently handling tasks with extended contexts. While recent state-space models (SSMs) have made significant progress in this area, they often lack input-dependent filtering or require substantial increases in model complexity to handle input variability. We address this gap by introducing S7, a simplified yet powerful SSM that can handle input dependence while incorporating stable reparameterization and specific design choices to dynamically adjust state transitions based on input content, maintaining efficiency and performance. We prove that this reparameterization ensures stability in long-sequence modeling by keeping state transitions well-behaved over time. Additionally, it controls the gradient norm, enabling efficient training and preventing issues like exploding or vanishing gradients. S7 significantly outperforms baselines across various sequence modeling tasks, including neuromorphic event-based datasets, Long Range Arena benchmarks, and various physical and biological time series. Overall, S7 offers a more straightforward approach to sequence modeling without relying on complex, domain-specific inductive biases, achieving significant improvements across key benchmarks.

The Model Context Protocol (MCP), introduced by Anthropic in November 2024, defines a standardized interface for connecting large language models (LLMs) to external tools, data sources, and services. Within months of release, hundreds of community-built MCP servers appeared on GitHub, but no software-maintenance literature has yet described how the ecosystem is being structured in production. This industry experience paper catalogues five recurring MCP server architectural patterns observed across an enumerated corpus of fifteen independently developed servers (five production servers from the ANSYR voice AI platform plus ten public servers from the official MCP registry): Resource Gateway, Tool Orchestrator, Stateful Session Server, Proxy Aggregator, and Domain-Specific Adapter. Each pattern is described in the structured form of Gamma et al.: context, problem, solution, and consequences. We also document four anti-patterns and a set of cross-cutting concerns around authentication, versioning, and observability. The quantitative evaluation contributes three measurements: inter-rater reliability of the taxonomy across two independent LLM raters on 54 held-out servers (Cohen's kappa = 0.76), which also localizes three pattern-boundary ambiguities; transport overhead measured end-to-end on loopback and modeled for cross-host paths; and a tool-count study showing tool-selection accuracy drops below 90% between 10 and 15 tools per context for Claude Haiku 4.5 and between 20 and 30 tools for Sonnet 4. Code, corpus, and prompts are released as a replication package.

Large Language Model (LLM)-based agents have fundamentally reshaped artificial intelligence by integrating external tools and planning capabilities. While memory mechanisms have emerged as the architectural cornerstone of these systems, current research remains fragmented, oscillating between operating system engineering and cognitive science. This theoretical divide prevents a unified view of technological synthesis and a coherent evolutionary perspective. To bridge this gap, this survey proposes a novel evolutionary framework for LLM agent memory mechanisms, formalizing the development process into three stages: Storage (trajectory preservation), Reflection (trajectory refinement), and Experience (trajectory abstraction). We first formally define these three stages before analyzing the three core drivers of this evolution: the necessity for long-range consistency, the challenges in dynamic environments, and the ultimate goal of continual learning. Furthermore, we specifically explore two transformative mechanisms in the frontier Experience stage: proactive exploration and cross-trajectory abstraction. By synthesizing these disparate views, this work offers robust design principles and a clear roadmap for the development of next-generation LLM agents.

Reliable deployment of language models requires two capabilities that appear distinct but share a common geometric foundation: predicting whether a model will accept targeted behavioral control, and detecting when its internal structure degrades. We show that geometric stability, the consistency of a representation's pairwise distance structure, addresses both. Supervised Shesha variants that measure task-aligned geometric stability predict linear steerability with near-perfect accuracy (ρ= 0.89-0.97) across 35-69 embedding models and three NLP tasks, capturing unique variance beyond class separability (partial ρ= 0.62-0.76). A critical dissociation emerges: unsupervised stability fails entirely for steering on real-world tasks (ρapprox 0.10), revealing that task alignment is essential for controllability prediction. However, unsupervised stability excels at drift detection, measuring nearly 2times greater geometric change than CKA during post-training alignment (up to 5.23times in Llama) while providing earlier warning in 73\% of models and maintaining a 6times lower false alarm rate than Procrustes. Together, supervised and unsupervised stability form complementary diagnostics for the LLM deployment lifecycle: one for pre-deployment controllability assessment, the other for post-deployment monitoring.

As large language models (LLMs) evolve into autonomous agents for long-horizon information-seeking, managing finite context capacity has become a critical bottleneck. Existing context management methods typically commit to a single fixed strategy throughout the entire trajectory. Such static designs may work well in some states, but they cannot adapt as the usefulness and reliability of the accumulated context evolve during long-horizon search. To formalize this challenge, we introduce a probabilistic framework that characterizes long-horizon success through two complementary dimensions: search efficiency and terminal precision. Building on this perspective, we propose AgentSwing, a state-aware adaptive parallel context management routing framework. At each trigger point, AgentSwing expands multiple context-managed branches in parallel and uses lookahead routing to select the most promising continuation. Experiments across diverse benchmarks and agent backbones show that AgentSwing consistently outperforms strong static context management methods, often matching or exceeding their performance with up to 3times fewer interaction turns while also improving the ultimate performance ceiling of long-horizon web agents. Beyond the empirical gains, the proposed probabilistic framework provides a principled lens for analyzing and designing future context management strategies for long-horizon agents.

Colloquially speaking, image generation models based upon diffusion processes are frequently said to exhibit "hallucinations," samples that could never occur in the training data. But where do such hallucinations come from? In this paper, we study a particular failure mode in diffusion models, which we term mode interpolation. Specifically, we find that diffusion models smoothly "interpolate" between nearby data modes in the training set, to generate samples that are completely outside the support of the original training distribution; this phenomenon leads diffusion models to generate artifacts that never existed in real data (i.e., hallucinations). We systematically study the reasons for, and the manifestation of this phenomenon. Through experiments on 1D and 2D Gaussians, we show how a discontinuous loss landscape in the diffusion model's decoder leads to a region where any smooth approximation will cause such hallucinations. Through experiments on artificial datasets with various shapes, we show how hallucination leads to the generation of combinations of shapes that never existed. Finally, we show that diffusion models in fact know when they go out of support and hallucinate. This is captured by the high variance in the trajectory of the generated sample towards the final few backward sampling process. Using a simple metric to capture this variance, we can remove over 95% of hallucinations at generation time while retaining 96% of in-support samples. We conclude our exploration by showing the implications of such hallucination (and its removal) on the collapse (and stabilization) of recursive training on synthetic data with experiments on MNIST and 2D Gaussians dataset. We release our code at https://github.com/locuslab/diffusion-model-hallucination.

The μ-parameterization (μP) provides a principled foundation for large language model (LLM) training by prescribing width-independent learning dynamics, which in turn enables predictable scaling behavior and robust hyperparameter transfer across model sizes. A central requirement of μP is the satisfaction of certain spectral conditions on weight matrices, which ensure consistent feature learning and optimization behavior as model width grows. While these conditions are well understood in theory, guaranteeing their validity in practical training for matrix-based optimizers such as Muon is still under studied. Existing works that study Muon under μP exhibit important limitations: they either do not ensure that the spectral conditions hold throughout the entire training horizon, or require repeated spectral normalization (or Newton-Schulz iterations) applied to both weights and updates, leading to significant computational overhead and reduced practicality. In this work, we show how to reliably guarantee the spectral conditions required by μP for Muon during the entire training process. Our key insight is that for moderately large models, maintaining spectral control at the level of optimizer updates alone is sufficient to preserve μP-compatible scaling, eliminating the need for explicit spectral normalization of the weights. Based on this principle, we develop a variant of Muon, namely Muon++, that satisfies spectral condition throughout the training process. Our results bridge the gap between the theoretical promises of μP and the practical deployment of matrix-based optimizers in long-horizon training. We also take the first step towards an adaptive spectral condition by incorporating data-dependent effects, making it better suited for long-horizon LLM training.

The impressive capabilities of Large Language Models (LLMs) across diverse tasks are now well-established, yet their effective deployment necessitates careful hyperparameter optimization. Through extensive empirical studies involving grid searches across diverse configurations, we discover universal scaling laws governing these hyperparameters: optimal learning rate follows a power-law relationship with both model parameters and data sizes, while optimal batch size scales primarily with data sizes. Our analysis reveals a convex optimization landscape for hyperparameters under fixed models and data size conditions. This convexity implies an optimal hyperparameter plateau. We contribute a universal, plug-and-play optimal hyperparameter tool for the community. Its estimated values on the test set are merely 0.07\% away from the globally optimal LLM performance found via an exhaustive search. These laws demonstrate remarkable robustness across variations in model sparsity, training data distribution, and model shape. To our best known, this is the first work that unifies different model shapes and structures, such as Mixture-of-Experts models and dense transformers, as well as establishes optimal hyperparameter scaling laws across diverse data distributions. This exhaustive optimization process demands substantial computational resources, utilizing nearly one million NVIDIA H800 GPU hours to train 3,700 LLMs of varying sizes and hyperparameters from scratch and consuming approximately 100 trillion tokens in total. To facilitate reproducibility and further research, we will progressively release all loss measurements and model checkpoints through our designated repository https://step-law.github.io/

Model uncertainty and limited data are fundamental challenges to robust management of human intervention in a natural system. These challenges are acutely highlighted by concerns that many ecological systems may contain tipping points, such as Allee population sizes. Before a collapse, we do not know where the tipping points lie, if they exist at all. Hence, we know neither a complete model of the system dynamics nor do we have access to data in some large region of state-space where such a tipping point might exist. We illustrate how a Bayesian Non-Parametric (BNP) approach using a Gaussian Process (GP) prior provides a flexible representation of this inherent uncertainty. We embed GPs in a Stochastic Dynamic Programming (SDP) framework in order to make robust management predictions with both model uncertainty and limited data. We use simulations to evaluate this approach as compared with the standard approach of using model selection to choose from a set of candidate models. We find that model selection erroneously favors models without tipping points -- leading to harvest policies that guarantee extinction. The GPDP performs nearly as well as the true model and significantly outperforms standard approaches. We illustrate this using examples of simulated single-species dynamics, where the standard model selection approach should be most effective, and find that it still fails to account for uncertainty appropriately and leads to population crashes, while management based on the GPDP does not, since it does not underestimate the uncertainty outside of the observed data.

Emerging world models autoregressively generate video frames in response to actions, such as camera movements and text prompts, among other control signals. Due to limited temporal context window sizes, these models often struggle to maintain scene consistency during revisits, leading to severe forgetting of previously generated environments. Inspired by the mechanisms of human memory, we introduce a novel framework to enhancing long-term consistency of video world models through a geometry-grounded long-term spatial memory. Our framework includes mechanisms to store and retrieve information from the long-term spatial memory and we curate custom datasets to train and evaluate world models with explicitly stored 3D memory mechanisms. Our evaluations show improved quality, consistency, and context length compared to relevant baselines, paving the way towards long-term consistent world generation.

A fundamental dilemma in generative modeling persists: iterative diffusion models achieve outstanding fidelity, but at a significant computational cost, while efficient few-step alternatives are constrained by a hard quality ceiling. This conflict between generation steps and output quality arises from restrictive training objectives that focus exclusively on either infinitesimal dynamics (PF-ODEs) or direct endpoint prediction. We address this challenge by introducing an exact, continuous-time dynamics equation that analytically defines state transitions across any finite time interval. This leads to a novel generative paradigm, Transition Models (TiM), which adapt to arbitrary-step transitions, seamlessly traversing the generative trajectory from single leaps to fine-grained refinement with more steps. Despite having only 865M parameters, TiM achieves state-of-the-art performance, surpassing leading models such as SD3.5 (8B parameters) and FLUX.1 (12B parameters) across all evaluated step counts. Importantly, unlike previous few-step generators, TiM demonstrates monotonic quality improvement as the sampling budget increases. Additionally, when employing our native-resolution strategy, TiM delivers exceptional fidelity at resolutions up to 4096x4096.

Recent advancements in Large Language Models (LLMs) have driven growing interest in LLM-based agents for complex planning tasks. To avoid costly agent training, many studies adopted memory mechanism that enhances LLM with offline experiences or online trajectory analysis. However, existing works focus on single-granularity memory derived from dynamic environmental interactions, which are inherently constrained by the quality of the collected experiences. This limitation, in turn, constrain the diversity of knowledge and the flexibility of planning. We propose Coarse-to-Fine Grounded Memory (), a novel framework that grounds coarse-to-fine memories with LLM, thereby fully leverage them for flexible adaptation to diverse scenarios. grounds environmental information into coarse-grained focus points to guide experience collection in training tasks, followed by grounding of actionable hybrid-grained tips from each experience. At inference, retrieves task-relevant experiences and tips to support planning. When facing environmental anomalies, the LLM grounds the current situation into fine-grained key information, enabling flexible self-QA reflection and plan correction.