Daily Papers

Learning an effective policy to control high-dimensional, overactuated systems is a significant challenge for deep reinforcement learning algorithms. Such control scenarios are often observed in the neural control of vertebrate musculoskeletal systems. The study of these control mechanisms will provide insights into the control of high-dimensional, overactuated systems. The coordination of actuators, known as muscle synergies in neuromechanics, is considered a presumptive mechanism that simplifies the generation of motor commands. The dynamical structure of a system is the basis of its function, allowing us to derive a synergistic representation of actuators. Motivated by this theory, we propose the Dynamical Synergistic Representation (DynSyn) algorithm. DynSyn aims to generate synergistic representations from dynamical structures and perform task-specific, state-dependent adaptation to the representations to improve motor control. We demonstrate DynSyn's efficiency across various tasks involving different musculoskeletal models, achieving state-of-the-art sample efficiency and robustness compared to baseline algorithms. DynSyn generates interpretable synergistic representations that capture the essential features of dynamical structures and demonstrates generalizability across diverse motor tasks.

We develop a dynamical mean-field theory for random recurrent networks with low-rank structure and firing-rate-driven adaptation. When the random connectivity is strong enough to generate chaos, increasing adaptation strength drives the network through four regimes: a static coherent state, noise-sustained oscillations that progress from regular to irregular, stochastic switching between symmetric wells, and a global limit cycle. The theory identifies two instability mechanisms, chaos onset from the random connectivity and a Hopf bifurcation of the coherent mode, and shows how adaptation shapes both through the frequency-dependent single-neuron transfer function. A reduced three-dimensional model captures the bifurcation structure of the full network. Above the chaos threshold, coherent population-level oscillations coexist with heterogeneous firing rates and network-generated stochasticity at the single-neuron level. The interaction of adaptation with random and low-rank connectivity produces a rich oscillatory repertoire, including waxing-and-waning rhythmic episodes, persistent state switching, and slow Up-Down alternations, dynamics that have been observed during wakefulness, sleep, and anesthesia.

Mixture of Experts (MoE) models scale capacity but often suffer from representation collapse and gradient instability. We propose Dynamic Subspace Composition (DSC), a framework that approximates context-dependent weights via a state-dependent, sparse expansion of a shared basis bank. Formally, DSC models the weight update as a residual trajectory within a Star- Shaped Domain, employing a Magnitude-Gated Simplex Interpolation to ensure continuity at the identity. Unlike standard Mixture-of-LoRAs, which incurs O(M rd) parameter complexity by retrieving independent rank-r matrices, DSC constructs a compositional rank-K approximation from decoupled unit-norm basis vectors. This reduces parameter complexity to O(M d) and memory traffic to O(Kd), while Frame-Theoretic regularization and spectral constraints provide rigorous worst-case bounds on the dynamic update. The code is available at https://github. com/VladimerKhasia/DSC

Large Transformer models function as Dense Associative Memories (DAMs), retrieving knowledge via high-dimensional attractor dynamics driven by the self-attention mechanism ramsauer2020hopfield, wu2024attention. However, adapting these frozen memory systems to new tasks presents a fundamental ``Plasticity-Stability'' dilemma. Current methods either risk catastrophic interference by modifying synaptic weights directly (e.g., LoRA) hu2021lora or degrade associative capacity by clogging the retrieval buffer with static prompt tokens (e.g., VPT) jia2022vpt. In this work, we propose H-Res (Hierarchical Residual Steering), a mechanism that modulates the effective energy landscape of the Transformer without altering its global equilibrium or expanding its sequence length. By formulating adaptation as a control problem on the activation manifold chen2018neuralode, H-Res learns a state-dependent vector field that steers token trajectories into task-specific basins of attraction. We formally prove that H-Res preserves the attention entropy of the foundation model and facilitates Neural Collapse papyan2020prevalence. Empirically, Manifold Steering outperforms global weight modification by 26\% on associative retrieval tasks and eliminates the computational overhead of prompt-based methods, scaling effectively to structured domains zha2023vtab.

Reinforcement learning (RL) enables robots to learn skills from interactions with the real world. In practice, the unstructured step-based exploration used in Deep RL -- often very successful in simulation -- leads to jerky motion patterns on real robots. Consequences of the resulting shaky behavior are poor exploration, or even damage to the robot. We address these issues by adapting state-dependent exploration (SDE) to current Deep RL algorithms. To enable this adaptation, we propose two extensions to the original SDE, using more general features and re-sampling the noise periodically, which leads to a new exploration method generalized state-dependent exploration (gSDE). We evaluate gSDE both in simulation, on PyBullet continuous control tasks, and directly on three different real robots: a tendon-driven elastic robot, a quadruped and an RC car. The noise sampling interval of gSDE permits to have a compromise between performance and smoothness, which allows training directly on the real robots without loss of performance. The code is available at https://github.com/DLR-RM/stable-baselines3.

Vision-Language Models (VLMs) adapted to remote sensing rely heavily on domain-specific image-text supervision, yet high-quality annotations for satellite and aerial imagery remain scarce and expensive to produce. Prevailing pseudo-labeling pipelines address this gap by distilling knowledge from large frontier models, but this dependence on large teachers is costly, limits scalability, and caps achievable performance at the ceiling of the teacher. We propose OSMDA: a self-contained domain adaptation framework that eliminates this dependency. Our key insight is that a capable base VLM can serve as its own annotation engine: by pairing aerial images with rendered OpenStreetMap (OSM) tiles, we leverage optical character recognition and chart comprehension capabilities of the model to generate captions enriched by OSM's vast auxiliary metadata. The model is then fine-tuned on the resulting corpus with satellite imagery alone, yielding OSMDA-VLM, a domain-adapted VLM that requires no manual labeling and no stronger external model. We conduct exhaustive evaluations spanning 10 benchmarks across image-text-to-text tasks and comparing against 9 competitive baselines. When equally mixed with real data, our method achieves state-of-the-art results, while being substantially cheaper to train than teacher-dependent alternatives. These results suggest that, given a strong foundation model, alignment with crowd-sourced geographic data is a practical and scalable path towards remote sensing domain adaptation. Dataset and model weights will be made publicly available.

Foundation models have demonstrated remarkable capabilities across various domains, but developing analogous models for knowledge graphs presents unique challenges due to their dynamic nature and the need for cross-domain reasoning. To address these issues, we introduce \textsc{GraphOracle}, a relation-centric foundation model that unifies reasoning across knowledge graphs by converting them into Relation-Dependency Graphs (RDG), explicitly encoding compositional patterns with fewer edges than prior methods. A query-dependent attention mechanism is further developed to learn inductive representations for both relations and entities. Pre-training on diverse knowledge graphs, followed by minutes-level fine-tuning, enables effective generalization to unseen entities, relations, and entire graphs. Through comprehensive experiments on 31 diverse benchmarks spanning transductive, inductive, and cross-domain settings, we demonstrate consistent state-of-the-art performance with minimal adaptation, improving the prediction performance by up to 35\% compared to the strongest baselines.

Adapting large-scale pre-trained video generators for Video Super-Resolution (VSR) in novel domains remains computationally prohibitive. Methods that reformulate generation as direct Low-Quality to High-Quality mappings deviate from the original generative formulation, demanding extensive fine-tuning. ControlNet-style adapters lose their efficiency under modern Diffusion Transformers since the absence of encoder-decoder hierarchy forces duplication of the entire backbone. We observe that flow matching offers a principled alternative for cross-domain VSR adaptation. By predicting a constant velocity field across all timesteps, the adaptation task reduces to learning a fixed injection pattern rather than time-varying transformations. Building on this insight, we propose LiteVSR, a minimalist framework that performs VSR using a completely frozen Diffusion Transformer with a lightweight State-Aware Adapter. The adapter employs a dual-stream architecture that extracts static structural cues from the LQ input and dynamic cues from intermediate denoising states, aligning them through time-dependent cross-attention to enable adaptive transition from structural alignment to texture refinement as denoising proceeds. LiteVSR achieves competitive restoration quality with only 11.25% trainable parameters and 12 GPU-hours of training on a single A100, while maintaining fast sampling (down to a single step) compatibility.

Existing bias auditing methods typically rely on model outputs, requiring costly benchmarks or judge models and potentially missing internal shifts that never appear in generated text. We propose a reference-based method that audits bias in hidden-state representations across related model variants, for example before and after fine-tuning. Because fine-tuning reshapes representation geometry, absolute hidden states are not directly comparable, so we encode each sentence by its similarities to a fixed set of anchor sentences, yielding relative representations in a shared comparison space. There we measure how target groups shift in their association with positive and negative attributes, a quantity we call the Representational Bias Shift ΔB. Across three model families and the WildGuardMix, DecodingTrust and ToxiGen benchmarks, ΔB correlates with output-level bias change in 15 of the 18 settings we test, reaching |r| = 0.84 (p < 0.001) under full fine-tuning and becoming more model-dependent under parameter-efficient adaptation. Thresholding ΔB detects checkpoints whose bias increased with ROC AUC between 0.65 and 0.99, and on WildGuardMix and DecodingTrust it separates them better than a SEAT-based baseline for all three families. ΔB is also stable under changes to the anchor set, attribute sets and target templates. Our method requires no task-specific evaluation data and audits a model in about three minutes, using 3-50times less compute than the output-level benchmarks considered here. We view it as complementary to output-based auditing rather than a replacement for it.

Robotic foundation models achieve impressive performance on standard manipulation benchmarks, yet these evaluations typically assume clean, timely, and consistent visual observations throughout execution. We introduce LIBERO-VPro, a benchmark for systematically evaluating the closed-loop visual robustness of robotic foundation models by perturbing the visual evidence available during execution. LIBERO-VPro covers four complementary dimensions, including Visual Evidence Degradation, Camera Staleness, Visual Source Consistency, and Task-Relevant Scene Variation, spanning 12 challenge categories, 96 experimental settings, and 3,296 task-condition cases. We evaluate three vision-language-action models and three world-action models over approximately 196,000 simulated episodes, complemented by 200 real-world rollouts on a Franka Research 3. Our results reveal that strong nominal performance can mask substantial weaknesses in visual grounding and adaptation. Models often remain successful despite severe object-level occlusion, yet degrade sharply when local interaction cues are disrupted or familiar spatial priors are violated. They are also highly sensitive to stale or missing observations and struggle when changed task preconditions require behavioral adaptation. Finally, VLAs and WAMs exhibit distinct robustness profiles, showing that visual robustness is multi-dimensional and architecture-dependent. LIBERO-VPro provides a systematic diagnostic framework for developing robotic foundation models that can more reliably ground and adapt their actions under challenging visual conditions.

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.

State Space Models (SSMs) have emerged as efficient alternatives to Transformers, mitigating their quadratic computational cost. However, the application of Parameter-Efficient Fine-Tuning (PEFT) methods to SSMs remains largely unexplored. In particular, prompt-based methods like Prompt Tuning and Prefix-Tuning, which are widely used in Transformers, do not perform well on SSMs. To address this, we propose state-based methods as a superior alternative to prompt-based methods. This new family of methods naturally stems from the architectural characteristics of SSMs. State-based methods adjust state-related features directly instead of depending on external prompts. Furthermore, we introduce a novel state-based PEFT method: State-offset Tuning. At every timestep, our method directly affects the state at the current step, leading to more effective adaptation. Through extensive experiments across diverse datasets, we demonstrate the effectiveness of our method. Code is available at https://github.com/furiosa-ai/ssm-state-tuning.

Phenotypic plasticity, the ability of cells to switch between states, is central to development, differentiation, and therapy resistance. Although it is modeled at several scales, from compartmental ODEs to phenotype-structured PDEs and single-cell stochastic equations, a framework connecting these descriptions is missing. We present such a framework. Starting from a general n-compartment ODE model encompassing nonlinear growth and linear transitions between phenotypes, we show, with a new, elementary and generalizable proof of a recent theorem, that under uniform competition, the long-term population distribution is solely governed by transition rates. All phenotypes become selectively neutral at saturation, and the imprint of fitness differences during growth fades at an explicit rate. Restricting transitions to neighboring states transforms the model into a discretization of a phenotype-structured reaction-diffusion-advection PDE. In this continuum model, diffusion and advection are identified from switching rates, and fitness remains asymptotically irrelevant. Interpreting the advection velocity as the negative gradient of an effective epigenetic potential transforms the PDE into a Fokker--Planck equation and converts single-cell trajectories into stochastic gradient descent (SGD) in the Langevin sense on the phenotypic landscape. Non-local transitions, such as mutations, are incorporated via an integro-differential term, yielding a unified model with reaction, gradient flow, diffusion, and jumps. State-dependent noise reshapes the effective landscape without altering the underlying potential. This gives cancer a route to elevated plasticity that static, single-cell snapshots cannot distinguish from a changed landscape. This framework provides a physical interpretation of Waddington's landscape, where cells perform SGD, and cancer corresponds to a corrupted landscape.

Test-time scaling has emerged as a prominent research direction in machine learning, enabling models to enhance their expressive capabilities during inference.Transformers, renowned for striking a delicate balance between efficiency and expressiveness, have benefited from test-time scaling techniques that leverage an expanding key-value (KV) cache to significantly improve performance.In this paper, we introduce a novel state-based approach to test-time scaling, which we term state tuning, tailored to the RNN-based RWKV-7 model.By exploiting the unique strengths of RWKV-7, our method achieves state-of-the-art performance on the target task without altering the model's pre-trained weights. Our approach centers on three key innovations. First, we develop an observer framework that allows a smaller model to replicate and learn the state dynamics of the RWKV-7 model. Second, we employ a kernel method to dynamically upscale the state size, enhancing the model's capacity to capture intricate patterns. Third, we integrate Decorrelated Backpropagation (DBP) to optimize the upscaled state matrix, thereby improving convergence and expressivity. By tuning only the state matrix, we demonstrate that a smaller model can outperform larger models on the given task. This method preserves the efficiency of the original RWKV-7 architecture while harnessing the power of test-time scaling to deliver superior results. Our findings underscore the potential of state tuning as an effective strategy for advancing model performance in resource-constrained settings. Our code is https://github.com/TorchRWKV/flash-linear-attention.

Masked diffusion language models (MDMs) admit flexible generation orders, making the unmasking strategy an inference decision. Existing methods vary in how they prioritize positions, control parallelism, restrict selection regions, revise predictions, or plan future denoising, yet it remains unclear when these choices should change during generation. We study this question through strategy reversals, where an alternative action becomes preferable to a fixed choice. We organize MDM inference into five axes--score, cardinality, region, commitment, and planning--and define adaptation opportunity as the one-step utility advantage of the best candidate action over a validation-selected fixed action. This view shows that adaptation value depends on both the frequency and magnitude of such reversals. Across three MDMs and ten tasks, adaptation opportunities are highly heterogeneous, with some regimes exhibiting concentrated and predictable one-step gains. This motivates selective adaptation: lightweight detectors calibrated on validation prompts identify high-opportunity states, capturing, for example, 56.9 percent of the candidate-set oracle opportunity by adapting only the top 10 percent of states on LLaDA-8B constrained JSON filling. Our transition-level results suggest that state adaptation is most useful when applied selectively rather than uniformly.

State-Space Models (SSMs) have recently emerged as a powerful and efficient alternative to the long-standing transformer architecture. However, existing SSM conceptualizations retain deeply rooted biases from their roots in natural language processing. This constrains their ability to appropriately model the spatially-dependent characteristics of visual inputs. In this paper, we address these limitations by re-deriving modern selective state-space techniques, starting from a natively multidimensional formulation. Currently, prior works attempt to apply natively 1D SSMs to 2D data (i.e. images) by relying on arbitrary combinations of 1D scan directions to capture spatial dependencies. In contrast, Mamba2D improves upon this with a single 2D scan direction that factors in both dimensions of the input natively, effectively modelling spatial dependencies when constructing hidden states. Mamba2D shows comparable performance to prior adaptations of SSMs for vision tasks, on standard image classification evaluations with the ImageNet-1K dataset. Source code is available at https://github.com/cocoalex00/Mamba2D.

Low-Rank Adaptive Residual Connections (LARC) give a frozen model a compact numerical state that can learn from feedback. The map h+BAh adds a low-rank correction to a hidden representation. A slow state ρ learns starting factors across tasks; a private fast state Φ copies them, changes with feedback, and resets to the trained initialization. This report specifies an input-side realization of the numerical policy carrier in Memory-Mediated Learning Architecture and examines its factor-space dynamics and learning lifetime. We study a rank-4 input residual with 12,288 trainable parameters on a frozen MiniCPM5-1B-SFT substrate. In a four-candidate program-selection task, two feedback-gradient steps reduce expected query execution error by 24.65 and 36.65 percentage points relative to resetting to the respective trained static and post-adaptation initializations. These development results cover 16 parameter groups and three paired training seeds. A direct support-loss selection rule is much more accurate, reaching 0.78125% error. In a repository-balanced chronological replay of public continuous-integration jobs, retaining online updates raises half-Brier loss from 0.1274 to 0.1808. A fixed follow-up intervention records same-batch non-descent and inconsistent future benefit from shrinking updates. Together, the algebra and measurements distinguish residual capacity, adaptation relative to a starting point, and usefulness on later decisions.

Exposing meaningful and interpretable neural interactions is critical to understanding neural circuits. Inferred neural interactions from neural signals primarily reflect functional interactions. In a long experiment, subject animals may experience different stages defined by the experiment, stimuli, or behavioral states, and hence functional interactions can change over time. To model dynamically changing functional interactions, prior work employs state-switching generalized linear models with hidden Markov models (i.e., HMM-GLMs). However, we argue they lack biological plausibility, as functional interactions are shaped and confined by the underlying anatomical connectome. Here, we propose a novel prior-informed state-switching GLM. We introduce both a Gaussian prior and a one-hot prior over the GLM in each state. The priors are learnable. We will show that the learned prior should capture the state-constant interaction, shedding light on the underlying anatomical connectome and revealing more likely physical neuron interactions. The state-dependent interaction modeled by each GLM offers traceability to capture functional variations across multiple brain states. Our methods effectively recover true interaction structures in simulated data, achieve the highest predictive likelihood with real neural datasets, and render interaction structures and hidden states more interpretable when applied to real neural data.

Causal discovery, i.e., inferring underlying cause-effect relationships from observations of a scene or system, is an inherent mechanism in human cognition, but has been shown to be highly challenging to automate. The majority of approaches in the literature aiming for this task consider constrained scenarios with fully observed variables or data from stationary time-series. In this work we aim for causal discovery in a more general class of scenarios, scenes with non-stationary behavior over time. For our purposes we here regard a scene as a composition objects interacting with each other over time. Non-stationarity is modeled as stationarity conditioned on an underlying variable, a state, which can be of varying dimension, more or less hidden given observations of the scene, and also depend more or less directly on these observations. We propose a probabilistic deep learning approach called State-Dependent Causal Inference (SDCI) for causal discovery in such conditionally stationary time-series data. Results in two different synthetic scenarios show that this method is able to recover the underlying causal dependencies with high accuracy even in cases with hidden states.

Neural networks require a careful design in order to perform properly on a given task. In particular, selecting a good activation function (possibly in a data-dependent fashion) is a crucial step, which remains an open problem in the research community. Despite a large amount of investigations, most current implementations simply select one fixed function from a small set of candidates, which is not adapted during training, and is shared among all neurons throughout the different layers. However, neither two of these assumptions can be supposed optimal in practice. In this paper, we present a principled way to have data-dependent adaptation of the activation functions, which is performed independently for each neuron. This is achieved by leveraging over past and present advances on cubic spline interpolation, allowing for local adaptation of the functions around their regions of use. The resulting algorithm is relatively cheap to implement, and overfitting is counterbalanced by the inclusion of a novel damping criterion, which penalizes unwanted oscillations from a predefined shape. Experimental results validate the proposal over two well-known benchmarks.

State-space models (SSMs) are a new class of foundation models that have emerged as a compelling alternative to Transformers and their attention mechanisms for sequence processing tasks. This paper provides a detailed theoretical analysis of selective SSMs, the core components of the Mamba and Mamba-2 architectures. We leverage the connection between selective SSMs and the self-attention mechanism to highlight the fundamental similarities between these models. Building on this connection, we establish a length independent covering number-based generalization bound for selective SSMs, providing a deeper understanding of their theoretical performance guarantees. We analyze the effects of state matrix stability and input-dependent discretization, shedding light on the critical role played by these factors in the generalization capabilities of selective SSMs. Finally, we empirically demonstrate the sequence length independence of the derived bounds on two tasks.

A high-performance image compression algorithm is crucial for real-time information transmission across numerous fields. Despite rapid progress in image compression, computational inefficiency and poor redundancy modeling still pose significant bottlenecks, limiting practical applications. Inspired by the effectiveness of state space models (SSMs) in capturing long-range dependencies, we leverage SSMs to address computational inefficiency in existing methods and improve image compression from multiple perspectives. In this paper, we integrate the advantages of SSMs for better efficiency-performance trade-off and propose an enhanced image compression approach through refined context modeling, which we term MambaIC. Specifically, we explore context modeling to adaptively refine the representation of hidden states. Additionally, we introduce window-based local attention into channel-spatial entropy modeling to reduce potential spatial redundancy during compression, thereby increasing efficiency. Comprehensive qualitative and quantitative results validate the effectiveness and efficiency of our approach, particularly for high-resolution image compression. Code is released at https://github.com/AuroraZengfh/MambaIC.

State Space Models (SSMs) offer an efficient alternative to Transformers for sequence modeling, yet conditioning pre-trained SSMs for iterative generation typically operates outside the recurrent operator, through input injection or activation modulation. While such mechanisms expose the model to conditioning information, they leave the underlying temporal dynamics fixed. We introduce MaRK (Markov-adapted Recurrent Kernels), a dynamic operator-conditioning framework that maps context vectors directly into bounded modulations of a frozen SSM's recurrence (A), read-in (B), read-out (C), skip (D), and discretization (Δ) parameters. Viewed through the lens of LPV-SSM systems, MaRK induces a context-indexed family of Markov parameter sequences, allowing each diffusion timestep to reshape the model's input-output memory kernel. We instantiate MaRK on a frozen 111M-parameter Hydra SSM backbone and study three adapter geometries: Hypernet, Chebyshev polynomial, and Discrete Cosine Transform kernels. Since these adapters modify the Markov parameter sequence through low-rank auxiliary maps on the frozen backbone, parameter-efficient fine-tuning arises as a structural consequence of the adaptation mechanism itself, requiring only 6.3--11M trainable auxiliary parameters to transition from a bidirectional objective to an iterative diffusion regime. The bounded recurrence parameterization further yields an analytic Affine Quadratic Stability certificate for the modulated recurrence. Through synthetic LPV recovery experiments and Markov-operator diagnostics, we show that MaRK recovers coordinate-invariant temporal operators under matched assumptions and produces distinct, stable timestep-conditioned memory profiles. Empirically, the Chebyshev variant yields the strongest performance, achieving an average validation loss of 2.55, followed by the DCT (2.59) and Hypernet (3.77) geometries.

In real-world scenarios, the application of reinforcement learning is significantly challenged by complex non-stationarity. Most existing methods attempt to model changes in the environment explicitly, often requiring impractical prior knowledge of environments. In this paper, we propose a new perspective, positing that non-stationarity can propagate and accumulate through complex causal relationships during state transitions, thereby compounding its sophistication and affecting policy learning. We believe that this challenge can be more effectively addressed by implicitly tracing the causal origin of non-stationarity. To this end, we introduce the Causal-Origin REPresentation (COREP) algorithm. COREP primarily employs a guided updating mechanism to learn a stable graph representation for the state, termed as causal-origin representation. By leveraging this representation, the learned policy exhibits impressive resilience to non-stationarity. We supplement our approach with a theoretical analysis grounded in the causal interpretation for non-stationary reinforcement learning, advocating for the validity of the causal-origin representation. Experimental results further demonstrate the superior performance of COREP over existing methods in tackling non-stationarity problems.

In real-world applications of reinforcement learning, it is often challenging to obtain a state representation that is parsimonious and satisfies the Markov property without prior knowledge. Consequently, it is common practice to construct a state larger than necessary, e.g., by concatenating measurements over contiguous time points. However, needlessly increasing the dimension of the state may slow learning and obfuscate the learned policy. We introduce the notion of a minimal sufficient state in a Markov decision process (MDP) as the subvector of the original state under which the process remains an MDP and shares the same reward function as the original process. We propose a novel SEquEntial Knockoffs (SEEK) algorithm that estimates the minimal sufficient state in a system with high-dimensional complex nonlinear dynamics. In large samples, the proposed method achieves selection consistency. As the method is agnostic to the reinforcement learning algorithm being applied, it benefits downstream tasks such as policy learning. Empirical experiments verify theoretical results and show the proposed approach outperforms several competing methods regarding variable selection accuracy and regret.

Autonomous agentic systems are largely static after deployment: they do not learn from user interactions, and recurring failures persist until the next human-driven update ships a fix. Self-evolving agents have emerged in response, but all confine evolution to text-mutable artifacts -- skill files, prompt configurations, memory schemas, workflow graphs -- and leave the agent harness untouched. Since routing, hook ordering, state invariants, and dispatch live in code rather than in any text artifact, an entire class of structural failure is physically unreachable from the text layer. We argue that source-level adaptation is a fundamentally more general medium: it is Turing-complete, a strict superset of every text-mutable scope, takes effect deterministically rather than through base-model compliance, and does not erode under long-context drift. We present MOSS, a system that performs self-rewriting at the source level on production agentic substrates. Each evolution is anchored to an automatically curated batch of production-failure evidence and proceeds through a deterministic multi-stage pipeline; code modification is delegated to a pluggable external coding-agent CLI while MOSS retains stage ordering and verdicts. Candidates are verified by replaying the batch against the candidate image in ephemeral trial workers, then promoted via user-consent-gated, in-place container swap with health-probe-gated rollback. On OpenClaw, MOSS lifts a four-task mean grader score from 0.25 to 0.61 in a single cycle without human intervention.

Recent 3D world models increasingly use features from geometry foundation models (GFMs) as predictive world states, benefiting from their rich geometric priors. However, the view dependence of these features entangles scene dynamics with camera-induced variation, making the resulting state evolution harder to predict. We propose GeoState, a view-decoupled geometry representation for predictive 3D world modeling that separates scene-state evolution from camera-dependent observation. Specifically, a scene tokenizer aggregates multi-view GFM features into a view-decoupled scene state, which a geometry decoder queries using camera rays. An autoregressive world model then predicts future scene states, while camera motion is modeled separately. The predicted states can therefore be decoded under either predicted or externally specified cameras, while retaining a single context-derived scale throughout the rollout without per-frame scale alignment. Experiments show that GeoState outperforms prior 3D world models on Waymo, supports geometrically consistent cross-view querying, and generalizes zero-shot to KITTI and nuScenes. Project page: https://hongchang-liu.github.io/GeoState-project-page/

Autoregressive video diffusion models generate streaming video by producing frames sequentially, conditioning each chunk on previously generated content. These models are structurally anchored to the first frame: its key-value representation occupies a privileged position in the attention cache and serves as the primary scene reference throughout generation. As the cleanest and most error-free position in the cache, this anchor draws disproportionate attention, suppressing video dynamics, and locking scene composition to the initial viewpoint even as the scene naturally evolves. The result is a temporally shallow video in which motion, camera movement, and scene progression are dampened in favor of static consistency. To address this, we replace the static anchor with an adaptive state, a hidden latent that the model denoises alongside content at every chunk but never renders. Rather than referencing a frozen first frame, the model generates its own scene anchor at each step by attending to both the previous state and the current content, producing a reference that evolves with the generated content. Unlike standard video generation, which encodes an absolute notion of time, our formulation treats time as relative: every generation step sees the same positional structure regardless of how far generation has progressed, and the state transition is identical at every chunk. Together, these properties introduce a recurrence into the generation process, where denoising serves as the transition function, and the KV cache serves as the carrier, requiring no external module. Experiments demonstrate that the adaptive state substantially improves video dynamics, enabling richer motion and natural scene progression within generated videos.

Model-based reinforcement learning (RL) often achieves higher sample efficiency in practice than model-free RL by learning a dynamics model to generate samples for policy learning. Previous works learn a dynamics model that fits under the empirical state-action visitation distribution for all historical policies, i.e., the sample replay buffer. However, in this paper, we observe that fitting the dynamics model under the distribution for all historical policies does not necessarily benefit model prediction for the current policy since the policy in use is constantly evolving over time. The evolving policy during training will cause state-action visitation distribution shifts. We theoretically analyze how this distribution shift over historical policies affects the model learning and model rollouts. We then propose a novel dynamics model learning method, named Policy-adapted Dynamics Model Learning (PDML). PDML dynamically adjusts the historical policy mixture distribution to ensure the learned model can continually adapt to the state-action visitation distribution of the evolving policy. Experiments on a range of continuous control environments in MuJoCo show that PDML achieves significant improvement in sample efficiency and higher asymptotic performance combined with the state-of-the-art model-based RL methods.

Memory-Mediated Learning Architecture (MMLA) separates slow base parameters theta, a bounded numerical policy carrier Phi, and a bounded authoritative memory M. Predictive Dual-State Adaptation (PDSA) lets feedback update Phi while one problem remains active and lets a trusted lifecycle atomically commit one typed row or exact NULL. Later reasoning may read both states, but their writers, resets, rollback domains, and ledgers remain distinct. Realized futures supervise values only during training; deployment is causal and future-blind. We give conditional theory and falsifiable contracts for reasoning-time updates, completed-segment consolidation, predictive admission, authoritative memory, and dual-state attribution. Assumptions, counterexamples, capacity and cost ledgers, recovery duties, and identifying experiments are explicit; these are not implementation guarantees. Controlled studies show exact lifecycle execution on 300/300 held-out records for each of three seeds, calibrated retrieval gains over frozen-hidden dense and BM25 baselines, and exact typed anchor-filler transport on 240/240 held-out records per seed. These validate restricted components, not natural-language memory management or complete PDSA. Post-training studies retain positive and negative evidence. Later protocols obtain restricted readout progress, but a nine-trajectory comparison finds that matched latent readout, a full-width bridge, and bridge plus frozen text-teacher alignment all fail continuous-event qualification across both task families. A separately adapted text reference and restoration checks pass. At the September 13, 2026 evidence cutoff, no strict policy-only reasoning-time-training effect, predictive-admission oracle margin, learned future-blind admission policy, or policy-by-memory factorial advantage is established.

Selective state space models (SSMs), such as Mamba, achieve strong per-token expressivity by making the time discretization step TildeΔ a learned function of the input. However, in doing so, TildeΔ no longer equals the physical time gap Δ between consecutive observations, limiting the ability of these models to handle irregular time series. Continuous time SSMs, such as S5, keep TildeΔequivΔ and therefore handle irregular timestamps natively, but their dynamics remain linear time invariant (LTI), limiting per token expressivity. We propose TIDES, a selective SSM variant that reconciles selective and continuous architectures by moving input dependence off the step size and onto the diagonal state matrix. As a result, TildeΔequivΔ as in S5, allowing the model to handle irregular timestamps natively without sacrificing the per-token expressivity that makes selective SSMs effective. We show this on a novel Fading Flash experimental benchmark, a compact controlled diagnostic for sequence models that jointly tests input dependence and extrapolation to out-of-distribution Δ values, and isolates the distinct failure modes of current state-of-the-art architectures that TIDES avoids by construction. On large-scale benchmarks, TIDES sets the new best average rank on UEA time series classification and the Physiome ODE regression benchmark, and matches or exceeds the reference baseline model on 6 of 8 natively irregular datasets from astronomy, agriculture, neuromorphic sensing, and climate events. Code available at: https://github.com/TaylanSoydan/TIDES.

Long-horizon complex tasks require foundation models to accumulate information, maintain internal states, and adapt over extended interactions. Safety should be an intrinsic property of the model itself, rather than a behavioral constraint relying solely on external safeguards or post-hoc alignment such as supervised fine-tuning. This motivates Safety from Within, where safety-relevant capabilities are represented and invoked through the model's native computation. We present Safin-1, a family of foundation models realizing this principle through memory routing and state evolution. Safin-1 is built on Memory-Anchor Routing across Context History (MARCH), a network architecture that maintains structured memory states and selectively retrieves relevant historical information through content-conditioned routing. It supports test-time adaptation of persistent capability states without repeatedly modifying the backbone, enabling controlled specialization over a shared foundation. We investigate this interface on downstream safety tasks through a Safety State, demonstrating effective state-based adaptation with substantial safety improvements. More broadly, the routed-state interface unifies contextual memory and persistent capability adaptation within the model's native computation, reframing memory from a passive record of prior context into an active substrate for maintaining and evolving model behavior. Evaluations across general capabilities, long-context understanding, retrieval, and efficiency further validate Safin-1. These findings provide a path toward safety as a state-native and adaptively maintainable capability. This work is only an initial architectural exploration of Safety from Within, and substantial further work is needed to realize this broader vision.

Generating continuous-time, continuous-space stochastic processes (e.g., videos, weather forecasts) conditioned on partial observations (e.g., first and last frames) is a fundamental challenge. Existing approaches, (e.g., diffusion models), suffer from key limitations: (1) noise-to-data evolution fails to capture structural similarity between states close in physical time and has unstable integration in low-step regimes; (2) random noise injected is insensitive to the physical process's time elapsed, resulting in incorrect dynamics; (3) they overlook conditioning on arbitrary subsets of states (e.g., irregularly sampled timesteps, future observations). We propose ABC: Any-Subset Autoregressive Models via Non-Markovian Diffusion Bridges in Continuous Time and Space. Crucially, we model the process with one continual SDE whose time variable and intermediate states track the real time and process states. This has provable advantages: (1) the starting point for generating future states is the already-close previous state, rather than uninformative noise; (2) random noise injection scales with physical time elapsed, encouraging physically plausible dynamics with similar time-adjacent states. We derive SDE dynamics via changes-of-measure on path space, yielding another advantage: (3) path-dependent conditioning on arbitrary subsets of the state history and/or future. To learn these dynamics, we derive a path- and time-dependent extension of denoising score matching. Our experiments show ABC's superiority to competing methods on multiple domains, including video generation and weather forecasting.

This work explores the in-context learning capabilities of State Space Models (SSMs) and presents, to the best of our knowledge, the first theoretical explanation of a possible underlying mechanism. We introduce a novel weight construction for SSMs, enabling them to predict the next state of any dynamical system after observing previous states without parameter fine-tuning. This is accomplished by extending the HiPPO framework to demonstrate that continuous SSMs can approximate the derivative of any input signal. Specifically, we find an explicit weight construction for continuous SSMs and provide an asymptotic error bound on the derivative approximation. The discretization of this continuous SSM subsequently yields a discrete SSM that predicts the next state. Finally, we demonstrate the effectiveness of our parameterization empirically. This work should be an initial step toward understanding how sequence models based on SSMs learn in context.

State space models have shown to be effective at modeling long range dependencies, specially on sequence classification tasks. In this work we focus on autoregressive sequence modeling over English books, Github source code and ArXiv mathematics articles. Based on recent developments around the effectiveness of gated activation functions, we propose a new layer named Gated State Space (GSS) and show that it trains significantly faster than the diagonal version of S4 (i.e. DSS) on TPUs, is fairly competitive with several well-tuned Transformer-based baselines and exhibits zero-shot generalization to longer inputs while being straightforward to implement. Finally, we show that leveraging self-attention to model local dependencies improves the performance of GSS even further.

Language-model agents are increasingly used as persistent coworkers that assist users across multiple working days. During such workflows, the surrounding environment may change independently of the agent: new emails arrive, calendar entries shift, knowledge-base records are updated, and evidence appears across images, scanned PDFs, audio, video, and spreadsheets. Existing benchmarks do not adequately evaluate this setting because they typically run within a single static episode and remain largely text-centric. We introduce , a benchmark for coworker agents built around multi-turn multi-day tasks, a stateful sandboxed service environment whose state evolves between turns, and rule-based verification. The current release contains 100 tasks across 13 professional scenarios, executed against five stateful sandboxed services (filesystem, email, calendar, knowledge base, spreadsheet) and scored by 1537 deterministic Python checkers over post-execution service state; no LLM-as-judge is invoked during scoring. We benchmark seven frontier agent systems. The strongest model reaches 75.8 weighted score, but the best strict Task Success is only 20.0\%, indicating that partial progress is common while complete end-to-end workflow completion remains rare. Turn-level analysis shows that performance drops after the first exogenous environment update, highlighting adaptation to changing state as a key open challenge. We release the benchmark, evaluation harness, and construction pipeline to support reproducible coworker-agent evaluation.

Training LLM agents commonly relies on supervised fine-tuning from expert trajectories or online reinforcement learning over human-specified tasks with handcrafted verifiers. Though effective, both remain bottlenecked by externally specified tasks and supervision signals, limiting the scalability and diversity of agent training. We study an environment learning paradigm in which agents acquire interaction and manipulation capabilities solely through environment interaction, without externally specified tasks. We propose State2State, an environment-derived mid-training method that converts explored environment states into training objectives, challenging agents to reach a specified target state. By deriving tasks from environment exploration and verifying success through rule-based state matching, State2State provides scalable and verifiable training objectives without expert supervision or manual task design. Experiments on ALFWorld and ScienceWorld show that State2State improves agent performance as a standalone environment-learning stage in most settings. As initialization for downstream RL, it further improves final performance and learning efficiency, with promising evidence of cross-environment generalization.

Few-shot class-incremental learning (FSCIL) confronts the challenge of integrating new classes into a model with minimal training samples while preserving the knowledge of previously learned classes. Traditional methods widely adopt static adaptation relying on a fixed parameter space to learn from data that arrive sequentially, prone to overfitting to the current session. Existing dynamic strategies require the expansion of the parameter space continually, leading to increased complexity. To address these challenges, we integrate the recently proposed selective state space model (SSM) into FSCIL. Concretely, we propose a dual selective SSM projector that dynamically adjusts the projection parameters based on the intermediate features for dynamic adaptation. The dual design enables the model to maintain the robust features of base classes, while adaptively learning distinctive feature shifts for novel classes. Additionally, we develop a class-sensitive selective scan mechanism to guide dynamic adaptation. It minimizes the disruption to base-class representations caused by training on novel data, and meanwhile, forces the selective scan to perform in distinct patterns between base and novel classes. Experiments on miniImageNet, CUB-200, and CIFAR-100 demonstrate that our framework outperforms the existing state-of-the-art methods. The code is available at https://github.com/xiaojieli0903/Mamba-FSCIL.

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.

Offline-to-online reinforcement learning (RL) is a training paradigm that combines pre-training on a pre-collected dataset with fine-tuning in an online environment. However, the incorporation of online fine-tuning can intensify the well-known distributional shift problem. Existing solutions tackle this problem by imposing a policy constraint on the policy improvement objective in both offline and online learning. They typically advocate a single balance between policy improvement and constraints across diverse data collections. This one-size-fits-all manner may not optimally leverage each collected sample due to the significant variation in data quality across different states. To this end, we introduce Family Offline-to-Online RL (FamO2O), a simple yet effective framework that empowers existing algorithms to determine state-adaptive improvement-constraint balances. FamO2O utilizes a universal model to train a family of policies with different improvement/constraint intensities, and a balance model to select a suitable policy for each state. Theoretically, we prove that state-adaptive balances are necessary for achieving a higher policy performance upper bound. Empirically, extensive experiments show that FamO2O offers a statistically significant improvement over various existing methods, achieving state-of-the-art performance on the D4RL benchmark. Codes are available at https://github.com/LeapLabTHU/FamO2O.

One of the key challenges in deploying RL to real-world applications is to adapt to variations of unknown environment contexts, such as changing terrains in robotic tasks and fluctuated bandwidth in congestion control. Existing works on adaptation to unknown environment contexts either assume the contexts are the same for the whole episode or assume the context variables are Markovian. However, in many real-world applications, the environment context usually stays stable for a stochastic period and then changes in an abrupt and unpredictable manner within an episode, resulting in a segment structure, which existing works fail to address. To leverage the segment structure of piecewise stable context in real-world applications, in this paper, we propose a \textbf{Segmented Context Belief Augmented Deep~(SeCBAD)} RL method. Our method can jointly infer the belief distribution over latent context with the posterior over segment length and perform more accurate belief context inference with observed data within the current context segment. The inferred belief context can be leveraged to augment the state, leading to a policy that can adapt to abrupt variations in context. We demonstrate empirically that SeCBAD can infer context segment length accurately and outperform existing methods on a toy grid world environment and Mujuco tasks with piecewise-stable context.

Sensory systems across all modalities and species exhibit adaptation to continuously changing input statistics. Individual neurons have been shown to modulate their response gains so as to maximize information transmission in different stimulus contexts. Experimental measurements have revealed additional, nuanced sensory adaptation effects including changes in response maxima and minima, tuning curve repulsion from the adapter stimulus, and stimulus-driven response decorrelation. Existing explanations of these phenomena rely on changes in inter-neuronal synaptic efficacy, which, while more flexible, are unlikely to operate as rapidly or reversibly as single neuron gain modulations. Using published V1 population adaptation data, we show that propagation of single neuron gain changes in a recurrent network is sufficient to capture the entire set of observed adaptation effects. We propose a novel adaptive efficient coding objective with which single neuron gains are modulated, maximizing the fidelity of the stimulus representation while minimizing overall activity in the network. From this objective, we analytically derive a set of gains that optimize the trade-off between preserving information about the stimulus and conserving metabolic resources. Our model generalizes well-established concepts of single neuron adaptive gain control to recurrent populations, and parsimoniously explains experimental adaptation data.

An agent can improve its behavior within an unresolved problem by changing how it acts and which experience it retains. We propose MMLA-RSI, a recursive self-improvement scheme with two implementations in Memory-Mediated Learning Architecture: Reasoning-Time Training (RTT) changes the policy state Φ, while Reasoning-Time Memory Adaptation (RTMA) changes authoritative memory M. Each route also makes its adaptation method an object of improvement. A current numerical updater trains the policy proposing its successor; a current memory manager chooses the records available to the process proposing its successor. An independently admitted successor takes over the same role in the next generation. We give bounded executable rule languages, shared task/proposal interfaces, and one algorithm for either route or their composition. The RTT instance changes scalar schedules in a clipped-momentum update. The RTMA instance chooses NULL or a complete-row write with possible eviction. A fixed interpreter, trusted committer, and independent evaluator bound what can change. State versions, read closures, and conditional properties describe causal execution, accepted transitions, and finite work. Existing numerical-component studies motivate the construction. In four-candidate program selection, retaining LARC feedback updates reduces expected error by 24.65 and 36.65 percentage points for two trained initializations. In chronological continuous-integration replay, feedback binding is positive while retention increases loss. Completed SQL studies improve substantially over an unadapted substrate but do not establish the required additional online benefit. These results characterize their declared components. The two recursive routes and their joint realization are specified here; their beneficial recursive chains and discovery efficiency remain to be evaluated.

In a recent work, Laforgue et al. introduce the model of last switch dependent (LSD) bandits, in an attempt to capture nonstationary phenomena induced by the interaction between the player and the environment. Examples include satiation, where consecutive plays of the same action lead to decreased performance, or deprivation, where the payoff of an action increases after an interval of inactivity. In this work, we take a step towards understanding the approximability of planning LSD bandits, namely, the (NP-hard) problem of computing an optimal arm-pulling strategy under complete knowledge of the model. In particular, we design the first efficient constant approximation algorithm for the problem and show that, under a natural monotonicity assumption on the payoffs, its approximation guarantee (almost) matches the state-of-the-art for the special and well-studied class of recharging bandits (also known as delay-dependent). In this attempt, we develop new tools and insights for this class of problems, including a novel higher-dimensional relaxation and the technique of mirroring the evolution of virtual states. We believe that these novel elements could potentially be used for approaching richer classes of action-induced nonstationary bandits (e.g., special instances of restless bandits). In the case where the model parameters are initially unknown, we develop an online learning adaptation of our algorithm for which we provide sublinear regret guarantees against its full-information counterpart.

State space models (SSM) have recently been shown to be very effective as a deep learning layer as a promising alternative to sequence models such as RNNs, CNNs, or Transformers. The first version to show this potential was the S4 model, which is particularly effective on tasks involving long-range dependencies by using a prescribed state matrix called the HiPPO matrix. While this has an interpretable mathematical mechanism for modeling long dependencies, it introduces a custom representation and algorithm that can be difficult to implement. On the other hand, a recent variant of S4 called DSS showed that restricting the state matrix to be fully diagonal can still preserve the performance of the original model when using a specific initialization based on approximating S4's matrix. This work seeks to systematically understand how to parameterize and initialize such diagonal state space models. While it follows from classical results that almost all SSMs have an equivalent diagonal form, we show that the initialization is critical for performance. We explain why DSS works mathematically, by showing that the diagonal restriction of S4's matrix surprisingly recovers the same kernel in the limit of infinite state dimension. We also systematically describe various design choices in parameterizing and computing diagonal SSMs, and perform a controlled empirical study ablating the effects of these choices. Our final model S4D is a simple diagonal version of S4 whose kernel computation requires just 2 lines of code and performs comparably to S4 in almost all settings, with state-of-the-art results for image, audio, and medical time-series domains, and averaging 85\% on the Long Range Arena benchmark.

Adaptive hierarchical systems accumulate routing state as they learn which components to select. We show that this state already defines a coherent attribution over the hierarchy. A leaf receives the product of the local routing weights on its path, while an internal node receives the corresponding prefix product. The same learned state can therefore be read consistently at group and component levels, and every finer readout sums exactly to its coarser counterpart. This attribution describes the preferences learned by the deployed router rather than an intrinsic or counterfactual value of a component. Across LLM, Census, agentic, and telecom-network hierarchies, the learned state contains meaningful structure at several levels, and the clearest organisation need not occur at the leaves. In the telecom study, Site- or Region-level readouts usually reveal clearer structure than Cell-level readouts. Comparison with Shapley attribution can then show whether the preferences learned in deployment match capabilities revealed by counterfactual coalitions. The result is a hierarchical explanation that requires no separate attribution model: the same routing state supports consistent explanations at several levels of the system.

Supervised fine-tuning (SFT) learns most aggressively from tokens that the model deems least likely. This helps acquire new behaviors, but also amplifies noisy or conflicting supervision and can overwrite useful pretrained knowledge. Through a unified policy-loss view, we revisit existing token-reweighting methods and show that they assign nonnegative coefficients to demonstrated tokens. Consequently, they can suppress or amplify supervised updates, but cannot reverse harmful features once learned. Moreover, larger training weights do not amount to feature extrapolation, since they change the optimization trajectory rather than scale a fixed SFT direction. We argue that reversal and extrapolation require a stable reference frame defined by a fixed SFT delta. Motivated by this, we propose SCALE (Selective Control of Adaptation via Local Entropy), an entropy-guided adaptation-strength-control method that freezes the pretrained model and the SFT delta and learns bounded token- and module-specific gates by minimizing predictive entropy alone. These gates suppress, reverse, or extrapolate frozen SFT features according to their alignment with entropy reduction. Across Qwen2.5-Math-1.5B, Qwen2.5-Math-7B, and Qwen3-4B-Base, SCALE achieves mathematical-reasoning averages of 37.84, 43.60, and 36.57, exceeding the strongest corresponding baselines while remaining competitive on general-retention benchmarks. It also attains the best average code-generation performance across HumanEval, HumanEval+, and MBPP for all three models. These results suggest that effective SFT correction can benefit from controlling how already learned residuals are used, rather than only modifying how they are learned.

In reinforcement learning, agents collect state information and rewards through environmental interactions, essential for policy refinement. This process is notably time-consuming, especially in complex robotic simulations and real-world applications. Traditional algorithms usually re-engage with the environment after processing a single batch of samples, thereby failing to fully capitalize on historical data. However, frequently observed states, with reliable value estimates, require minimal updates; in contrast, rare observed states necessitate more intensive updates for achieving accurate value estimations. To address uneven sample utilization, we propose Novelty-guided Sample Reuse (NSR). NSR provides extra updates for infrequent, novel states and skips additional updates for frequent states, maximizing sample use before interacting with the environment again. Our experiments show that NSR improves the convergence rate and success rate of algorithms without significantly increasing time consumption. Our code is publicly available at https://github.com/ppksigs/NSR-DDPG-HER.

Closed-loop human-AI systems generate high-dimensional behavioural trajectories whose collective dynamics remain obscure. Using 297,915 learners' adaptive-tutoring histories, we define semantic order variables before model fitting and test them in user-disjoint cohorts. The state exhibits reproducible basin-like flow and operationally defined, state-heterogeneous metastable-like kinetics. A construction-matched null distinguishes normalised-memory relaxation from a reproducible excess field. A four-term conditional mechanism recovers population drift (r = 0.946; learner-bootstrap 95% CI, 0.935-0.955). Predictive event-level self-supervised learning recovers the state and learned-plane flow; null-referenced corrections retain directional, partial-amplitude excess-field structure without full calibration. Shuffled-order training reverses learned-plane flow on ordered trajectories; support-alignment randomisation selectively reduces inward transport. Both axes remain linearly accessible without state supervision. Without cross-model fitting, the models share leading population drift (r = 0.866; learner-bootstrap 95% CI, 0.857-0.875) and persistence ordering; residual directions remain model-specific. These results identify an externally anchored leading-order effective field linking empirical dynamics, an interpretable mechanism and neural computation.

Modern Recurrent Neural Networks (RNNs), such as RWKV, are distinguished by their powerful short-range modeling capabilities and efficient fixed-size states, which constitute a core advantage over standard Transformers. However, there is a significant lack of research into their internal state as an editable knowledge representation. To fill this gap, we first explore the representational properties of the RWKV state by proposing the DREAMSTATE framework. This framework utilizes a conditional Diffusion Transformer (DiT) to directly model the probability manifold of the state, enabling its generation and editing. The structural nature of this representation is validated through t-SNE visualizations and controlled generation experiments. After successfully uncovering and modeling the state's representational potential, we further propose a novel hybrid architecture that combines the local advantages of RNNs with global context adaptability. This architecture features a parallel DiT that processes a variable-length global context to dynamically generate and adjust the core recurrent module's WKV parameters, transforming the fixed recurrence mechanism into a context-aware dynamic function. Experiments demonstrate that this hybrid model can be trained stably via a multi-objective loss, validating its design feasibility. Our work not only opens a new research direction for RNN state representation but also provides a concrete architectural reference for future model design. The code is publicly available at: https://huggingface.co/2dgx41s/DreamState.

Supervised Fine-Tuning (SFT) is the standard paradigm for domain adaptation, yet it frequently incurs the cost of catastrophic forgetting. In sharp contrast, on-policy Reinforcement Learning (RL) effectively preserves general capabilities. We investigate this discrepancy and identify a fundamental distributional gap: while RL aligns with the model's internal belief, SFT forces the model to fit external supervision. This mismatch often manifests as "Confident Conflicts" tokens characterized by low probability but low entropy. In these instances, the model is highly confident in its own prediction but is forced to learn a divergent ground truth, triggering destructive gradient updates. To address this, we propose Entropy-Adaptive Fine-Tuning (EAFT). Unlike methods relying solely on prediction probability, EAFT utilizes token-level entropy as a gating mechanism to distinguish between epistemic uncertainty and knowledge conflict. This allows the model to learn from uncertain samples while suppressing gradients on conflicting data. Extensive experiments on Qwen and GLM series (ranging from 4B to 32B parameters) across mathematical, medical, and agentic domains confirm our hypothesis. EAFT consistently matches the downstream performance of standard SFT while significantly mitigating the degradation of general capabilities.

Generalizing policies across different domains with dynamics mismatch poses a significant challenge in reinforcement learning. For example, a robot learns the policy in a simulator, but when it is deployed in the real world, the dynamics of the environment may be different. Given the source and target domain with dynamics mismatch, we consider the online dynamics adaptation problem, in which case the agent can access sufficient source domain data while online interactions with the target domain are limited. Existing research has attempted to solve the problem from the dynamics discrepancy perspective. In this work, we reveal the limitations of these methods and explore the problem from the value difference perspective via a novel insight on the value consistency across domains. Specifically, we present the Value-Guided Data Filtering (VGDF) algorithm, which selectively shares transitions from the source domain based on the proximity of paired value targets across the two domains. Empirical results on various environments with kinematic and morphology shifts demonstrate that our method achieves superior performance compared to prior approaches.

Agent harness evolution improves frozen language-model agents by modifying the executable structures around them. We study this paradigm as a form of sample-efficient fast adaptation: instead of updating model weights, an agent can acquire task-specific competence by changing its external harness, while leaving the base model's general capabilities intact. Prior work shows that self-generated rollouts can support harness search, suggesting that agents may acquire new task competence through practice. Yet in long-horizon stochastic environments, self-practice becomes fragile: rewards are sparse, outcomes are high-variance, and failures are hard to attribute to concrete harness mechanisms. We introduce DemoEvolve, a demonstration-bootstrapped approach to harness evolution. When reward-only search is too broad and noisy, competent human trajectories serve as expert reference experience for the coding proposer, guiding harness-level diagnosis and editing. Experiments on Liar's Dice show that self-rollout evolution can work when episodes are short and failures are attributable. In contrast, Balatro exposes a harder long-horizon stochastic regime, where self-rollout evolution is misled by sparse feedback and candidate-selection noise, while tutorial-like textual knowledge alone does not yield stable improvement. Under the same limited budget, DemoEvolve produces more effective and auditable harness edits and achieves better performance. Overall, demonstrations make sparse-feedback harness evolution more diagnosable, localizable, and stable.

Interactive language-model agents increasingly solve complex tasks through long-horizon, multi-call reasoning, where errors in beliefs or actions can compound across tool interactions. Retrospective search can recover from such failures but is prone to misallocation. Delayed outcomes obscure the contribution of intermediate search decisions, leading to Attribution Complexity, while evolving execution evidence leads to Adaptation Complexity, where previously learned estimates become stale. To address these challenges, we first introduce Search Value Dynamics (SVD), which characterizes the evolving trade-off between the gain and cost of retrospective search. Building on SVD, we propose ForkPilot, a self-evolving two-stage policy-learning framework. In the first stage, ForkPilot learns a search-value policy offline from completed trajectories through automatically constructed outcome comparisons. In the second stage, it makes search decisions based on current observations and then self-evolves by incorporating newly completed trajectories into subsequent policy updates. We evaluate ForkPilot across 6 diverse benchmarks and 7 widely used LLM backbone families, including four open-source families, GPT-5.6 Sol, and Opus 4.8 in a production agentic system, against 9 competitive baselines, including a real-world harness deployment used by hundreds of thousands of paid users. ForkPilot achieves comparable state-of-the-art performance while reducing token usage by up to 59.2%, demonstrating its efficacy.

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.

Combining the classical Kalman filter (KF) with a deep neural network (DNN) enables tracking in partially known state space (SS) models. A major limitation of current DNN-aided designs stems from the need to train them to filter data originating from a specific distribution and underlying SS model. Consequently, changes in the model parameters may require lengthy retraining. While the KF adapts through parameter tuning, the black-box nature of DNNs makes identifying tunable components difficult. Hence, we propose Adaptive KalmanNet (AKNet), a DNN-aided KF that can adapt to changes in the SS model without retraining. Inspired by recent advances in large language model fine-tuning paradigms, AKNet uses a compact hypernetwork to generate context-dependent modulation weights. Numerical evaluation shows that AKNet provides consistent state estimation performance across a continuous range of noise distributions, even when trained using data from limited noise settings.

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.

We propose a method for adapting neural networks to distribution shifts at test-time. In contrast to training-time robustness mechanisms that attempt to anticipate and counter the shift, we create a closed-loop system and make use of a test-time feedback signal to adapt a network on the fly. We show that this loop can be effectively implemented using a learning-based function, which realizes an amortized optimizer for the network. This leads to an adaptation method, named Rapid Network Adaptation (RNA), that is notably more flexible and orders of magnitude faster than the baselines. Through a broad set of experiments using various adaptation signals and target tasks, we study the efficiency and flexibility of this method. We perform the evaluations using various datasets (Taskonomy, Replica, ScanNet, Hypersim, COCO, ImageNet), tasks (depth, optical flow, semantic segmentation, classification), and distribution shifts (Cross-datasets, 2D and 3D Common Corruptions) with promising results. We end with a discussion on general formulations for handling distribution shifts and our observations from comparing with similar approaches from other domains.

Self-evolving skill systems promise to improve agents by turning execution feedback into persistent skill updates without changing the underlying model. Yet it remains unclear when further evolution helps, how successful and failed trajectories shape revision, and whether extra test-time computation can recover the same gains. To address these questions, we present a controlled evaluation framework across five benchmarks and three models. Our primary study contains 42 feedback runs across 14 supported model-benchmark settings. Within each setting, we hold the executor and optimizer configuration, revision procedure, validation rule, and round budget fixed, while varying only the feedback shown to the optimizer: successes and failures (Normal), failures only, or successes only. Evolution is sparse: only 55 of 388 candidates establish byte-distinct validation bests. Validation-based selection chooses an evolved skill in 11 of 14 settings, nine of which improve released-test performance. All 11 selections come from feedback conditions that include failed trajectories, although the relative ranking of Normal and Fail-only varies across settings. Validation and downstream evaluations on test, robustness, and transfer sometimes favor different feedback views. A broader SearchQA analysis covering eight models shows similarly sparse, feedback-dependent dynamics. In the GPT-5.5 test-time-scaling controls, oracle Parallel Sampling comes within 0.43 points of the evolved SearchQA skill but remains 30.96 points behind on SpreadsheetBench; Sequential Refinement recovers neither gain. Overall, persistent skill self-evolution is better understood as sparse, validation-filtered search with model- and benchmark-dependent returns, rather than steady improvement from additional rounds. The implementation is available at https://github.com/HKUST-KnowComp/rethinkskill.

Large language model (LLM) agents may recover from a failure within an episode or after a retry, yet the same execution failure can recur in later tasks because post-episode feedback rarely revises the persistent harness that guides future interactions. Static harnesses improve reliability through fixed tools, context, memory, and workflow structures, but remain unchanged after deployment. We propose Living-Harness, a self-evolving agent harness that converts each completed trajectory and its evaluator signals into posterior evidence for bounded harness updates. Guided by a domain-level Evolution-SOP (Standard Operating Procedure), Living-Harness extracts an episode abstraction and structured update evidence, and writes two complementary forms of procedural knowledge: episodic memory that records trigger conditions, failure patterns, and recovery actions, and a state graph that records state nodes, repair edges, and transition rules. The updated harness state is retrieved to guide future interactions, while tools and base context remain frozen, allowing procedural repairs to accumulate across evolution cycles. On eight interactive environments derived from τ^2-Bench and MultiWOZ-2.4, Living-Harness improves average Pass@1 over the strongest interactive baseline by 10.07 and 9.91 percentage points, respectively, and supports retrieval-only reuse of the evolved harness state across model backbones.

We introduce Adaptive Filter Attention (AFA), a novel attention mechanism that incorporates a learnable dynamics model directly into the computation of attention weights. Rather than comparing queries and keys directly, we model the input sequence as discrete observations of a linear stochastic differential equation (SDE). By imposing a linear dynamics model with simultaneously diagonalizable state matrices and noise covariances, we can make use of a closed-form solution to the differential Lyapunov equation to efficiently propagate pairwise uncertainties through the dynamics. Attention naturally arises as the maximum likelihood solution for this linear SDE, with attention weights corresponding to robust residual-based reweightings of the propagated pairwise precisions. Imposing an additional constraint on the state matrix's eigenvalues leads to a simplified variant with the same computational and memory complexity as standard attention. In the limit of vanishing dynamics and process noise, and using a small-angle approximation, we recover ordinary dot-product attention.

Agent frameworks increasingly delegate work by forking sub-agents; a common default makes the child inherit the parent's full working context. We measure how the effect of inherited state changes with capability, where C_m denotes clean fork-fresh accuracy. We compare 3 inheritance policies: Reset (fork fresh: base evidence only), Selective (curated handoff: + the useful prior conclusion), and Full (implicit fork: + the useful conclusion and d copies of a superseded conclusion) over a same-family ladder (Qwen3 0.6/1.7/4/8B) on a frozen, closed-set, action-scored benchmark. Every task is solvable from the base evidence, so performance loss can be attributed to reliance on stale state. (1) Deference to superseded state falls sharply with measured capability C_m (the slope's confidence interval, CI, excludes zero on every family) across 2 synthetic primitives plus MuSiQue and HotpotQA. (2) On the Qwen3 synthetic ladder, net inheritance harm follows a nonmonotone pattern: a mid-capability model (Qwen3-1.7B) is a statistically significant local minimum of net harm, falling below its fork-fresh baseline (Δ(32)=-0.19 [-0.25, -0.12]) and both neighbors, while the weakest model stays near-neutral and the strongest models stay robust. We call this harmful capability range a danger band. A within-model counting-difficulty sweep shows that the effect depends on model class even at matched C_m, and a live parent-to-child fork reproduces the mid-model harm. (3) Curated Selective handoff improves average accuracy over Full on all 3 datasets, largest at the in-band model, while the fixed-threshold capability router fails on the other datasets; a transferable router would need to predict the balance between reuse benefit and stale-context penalty. The benchmark is frozen and version-hashed.

Recent offline meta-reinforcement learning (meta-RL) methods typically utilize task-dependent behavior policies (e.g., training RL agents on each individual task) to collect a multi-task dataset. However, these methods always require extra information for fast adaptation, such as offline context for testing tasks. To address this problem, we first formally characterize a unique challenge in offline meta-RL: transition-reward distribution shift between offline datasets and online adaptation. Our theory finds that out-of-distribution adaptation episodes may lead to unreliable policy evaluation and that online adaptation with in-distribution episodes can ensure adaptation performance guarantee. Based on these theoretical insights, we propose a novel adaptation framework, called In-Distribution online Adaptation with uncertainty Quantification (IDAQ), which generates in-distribution context using a given uncertainty quantification and performs effective task belief inference to address new tasks. We find a return-based uncertainty quantification for IDAQ that performs effectively. Experiments show that IDAQ achieves state-of-the-art performance on the Meta-World ML1 benchmark compared to baselines with/without offline adaptation.

As video content creation shifts toward long-form narratives, composing short clips into coherent storylines becomes increasingly important. However, prevailing retrieval formulations remain context-agnostic at inference time, prioritizing local semantic alignment while neglecting state and identity consistency. To address this structural limitation, we formalize the task of Consistent Video Retrieval (CVR) and introduce a diagnostic benchmark spanning YouCook2, COIN, and CrossTask. We propose CAST (Context-Aware State Transition), a lightweight, plug-and-play adapter compatible with diverse frozen vision-language embedding spaces. By predicting a state-conditioned residual update (Δ) from visual history, CAST introduces an explicit inductive bias for latent state evolution. Extensive experiments show that CAST improves performance on YouCook2 and CrossTask, remains competitive on COIN, and consistently outperforms zero-shot baselines across diverse foundation backbones. Furthermore, CAST provides a useful reranking signal for black-box video generation candidates (e.g., from Veo), promoting more temporally coherent continuations.

Multi-Agent Reinforcement Learning (MARL) has shown clear effectiveness in coordinating multiple agents across simulated benchmarks and constrained scenarios. However, its deployment in real-world multi-agent systems (MAS) remains limited, primarily due to the complex and dynamic nature of such environments. These challenges arise from multiple interacting sources of variability, including fluctuating agent populations, evolving task goals, and inconsistent execution conditions. Together, these factors demand that MARL algorithms remain effective under continuously changing system configurations and operational demands. To better capture and assess this capacity for adjustment, we introduce the concept of adaptability as a unified and practically grounded lens through which to evaluate the reliability of MARL algorithms under shifting conditions, broadly referring to any changes in the environment dynamics that may occur during learning or execution. Centred on the notion of adaptability, we propose a structured framework comprising three key dimensions: learning adaptability, policy adaptability, and scenario-driven adaptability. By adopting this adaptability perspective, we aim to support more principled assessments of MARL performance beyond narrowly defined benchmarks. Ultimately, this survey contributes to the development of algorithms that are better suited for deployment in dynamic, real-world multi-agent systems.

We analyze the operation of transformer language adapters, which are small modules trained on top of a frozen language model to adapt its predictions to new target languages. We show that adapted predictions mostly evolve in the source language the model was trained on, while the target language becomes pronounced only in the very last layers of the model. Moreover, the adaptation process is gradual and distributed across layers, where it is possible to skip small groups of adapters without decreasing adaptation performance. Last, we show that adapters operate on top of the model's frozen representation space while largely preserving its structure, rather than on an 'isolated' subspace. Our findings provide a deeper view into the adaptation process of language models to new languages, showcasing the constraints imposed on it by the underlying model and introduces practical implications to enhance its efficiency.

Real-world data analysis is inherently iterative, yet existing benchmarks mostly evaluate isolated or short interactive tasks, leaving agents' ability to track evolving analytical context over long horizons untested. We introduce LongDS, a benchmark for long-horizon, multi-turn data analysis where agents must maintain, update, restore, and compose evolving analytical states. LongDS comprises 68 tasks constructed from real-world Kaggle notebooks, spanning 2,225 turns across six domains including Geoscience, Business, and Education. Tasks are designed around state-evolution patterns (e.g., counterfactual perturbation, rollback, multi-state composition), with an average dependency span of 11.3 turns. Evaluating five state-of-the-art models, we find that the best model reaches only 48.45% average accuracy, performance drops nearly 47 points from early to late turns, and long-horizon errors account for 52%--69% of failures. Further analysis shows that additional agent steps do not necessarily improve performance, suggesting that the key bottleneck is maintaining a correct analytical state rather than increasing interaction budget. We release LongDS to support research on reliable long-horizon agentic data analysis. Code and data will be released at https://github.com/zjunlp/DataMind.

Large language models offer broad capabilities, but adapting them to evolving domains, tools, and requirements often entails repeated post-training. Autonomous systems automate parts of this process by proposing updates, training candidates, and using evaluation feedback to select subsequent proposals. As evidence accumulates, a central problem emerges: which past update evidence remains actionable after subsequent training has changed the parent model? An update's effect depends on its parent, data, and training stage. Treating past success as context-free permission can waste compute. If the resulting child is promoted, it can also degrade the subsequent training trajectory. We formulate this problem as conditional experience transfer and introduce Boundary-Calibrated Intervention Transfer (BCIT), a method that authorizes experience reuse before weight-changing training. BCIT binds an observed effect to its source context, checks applicability conditions, vetoes candidates with named hard conflicts, and obtains current-state evidence through a bounded training trial when needed. Fully trained candidates still face a shared adoption rule, and only observed events extend memory. On one 4B model adapted across finance reasoning, text-to-SQL, and function calling, candidate updates exhibit heterogeneous target and retention effects across the evaluated contexts. Under matched candidates, evidence, and compute, BCIT authorizes fewer harmful updates and attains higher equal-budget final-model quality than the evaluated alternatives. These results support treating experience authorization as a distinct problem in autonomous post-training.

Long-horizon agents can fail even when their underlying models can solve the constituent steps. They may lose track of mutable state, fail to reactivate lessons from earlier executions, skip known procedures, or stop prematurely. We bet on harness scaling to improve the execution system around an agent without changing its model weights. We introduce StateM, an agent-native runtime that organizes execution around durable states, phase-local context, checked transitions, recoverable runbooks, and versioned procedural practices that agents and users can inspect together. On Terminal-Bench 2.1, StateM raises GPT-5.5 xhigh to 92.1\%, versus 83.1\% reference and GPT-5.6 Sol Ultra at 91.9\%. The runbook transfers unchanged to GPT-5.6. With GPT-5.6 Sol xhigh, StateM reaches 95.3\% raw accuracy across 445 trials and succeeds on all 89 tasks at least once. The frozen profile raises GPT-5.6 Luna from 76.7 to 85.4\%, above the 84.9\% Sol xhigh reference. Using the same runtime, runbook structure, and golden rules, less than \38 of adaptation raises DeepSeek-V4 Flash from 82.7 to 88.1% under standard timeouts and to 89.1% on an 88-task common core. Extending only the remaining latency-sensitive task matches the reported 88.8% GPT-5.6 Sol max result. Final-score API usage is about 15 versus \574.68 for the GPT reference; total DeepSeek expenditure is 52.22. On BusinessBench, family-specific runbooks built on development sets yield held-out gains of 0.55 macro and 1.34 micro points; two mechanism-matched families improve by 10.04 points. Concrete rules generalize when tasks share execution structure, while the control methodology applies broadly. StateM turns selected postmortem findings into persistent, executable preconditions and practices, making learned controls explicit and enforceable through stateful controls. Code at github.com/henryqin1997/statem.

Wild Test-Time Adaptation (WTTA) is proposed to adapt a source model to unseen domains under extreme data scarcity and multiple shifts. Previous approaches mainly focused on sample selection strategies, while overlooking the fundamental problem on underlying optimization. Initially, we critically analyze the widely-adopted entropy minimization framework in WTTA and uncover its significant limitations in noisy optimization dynamics that substantially hinder adaptation efficiency. Through our analysis, we identify region confidence as a superior alternative to traditional entropy, however, its direct optimization remains computationally prohibitive for real-time applications. In this paper, we introduce a novel region-integrated method ReCAP that bypasses the lengthy process. Specifically, we propose a probabilistic region modeling scheme that flexibly captures semantic changes in embedding space. Subsequently, we develop a finite-to-infinite asymptotic approximation that transforms the intractable region confidence into a tractable and upper-bounded proxy. These innovations significantly unlock the overlooked potential dynamics in local region in a concise solution. Our extensive experiments demonstrate the consistent superiority of ReCAP over existing methods across various datasets and wild scenarios.

We define an atomic generation fact f=(u,tau,omega,z;rho), recording the origin, realized transformation, concrete occurrence, generated result and relation role. Compiled into a Generation-Fact Graph (GFG), these facts provide an AI-native, compilable scientific fact substrate preserving generation histories. We establish a GFG-based recursive scientific process in which analysis, intervention, replay and validation form facts for later cycles. Using nanoGPT, we establish unified training-learning dynamics. Training is the evolution of a parameter-optimizer system with state and memory: each actual training action enters the receiving state and produces a finite-amplitude nonlinear functional response conditioned by that state and target-specific update geometry. Learning is the persistent reorganization of distributed functional support by these responses; capability formation, maintenance, decline or recovery becomes observable when target-specific states are evaluated against their readout boundaries. Three primary coordinates - target-boundary state, target-specific update geometry and parameter-Adam receiving state - yield a second-order predictor operating before post-update outputs are read. On held-out runs, it achieved 91.43% accuracy and 91.49% macro-averaged recall across four transitions. We further establish inference as a frozen projection of training-learning dynamics. Component gating and rollback show causal recruitment and non-additive combination of query-conditioned support formed during training, deriving organizational conditions realized by Attention. Controlled feedback indicates possible double-edged reinforcement effects. ResNet/CIFAR-100 and diffusion/CIFAR-10 experiments confirm receiving-state-conditioned responses, persistent support reorganization and frozen inference projection beyond nanoGPT.

Foundation models (FMs) have transformed natural language processing, but their success has not yet translated to time series forecasting. Existing time series foundation models (TSFMs), often based on transformer variants, struggle with generalization across varying context and target lengths, lack adaptability to different sampling rates, and are computationally inefficient. We introduce FlowState, a novel TSFM architecture that addresses these challenges through two key innovations: a state space model (SSM) based encoder and a functional basis decoder. This design enables continuous-time modeling and dynamic time-scale adjustment, allowing FlowState to inherently generalize across all possible temporal resolutions, and dynamically adjust the forecasting horizons. In contrast to other state-of-the-art TSFMs, which require training data across all possible sampling rates to memorize patterns at each scale, FlowState inherently adapts its internal dynamics to the input scale, enabling smaller models, reduced data requirements, and improved efficiency. We further propose an efficient pretraining strategy that improves robustness and accelerates training. Despite being the smallest model, FlowState outperforms all other models and is state-of-the-art for the GIFT-ZS and the Chronos-ZS benchmarks. Ablation studies confirm the effectiveness of its components, and we demonstrate its unique ability to adapt online to varying input sampling rates.

Machine learning methods can be a valuable aid in the scientific process, but they need to face challenging settings where data come from inhomogeneous experimental conditions. Recent meta-learning methods have made significant progress in multi-task learning, but they rely on black-box neural networks, resulting in high computational costs and limited interpretability. Leveraging the structure of the learning problem, we argue that multi-environment generalization can be achieved using a simpler learning model, with an affine structure with respect to the learning task. Crucially, we prove that this architecture can identify the physical parameters of the system, enabling interpreable learning. We demonstrate the competitive generalization performance and the low computational cost of our method by comparing it to state-of-the-art algorithms on physical systems, ranging from toy models to complex, non-analytical systems. The interpretability of our method is illustrated with original applications to physical-parameter-induced adaptation and to adaptive control.

Transformer-based architectures have dominated sequence modeling, largely due to the expressive power of attention mechanisms. However, for a class of deterministic state tracking tasks---such as parity checking, modular counting, and parenthesis matching---attention may be overkill. In this paper, we show that state propagation alone is sufficient. We propose the Complex State Propagator (CSP), a minimalistic recurrent architecture that only propagates hidden states across layers without output projections at intermediate steps. The state is represented as a complex-valued vector, updated via input-dependent rotations in the complex domain. To enable deep propagation without gradient vanishing or degradation, we introduce a block-level skip connection alongside element-wise complex normalization and SiLU activation at sequence boundaries. Applied with Focal Loss, CSP achieves 100\% accuracy with perfect F1 scores across canonical tasks.

Test-time adaptation harnesses test inputs to improve the accuracy of a model trained on source data when tested on shifted target data. Existing methods update the source model by (re-)training on each target domain. While effective, re-training is sensitive to the amount and order of the data and the hyperparameters for optimization. We instead update the target data, by projecting all test inputs toward the source domain with a generative diffusion model. Our diffusion-driven adaptation method, DDA, shares its models for classification and generation across all domains. Both models are trained on the source domain, then fixed during testing. We augment diffusion with image guidance and self-ensembling to automatically decide how much to adapt. Input adaptation by DDA is more robust than prior model adaptation approaches across a variety of corruptions, architectures, and data regimes on the ImageNet-C benchmark. With its input-wise updates, DDA succeeds where model adaptation degrades on too little data in small batches, dependent data in non-uniform order, or mixed data with multiple corruptions.

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.

Classical continual learning (CL) has primarily focused on enabling models to update and retain knowledge through parameter-centric mechanisms, e.g., training strategies, architectural designs, and weight adaptation. However, emerging paradigms are reshaping the scope of CL beyond this traditional model adaptation view. For instance, on-policy learning broadens the space of update mechanisms; test-time training extends CL from the training phase to inference; and external harness components such as memory, skill libraries, and interaction protocols extend the evolutionary boundaries of model capabilities far beyond the static parameter space. Collectively, these developments indicate a transition from parameter-centric learning toward system-level adaptation. To characterize this transition, we examine the evolution of continual learning through three dimensions: When, How, and Where learning occurs. The How dimension encompasses off-policy, on-policy, and beyond-gradient optimization mechanics. The When dimension captures evolution across pre-training, post-training, and inference-time stages. The Where dimension delineates updates occurring within internal parameters versus external structural constraints. Anchored by this tri-axial framework, we systematically survey representative methods, trace the ongoing transition of continual learning, and discuss the key challenges, broader implications, and future directions arising from this paradigm shift.

We study variance-dependent regret bounds for Markov decision processes (MDPs). Algorithms with variance-dependent regret guarantees can automatically exploit environments with low variance (e.g., enjoying constant regret on deterministic MDPs). The existing algorithms are either variance-independent or suboptimal. We first propose two new environment norms to characterize the fine-grained variance properties of the environment. For model-based methods, we design a variant of the MVP algorithm (Zhang et al., 2021a). We apply new analysis techniques to demonstrate that this algorithm enjoys variance-dependent bounds with respect to the norms we propose. In particular, this bound is simultaneously minimax optimal for both stochastic and deterministic MDPs, the first result of its kind. We further initiate the study on model-free algorithms with variance-dependent regret bounds by designing a reference-function-based algorithm with a novel capped-doubling reference update schedule. Lastly, we also provide lower bounds to complement our upper bounds.

Do LLM scientific agents rely only on their initial task context, or do they adapt their decisions in response to experimental feedback? We study this question in neural operator adaptation, where a large language model (LLM) selects fine-tuning configurations under a limited trial budget. Across transfers within and between partial differential equation (PDE) families, the LLM achieves lower held-out test nRMSE than random search and Bayesian optimisation in nearly every matched comparison. Endpoint performance alone cannot distinguish what happens, so we verify each attribution with controlled interventions. Before observing any validation score, the LLM's first configuration already ranks near the top of the corresponding random-search pool, indicating a useful initial bias. A complementary cold-start intervention shows that the selected base learning rate shifts with the PDE description. Once feedback becomes available, reassigning validation scores among evaluated configurations changes the next proposal in every case tested, whereas a value-preserving rewrite produces no comparable aggregate effect. These interventions establish that the LLM's decision-level actions respond to the given task and observed outcomes, showing that it combines a task-dependent prior with sensitivity to experimental feedback.

Test-Time Learning (TTL) enables language agents to iteratively refine their performance through repeated interactions with the environment at inference time. At the core of TTL is an adaptation policy that updates the actor policy based on experience from previous episodes, thereby improving future behavior. Existing methods rely on fixed, hand-crafted adaptation policies rather than optimizing them for downstream improvement. We argue that optimal adaptation policies should be learned from task environments, not hand-engineered based on human intuition. To achieve this, we introduce Meta-TTL, a framework that formulates the discovery of effective adaptation policies as a bi-level optimization problem. Within this framework, the inner loop executes the standard TTL process, measuring how effectively a candidate adaptation policy helps an agent correct errors across sequential episodes. Guided by the agent's performance, the outer loop employs evolutionary search over a diverse distribution of training tasks to iteratively refine the adaptation policy. We evaluate Meta-TTL on Jericho and WebArena-Lite across both in-distribution (ID) and out-of-distribution (OOD) settings, using multiple meta-agent backbones. Results on both benchmarks show that Meta-TTL consistently outperforms hand-crafted baselines, suggesting that the optimized adaptation policy encodes transferable strategies that generalize beyond the training task distribution.

World models construct latent states that support prediction, planning, and reasoning about an underlying system. Joint-embedding predictive architectures (JEPAs) offer a direct way to learn such states by predicting targets in representation space instead of reconstructing every detail of the observation. Standard JEPAs, however, organize all predictable content through one target embedding and one prediction pathway. In complex systems, this monolithic state can allocate redundant capacity to dominant signals while providing weak or conflicting gradients to less dominant predictive structure. We introduce \method, a latent world-modeling framework based on orthogonal predictive factorization. Learned basis matrices analyze each target state into multiple components, and a dedicated prediction branch estimates each component from a shared context representation. Predictive regression preserves the factor magnitudes required for state synthesis, an orthogonality objective discourages repeated directions, factor-activity regularization maintains variation in projected targets, and online variance regularization discourages coordinate-wise encoder collapse. Predicted components are synthesized into a complete latent state that can be used by a readout, decoder, planner, or autoregressive rollout. The same predictive-state mechanism applies when the target is temporally future, spatially hidden, or another partial observation of the same system. Experiments on controlled vision, single-cell transcriptomics, longitudinal health records, continuous control, and molecular dynamics evaluate representation quality, forecasting, planning, and long-horizon stability.

Foundation models are transitioning from offline predictors to deployed systems expected to operate over long time horizons. In real deployments, objectives are not fixed: domains drift, user preferences evolve, and new tasks appear after the model has shipped. This elevates continual learning and instant personalization from optional features to core architectural requirements. Yet most adaptation pipelines still follow a static weight paradigm: after training (or after any adaptation step), inference executes a single parameter vector regardless of user intent, domain, or instance-specific constraints. This treats the trained or adapted model as a single point in parameter space. In heterogeneous and continually evolving regimes, distinct objectives can induce separated feasible regions over parameters, forcing any single shared update into compromise, interference, or overspecialization. As a result, continual learning and personalization are often implemented as repeated overwriting of shared weights, risking degradation of previously learned behaviors. We propose HY-WU (Weight Unleashing), a memory-first adaptation framework that shifts adaptation pressure away from overwriting a single shared parameter point. HY-WU implements functional (operator-level) memory as a neural module: a generator that synthesizes weight updates on-the-fly from the instance condition, yielding instance-specific operators without test-time optimization.

State-based sequence models like RWKV-7 offer a compelling alternative to Transformer architectures, achieving linear complexity while demonstrating greater expressive power in short-context scenarios and enabling state tracking beyond the \(TC^0\) complexity class. However, RWKV-7 lacks mechanisms for token-parameter interactions and native scalability, limiting its adaptability and growth without retraining. In this paper, we propose Meta-State, a novel extension to RWKV-7 that replaces attention mechanisms with a fully state-driven approach, integrating token-parameter interactions through a Self-State Encoder (SSE) mechanism. The SSE repurposes a portion of the RWKV-7 Weighted Key-Value (WKV) state as transformation weights to encode token-parameter interactions in a linear, state-driven manner without introducing new trainable matrices or softmax operations, while preserving the autoregressive property of token processing. Meta-State supports progressive model scaling by expanding the WKV state and parameter tokens, reusing existing parameters without retraining. Our approach bridges the gap between state-based modeling, token-parameter interactions, and scalable architectures, offering a flexible framework for efficient and adaptable sequence modeling with linear complexity and constant memory usage.

Transformers with linear attention allow for efficient parallel training but can simultaneously be formulated as an RNN with 2D (matrix-valued) hidden states, thus enjoying linear (with respect to output length) inference complexity. Recent works such as RetNet (Sun et al., 2023) and TransNormerLLM (Qin et al., 2023a) observe that adding a global decay term to the additive RNN update rule greatly improves performance, sometimes outperforming standard Transformers with softmax attention when trained at scale. In this work we show that adding a data-dependent gating mechanism further improves performance. We derive a parallel form of this gated linear attention layer that enables efficient training. However, a straightforward, numerically stable implementation of this parallel form requires generalized matrix multiplications in log-space for numerical stability, and thus cannot take advantage of tensor cores on modern GPUs which are optimized for standard matrix multiplications. We develop a hardware-efficient version of the parallel form that can still make use of tensor cores through block-parallel computations over sequence chunks. Experiments on moderate-scale language modeling (340M-parameter models trained on 15B tokens, 1.3B-parameter models trained on 100B tokens) show that gated linear attention (GLA) Transformers perform competitively against a strong LLaMA-architecture Transformer baseline (Touvron et al., 2023) as well as Mamba (Gu & Dao, 2023), a recently introduced state-space model with a data-dependent state transition mechanism. For training speed, our Triton-based implementation performs comparably to CUDA-optimized FlashAttention-2 (Dao, 2023) under the regular 2048 training length setting, while outperforming FlashAttention-2 when training on longer sequences beyond 4096.

Language-model agents increasingly face long-horizon tasks with evolving state, interdependent decisions, and delayed outcomes. Scaling their training requires diverse agentic environments, dependable outcome signals, and low extension cost. Existing generation pipelines commonly construct an environment before defining its outcome rule or annotating its trajectories, leaving dynamics and evaluation to be aligned post hoc. VHD-Play reverses this dependency by sampling and solving a mathematical model before a corpus-grounded setter renders its decision process as stateful tools. The executable dynamics and trajectory-scoring reference are inherited from the same solved model. The pipeline produces 3,300 diverse agentic environments at a cost of a few cents each. Training Qwen3.6-35B-A3B on three families raises its mean agentic score from 0.204 to 0.815 in a five-family diagnostic. Gains also appear on held-out instances from all three training families and eight unseen mechanism families, then extend beyond the generated substrate to external benchmarks for general function calling, travel planning, and 365-day e-commerce. On E-Commerce Bench, the trained checkpoint completes every run without bankruptcy and exceeds Qwen3.7-Max. We compare written-out problems with stateful versions that reveal or hide their parameters. The comparison shows that most of the learnable gap lies in stateful interaction rather than underlying problem solving. A frozen 35B setter realizes larger environments, and scale-matched training retains gains as mechanism size and horizon grow, indicating the potential for an evolving training substrate.

Large Language Models demonstrate remarkable proficiency in static reasoning, yet training them as autonomous agents through Reinforcement Learning (RL) for long-horizon tasks is often hindered by severe reward sparsity. While conventional agent-side warming up via supervised fine-tuning (SFT) can alleviate this, it is frequently limited by data scarcity and constrained exploration. To address this, we propose a paradigm shift to environment-side adaptation by constructing Feedback-Enriched Environments (FEEs). Through a pilot study, we establish a feedback design strategy that reformulates environments by transitioning from action guidance to observation enrichment during the later stages of both intra-episode exploration and inter-episode evolution. Large-scale experiments on SciWorld and BFCL benchmarks using various Qwen3 model scales and RL algorithms such as GRPO, GSPO, and DAPO demonstrate that FEEs consistently yield performance improvements over standard settings. Furthermore, our analysis reveals that training with FEEs (1) stabilizes training dynamics by reducing entropy volatility, (2) facilitates proactive state-space exploration in difficult tasks, (3) ensures the internalization of environmental guidance into policy weights rather than acting as a mere inference-time prior, and (4) identifies intra-group feedback consistency as a critical boundary for stable optimization.

While large-scale text-to-image generative models have achieved unprecedented visual performance, their inherent reliance on multi-step iterative solvers incurs severe inference latency. Few-step distillation targeting the Classifier-Free Guidance (CFG) trajectory has emerged as the prevalent dual-dimensional compression paradigm. However, existing frameworks remain subjugated by a coarse-grained blind injection paradigm that perpetually enforces a globally static guidance strength while indiscriminately sampling the supervisor timestep. This state-agnostic design completely disregards the intrinsic nature of image generation as a dynamic evolutionary process characterized by progressive entropy reduction, which not only restricts the performance boundary of few-step compression but also precipitates severe CFG over-conditioning artifacts. To transcend these limitations, we re-examine the distillation procedure through the theoretical lens of Information Theory, formally modeling it as a dynamic mutual information game constrained by the Information Bottleneck (IB) principle. Specifically, we dismantle traditional blind assumptions via a dual-track adaptive framework. To determine the injection target, we propose an instance-aware selection mechanism that transmutes the intractable KL divergence constraint into a zero-overhead closed-form solution predicated on the local vector field norm. To regulate the injection strength, we introduce an entropy-aware schedule that dynamically decays alongside the SNR, applying maximal thrust for initial structural anchoring before smoothly reverting to the natural manifold to refine micro-details. Extensive empirical evaluations corroborate that our framework fundamentally eradicates over-conditioning artifacts, shattering the performance ceiling to achieve SOTA generative fidelity under extremely stringent 2-step configurations.

We introduce Iterated Bellman Calibration, a simple, model-agnostic, post-hoc procedure for calibrating off-policy value predictions in infinite-horizon Markov decision processes. Bellman calibration requires that states with similar predicted long-term returns exhibit one-step returns consistent with the Bellman equation under the target policy. We adapt classical histogram and isotonic calibration to the dynamic, counterfactual setting by repeatedly regressing fitted Bellman targets onto a model's predictions, using a doubly robust pseudo-outcome to handle off-policy data. This yields a one-dimensional fitted value iteration scheme that can be applied to any value estimator. Our analysis provides finite-sample guarantees for both calibration and prediction under weak assumptions, and critically, without requiring Bellman completeness or realizability.

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.

Recent advancements in multivariate time series forecasting have been propelled by Linear-based, Transformer-based, and Convolution-based models, with Transformer-based architectures gaining prominence for their efficacy in temporal and cross-channel mixing. More recently, Mamba, a state space model, has emerged with robust sequence and feature mixing capabilities. However, the suitability of the vanilla Mamba design for time series forecasting remains an open question, particularly due to its inadequate handling of cross-channel dependencies. Capturing cross-channel dependencies is critical in enhancing the performance of multivariate time series prediction. Recent findings show that self-attention excels in capturing cross-channel dependencies, whereas other simpler mechanisms, such as MLP, may degrade model performance. This is counterintuitive, as MLP, being a learnable architecture, should theoretically capture both correlations and irrelevances, potentially leading to neutral or improved performance. Diving into the self-attention mechanism, we attribute the observed degradation in MLP performance to its lack of data dependence and global receptive field, which result in MLP's lack of generalization ability. Based on the above insights, we introduce a refined Mamba variant tailored for time series forecasting. Our proposed model, CMamba, incorporates a modified Mamba (M-Mamba) module for temporal dependencies modeling, a global data-dependent MLP (GDD-MLP) to effectively capture cross-channel dependencies, and a Channel Mixup mechanism to mitigate overfitting. Comprehensive experiments conducted on seven real-world datasets demonstrate the efficacy of our model in improving forecasting performance.

Large-scale video generation models have demonstrated emergent physical coherence, positioning them as potential world models. However, a gap remains between contemporary "stateless" video architectures and classic state-centric world model theories. This work bridges this gap by proposing a novel taxonomy centered on two pillars: State Construction and Dynamics Modeling. We categorize state construction into implicit paradigms (context management) and explicit paradigms (latent compression), while dynamics modeling is analyzed through knowledge integration and architectural reformulation. Furthermore, we advocate for a transition in evaluation from visual fidelity to functional benchmarks, testing physical persistence and causal reasoning. We conclude by identifying two critical frontiers: enhancing persistence via data-driven memory and compressed fidelity, and advancing causality through latent factor decoupling and reasoning-prior integration. By addressing these challenges, the field can evolve from generating visually plausible videos to building robust, general-purpose world simulators.

With the rapid progress of diffusion models and large-scale video generation, generative world models are increasingly expected to replace traditional simulators, including physics engines, game engines, and reinforcement-learning environments. Yet the remaining distance from generation to simulation lacks a systematic assessment. We present a capability-based study using an external yardstick: eight capabilities of a traditional simulator, namely asset construction, physics engine, interaction, controllability, stability, state feedback, diversity, and evaluation metrics. We trace three main technical routes--latent dynamics, video generation, and joint-embedding prediction--and map exactly 200 representative works published from 2018 to June 2026 onto these capabilities. Our analysis shows that world models have achieved functional substitution in interaction and controllability for specific scenarios, but remain short of traditional simulators in formal guarantees of physical laws, structured state feedback, and reproducible long-horizon evolution. State feedback is the most neglected cross-route shortcoming: only 6 of 163 implementation papers expose a runtime interface for querying entity states or physical parameters. We identify six research directions: formalized physics, a unified action interface, first-class state feedback, long-horizon stability, downstream-utility evaluation, and cross-route hybridization. Project page: https://github.com/AtongWang/world-model-simulators

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.

Wasserstein gradient flow extends gradient descent to probability measures. Its Hessian-guided perturbed variant (PWGF) adds Gaussian perturbations to escape saddle points in nonconvex problems. We investigate when its approximation by finitely many interacting particles remains accurate over growing time horizons. Our analysis retains the curvature accumulated along the population-driven reference path: negative curvature can amplify approximation errors, while subsequent positive curvature can damp their influence. This captures favorable scenarios in which temporary instability is compatible with accurate tracking over growing horizons. Under regularity assumptions and a prescribed common perturbation schedule, we prove particle and objective-value tracking bounds on a high-probability event for reference paths satisfying explicit conditions on accumulated curvature. To handle state-dependent Gaussian jumps, we construct a population-first coupling that preserves the reference particles' conditional independence and reduces jump errors to covariance comparison. We verify the conditions in a variance-plus-cosine model, where curvature recovery yields a growing-horizon tracking guarantee. We also establish local attraction, transverse descent, and positive second variation in two regions of a regularized matrix-factorization model, motivating a positive-negative-positive curvature pattern.

Harness self-evolution revises an agent's software scaffolding, including prompts, memory, workflows, and executable components, while keeping model weights fixed. We formalize a feedback-driven process in which accepted revisions persist across runs. The framework separates update targets from proposal and admission mechanisms. It distinguishes changes to interpreted state from revisions to tools and code, repository-level control logic, and plugin composition. We characterize search through evolutionary optimization and examine its reliability through continual PAC-learning. Under explicit assumptions, the analysis yields an expected generalization bound, a retention bound conditional on historical regression budgets, and a high-probability admission rule using fresh, independent validation data. We examine how persistent harness revisions affect knowledge sharing and organizational workflows, with implications for scientific reliability, physical safety, and institutional accountability. Cases from prior work illustrate model--harness co-design, distributed execution, and plugin reuse. Reliable deployment requires continual validation as task distributions and evaluators change, with independent safeguards for learning, runtime privileges, and consequential actions. We provide a comprehensive 66-page discussion of related work, theory, algorithms, evaluation, applications, and the broader impact of Harness RSI, together with continuously updated code and supplementary materials, at https://github.com/zgcagi/Harness-RSI.

Given an algorithmic predictor that is accurate on some source population consisting of strategic human decision subjects, will it remain accurate if the population respond to it? In our setting, an agent or a user corresponds to a sample (X,Y) drawn from a distribution D and will face a model h and its classification result h(X). Agents can modify X to adapt to h, which will incur a distribution shift on (X,Y). Our formulation is motivated by applications where the deployed machine learning models are subjected to human agents, and will ultimately face responsive and interactive data distributions. We formalize the discussions of the transferability of a model by studying how the performance of the model trained on the available source distribution (data) would translate to the performance on its induced domain. We provide both upper bounds for the performance gap due to the induced domain shift, as well as lower bounds for the trade-offs that a classifier has to suffer on either the source training distribution or the induced target distribution. We provide further instantiated analysis for two popular domain adaptation settings, including covariate shift and target shift.

Training state-of-the-art vision models has become prohibitively expensive for researchers and practitioners. For the sake of accessibility and resource reuse, it is important to focus on adapting these models to a variety of downstream scenarios. An interesting and practical paradigm is online test-time adaptation, according to which training data is inaccessible, no labelled data from the test distribution is available, and adaptation can only happen at test time and on a handful of samples. In this paper, we investigate how test-time adaptation methods fare for a number of pre-trained models on a variety of real-world scenarios, significantly extending the way they have been originally evaluated. We show that they perform well only in narrowly-defined experimental setups and sometimes fail catastrophically when their hyperparameters are not selected for the same scenario in which they are being tested. Motivated by the inherent uncertainty around the conditions that will ultimately be encountered at test time, we propose a particularly "conservative" approach, which addresses the problem with a Laplacian Adjusted Maximum-likelihood Estimation (LAME) objective. By adapting the model's output (not its parameters), and solving our objective with an efficient concave-convex procedure, our approach exhibits a much higher average accuracy across scenarios than existing methods, while being notably faster and have a much lower memory footprint. The code is available at https://github.com/fiveai/LAME.

Diffusion language models (DLMs) iteratively refine a sequence, allowing earlier predictions to be revised as context evolves. This rollback capability distinguishes them from irreversible autoregressive generation, but makes inference costly. Every denoising update alters the global context, forcing both prompt and response states to be recomputed even though only response tokens are revisable. Key-value (KV) caching could reduce this cost, yet conventional caching assumes immutable historical states and is therefore difficult to reconcile with rollback. In this paper, we introduce Adaptive Reuse of Cached Hidden States for Efficient Rollback (Archer), a training-free KV caching method for rollback-capable DLMs. Archer asymmetrically keeps the mutable response synchronized with the current hypothesis while reusing prompt K/V within a bounded state neighborhood. Although prompt representations also change under bidirectional attention, their token identities remain fixed; bounded reuse therefore amortizes repeated prompt computation without caching mutable response states. It also delays feedback from tentative tokens, reducing premature reinforcement of transient high-confidence errors and giving rollback more opportunity to correct them. Our analysis characterizes prompt reuse as a reversibility-aligned cache boundary, bounds its state-dependent approximation error, and gives a decoder-margin condition for preserving full-refresh decisions. Existing DLM acceleration often trades quality for speed. Archer shifts this frontier, attaining the best mean performance of 33.63% together with a 2.57x mean speedup on the main suite. Across evaluated settings, it improves Pass@1 by up to 3.05 points and reaches up to 2.95x speedup. Controlled analyses connect the quality gain to delayed prompt feedback and validate state-aware refresh. Our code is available at https://github.com/Hxnng/Archer.

Test-time adaptation (TTA) aims to adapt models to maintain reliable performance on non-stationary test streams without requiring labeled data. Despite its empirical success, the learnability of TTA under non-stationary streams remains unexplored. A key challenge is the lack of a principled theoretical framework that simultaneously aligns with the TTA objective and captures both continuously evolving distribution shifts and intrinsic information constraints. To address this gap, we propose the first theoretical framework for studying the learnability of TTA and introduce (ε,δ)-Recovery Complexity and (ε,ρ)-TTA Learnability. Recovery complexity measures the post-shift time needed to maintain excess risk below a target level with high probability, and is further extended to TTA learnability, which measures the long-term reliability of TTA. Within this framework, we introduce a novel discrete surrogate for non-stationary test streams, enabling a unified and tractable analysis of both gradual and abrupt shifts. We derive order-wise matching lower and upper bounds on recovery complexity, revealing fundamental limits of TTA and an intrinsic adaptivity-information trade-off. These results provide unified learnability guarantees for TTA that complement regret-based analyses.

Linear time-invariant state space models (SSM) are a classical model from engineering and statistics, that have recently been shown to be very promising in machine learning through the Structured State Space sequence model (S4). A core component of S4 involves initializing the SSM state matrix to a particular matrix called a HiPPO matrix, which was empirically important for S4's ability to handle long sequences. However, the specific matrix that S4 uses was actually derived in previous work for a particular time-varying dynamical system, and the use of this matrix as a time-invariant SSM had no known mathematical interpretation. Consequently, the theoretical mechanism by which S4 models long-range dependencies actually remains unexplained. We derive a more general and intuitive formulation of the HiPPO framework, which provides a simple mathematical interpretation of S4 as a decomposition onto exponentially-warped Legendre polynomials, explaining its ability to capture long dependencies. Our generalization introduces a theoretically rich class of SSMs that also lets us derive more intuitive S4 variants for other bases such as the Fourier basis, and explains other aspects of training S4, such as how to initialize the important timescale parameter. These insights improve S4's performance to 86% on the Long Range Arena benchmark, with 96% on the most difficult Path-X task.

Multi-modal agents have made significant progress in interacting with open worlds. However, their ability to self-evolve remains limited. Supervised fine-tuning enables imitation but not active experience organization, while outcome-based reinforcement learning promotes exploration yet underuses intermediate trajectory information. Therefore, we propose EvolvingBrain, which uses an adaptive skill system as the brain for agent self-evolution, consisting of two following components. Stratified Skill Self-Evolution: extracts Procedural Patterns and Problematic Patterns from model-specific trajectories, summarizes experience by generating skills, and evolves through multiple interactions with the open world, ultimately forming a Stratified Skill Architecture consisting of Domain, Plan, and Action/Trap Skills, which provides the agent with a multi-granularity knowledge repository and a novel evolution approach. State-Aware Adaptive Execution: summarizes long-horizon interactions into Structured Abstractive Memory and uses it to guide the State-Aware Skill Fusion Strategy, enabling the agent to utilize knowledge according to its current state. Experiments on VAB-Minecraft and DiscoveryWorld demonstrate that EvolvingBrain improves success rates on open-world tasks and exhibits generalization capabilities. Our code is provided in the supplementary materials and will be publicly released in the camera-ready version.

We present methodology for using dynamic evaluation to improve neural sequence models. Models are adapted to recent history via a gradient descent based mechanism, causing them to assign higher probabilities to re-occurring sequential patterns. Dynamic evaluation outperforms existing adaptation approaches in our comparisons. Dynamic evaluation improves the state-of-the-art word-level perplexities on the Penn Treebank and WikiText-2 datasets to 51.1 and 44.3 respectively, and the state-of-the-art character-level cross-entropies on the text8 and Hutter Prize datasets to 1.19 bits/char and 1.08 bits/char respectively.

I investigate a stronger form of regularization by deactivating neurons for extended periods, a departure from the temporary changes of methods like Dropout. However, this long-term dynamism introduces a critical challenge: severe training instability when neurons are revived with random weights. To solve this, I propose the Lifecycle (LC) principle, a regularization mechanism centered on a key innovation: state memory. Instead of re-initializing a revived neuron, my method restores its parameters to their last known effective state. This process preserves learned knowledge and avoids destructive optimization shocks. My theoretical analysis reveals that the LC principle smooths the loss landscape, guiding optimization towards flatter minima associated with better generalization. Experiments on image classification benchmarks demonstrate that my method improves generalization and robustness. Crucially, ablation studies confirm that state memory is essential for achieving these gains.

Vision-Language-Action models provide a strong foundation for general-purpose robot control, yet a vast majority of policies do not preserve and leverage episode-level information beyond the current observation. This limitation is consequential in history-dependent manipulation tasks that depend on information available only in past observations. Retaining past observations in context can aid in recovering this information, but at the significant cost of ever-growing, bloated context and inference latency. We thus introduce MemBodied, a fixed-size episodic memory with two complementary components: an associative state that records interactions across policy calls and an episode anchor that preserves a compact representation of the initial scene as a reference. At each policy call, the model conditions action generation on the current input and the memory components, rather than directly using past observations. Across five evaluated RMBench tasks requiring memory, MemBodied achieves 7.81times the mean success rate of a stateless policy and 2.98times of vanilla recurrent memory, while outperforming the strongest memory-augmented baseline by 1.3times with 10times fewer added parameters. On the fully observable LIBERO-Long suite, it reached 90.6%, a 5.4% improvement over the stateless π_0 policy. These findings support MemBodied as a practical alternative to expanding the policy context for history-dependent manipulation.

We present StateSMix, a fully self-contained lossless compressor that couples an online-trained Mamba-style State Space Model (SSM) with sparse n-gram context mixing and arithmetic coding. The model is initialised from scratch and trained token-by-token on the file being compressed, requiring no pre-trained weights, no GPU, and no external dependencies. The SSM (DM=32, NL=2, approximately 120K active parameters per file) provides a continuously-updated probability estimate over BPE tokens, while nine sparse n-gram hash tables (bigram through 32-gram, 16M slots each) add exact local and long-range pattern memorisation via a softmax-invariant logit-bias mechanism that updates only non-zero-count tokens. An entropy-adaptive scaling mechanism modulates the n-gram contribution based on the SSM's predictive confidence, preventing over-correction when the neural model is already well-calibrated. On the standard enwik8 benchmark, StateSMix achieves 2.123 bpb on 1 MB, 2.149 bpb on 3 MB, and 2.162 bpb on 10 MB, beating xz -9e (LZMA2) by 8.7%, 5.4%, and 0.7% respectively. Ablation experiments establish the SSM as the dominant compression engine: it alone accounts for a 46.6% size reduction over a frequency-count baseline and beats xz without any n-gram component, while n-gram tables provide a complementary 4.1% gain through exact context memorisation. OpenMP parallelisation of the training loop yields 1.9x speedup on 4 cores. The system is implemented in pure C with AVX2 SIMD and processes approximately 2,000 tokens per second on commodity x86-64 hardware.

In reinforcement learning and imitation learning, an object of central importance is the state distribution induced by the policy. It plays a crucial role in the policy gradient theorem, and references to it--along with the related state-action distribution--can be found all across the literature. Despite its importance, the state distribution is mostly discussed indirectly and theoretically, rather than being modeled explicitly. The reason being an absence of appropriate density estimation tools. In this work, we investigate applications of a normalizing flow-based model for the aforementioned distributions. In particular, we use a pair of flows coupled through the optimality point of the Donsker-Varadhan representation of the Kullback-Leibler (KL) divergence, for distribution matching based imitation learning. Our algorithm, Coupled Flow Imitation Learning (CFIL), achieves state-of-the-art performance on benchmark tasks with a single expert trajectory and extends naturally to a variety of other settings, including the subsampled and state-only regimes.

Structured state space sequence (S4) models have recently achieved state-of-the-art performance on long-range sequence modeling tasks. These models also have fast inference speeds and parallelisable training, making them potentially useful in many reinforcement learning settings. We propose a modification to a variant of S4 that enables us to initialise and reset the hidden state in parallel, allowing us to tackle reinforcement learning tasks. We show that our modified architecture runs asymptotically faster than Transformers in sequence length and performs better than RNN's on a simple memory-based task. We evaluate our modified architecture on a set of partially-observable environments and find that, in practice, our model outperforms RNN's while also running over five times faster. Then, by leveraging the model's ability to handle long-range sequences, we achieve strong performance on a challenging meta-learning task in which the agent is given a randomly-sampled continuous control environment, combined with a randomly-sampled linear projection of the environment's observations and actions. Furthermore, we show the resulting model can adapt to out-of-distribution held-out tasks. Overall, the results presented in this paper show that structured state space models are fast and performant for in-context reinforcement learning tasks. We provide code at https://github.com/luchris429/popjaxrl.

Despite the promising performance of state space models (SSMs) in long sequence modeling, limitations still exist. Advanced SSMs like S5 and S6 (Mamba) in addressing non-uniform sampling, their recursive structures impede efficient SSM computation via convolution. To overcome compatibility limitations in parallel convolutional computation, this paper proposes a novel non-recursive non-uniform sample processing strategy. Theoretical analysis of SSMs through the lens of Event-Triggered Control (ETC) theory reveals the Non-Stable State (NSS) problem, where deviations from sampling point requirements lead to error transmission and accumulation, causing the divergence of the SSM's hidden state. Our analysis further reveals that adjustments of input sequences with early memories can mitigate the NSS problem, achieving Sampling Step Adaptation (SSA). Building on this insight, we introduce a simple yet effective plug-and-play mechanism, State Memory Replay (SMR), which utilizes learnable memories to adjust the current state with multi-step information for generalization at sampling points different from those in the training data. This enables SSMs to stably model varying sampling points. Experiments on long-range modeling tasks in autoregressive language modeling and Long Range Arena demonstrate the general effectiveness of the SMR mechanism for a series of SSM models.

Predicting the behavior of complex systems is critical in many scientific and engineering domains, and hinges on the model's ability to capture their underlying dynamics. Existing methods encode the intrinsic dynamics of high-dimensional observations through latent representations and predict autoregressively. However, these latent representations lose the inherent spatial structure of spatiotemporal dynamics, leading to the predictor's inability to effectively model spatial interactions and neglect emerging dynamics during long-term prediction. In this work, we propose SparseDiff, introducing a test-time adaptation strategy to dynamically update the encoding scheme to accommodate emergent spatiotemporal structures during the long-term evolution of the system. Specifically, we first design a codebook-based sparse encoder, which coarsens the continuous spatial domain into a sparse graph topology. Then, we employ a graph neural ordinary differential equation to model the dynamics and guide a diffusion decoder for reconstruction. SparseDiff autoregressively predicts the spatiotemporal evolution and adjust the sparse topological structure to adapt to emergent spatiotemporal patterns by adaptive re-encoding. Extensive evaluations on representative systems demonstrate that SparseDiff achieves an average prediction error reduction of 49.99\% compared to baselines, requiring only 1\% of the spatial resolution.

Video world models are increasingly used as simulators, yet visual fidelity alone does not show that a model maintains the hidden state of the world. We examine this gap with an action-conditioned video Shell Game, a visual analog of S_5 state tracking that decouples visual rendering from compositing the hidden state underneath. Bidirectional and autoregressive Transformers, Mamba, and linear attention restricted to nonnegative transition eigenvalues all fit the training horizon of 5 swaps and then fall toward chance on longer swap chains (extrapolation) while still rendering plausible video with additional denoising steps providing no benefit. The pixel-based diffusion target never supervises the unseen hidden state, so the generated frames cannot carry it and the state has to live inside the architecture rather than in the tokens. For a Transformer, that architectural state is only an append-only KV cache, so the model has to re-derive the hidden arrangement from the whole history at every chunk. We find two mechanisms that do extrapolate, and both carry a state across chunks and revise it in place. Linear attention succeeds once its transition eigenvalues may be negative, and TTT with a nonlinear fast weight succeeds by updating the feature map through which it reads its own state. We further examine harder cases in dynamic world exploration tasks, and discuss the broader implications for building stateful video world models.

Recently, recurrent models such as state space models and linear attention have become popular due to their linear complexity in the sequence length. Thanks to their recurrent nature, in principle they can process arbitrarily long sequences, but their performance sometimes drops considerably beyond their training context lengths-i.e. they fail to length generalize. In this work, we provide comprehensive empirical and theoretical analysis to support the unexplored states hypothesis, which posits that models fail to length generalize when during training they are only exposed to a limited subset of the distribution of all attainable states (i.e. states that would be attained if the recurrence was applied to long sequences). Furthermore, we investigate simple training interventions that aim to increase the coverage of the states that the model is trained on, e.g. by initializing the state with Gaussian noise or with the final state of a different input sequence. With only 500 post-training steps (sim 0.1% of the pre-training budget), these interventions enable length generalization for sequences that are orders of magnitude longer than the training context (e.g. 2klongrightarrow 128k) and show improved performance in long context tasks, thus presenting a simple and efficient way to enable robust length generalization in general recurrent models.

Learning domain adaptive policies that can generalize to unseen transition dynamics, remains a fundamental challenge in learning-based control. Substantial progress has been made through domain representation learning to capture domain-specific information, thus enabling domain-aware decision making. We analyze the process of learning domain representations through dynamical prediction and find that selecting contexts adjacent to the current step causes the learned representations to entangle static domain information with varying dynamical properties. Such mixture can confuse the conditioned policy, thereby constraining zero-shot adaptation. To tackle the challenge, we propose DADP (Domain Adaptive Diffusion Policy), which achieves robust adaptation through unsupervised disentanglement and domain-aware diffusion injection. First, we introduce Lagged Context Dynamical Prediction, a strategy that conditions future state estimation on a historical offset context; by increasing this temporal gap, we unsupervisedly disentangle static domain representations by filtering out transient properties. Second, we integrate the learned domain representations directly into the generative process by biasing the prior distribution and reformulating the diffusion target. Extensive experiments on challenging benchmarks across locomotion and manipulation demonstrate the superior performance, and the generalizability of DADP over prior methods. More visualization results are available on the https://outsider86.github.io/DomainAdaptiveDiffusionPolicy/.

AI weather forecasting models are commonly trained on the ERA5 reanalysis, which is unavailable in real time. Operational deployment therefore relies on initial conditions produced by numerical or AI analysis systems that differ from those encountered during training. This mismatch can degrade forecast skill, while retraining for every analysis system is costly. Here, we present Domain-Adaptive Data Assimilation (DADA), an observation-guided framework that adapts external analyses to pretrained AI weather models. Starting from a background state, DADA optimizes only an initial-state perturbation while keeping the forecast model frozen. The perturbed state is propagated through the model, and its short-range trajectory is constrained by real-world observations through a learned observation operator. The resulting initial condition is shaped jointly by observational constraints and the dynamics learned by the target model. We evaluate DADA across five global AI weather models using backgrounds from the Global Forecast System and the AI-based HealDA. Across deterministic and probabilistic forecasts, DADA substantially reduces short-range skill loss caused by changes in the initial-condition source. More broadly, DADA turns observations into a common interface between independently developed analysis and forecasting systems, enabling pretrained AI weather models to accommodate evolving operational initial conditions without reconstructing ERA5 or retraining the forecast model.

Before acting upon an unobservable physical system, an autonomous agent must determine which latent distinctions govern downstream tasks, how many active interventions are necessary to certify them, and when to abstain to prevent catastrophic errors. Classical observability treats state reconstruction as an unconditioned binary predicate, failing when passive observations cannot break latent degeneracies without perturbation, full microscopic inversion is prohibitively costly, and distinguishing task-irrelevant degrees of freedom wastes interaction budgets. We formalize task-conditioned active observability complexity: the minimum worst-case expected interaction cost required to identify task-relevant states under certified error and safe abstention guarantees. We prove that task-predictive equivalence induces the unique minimal sufficient quotient H/!sim_τ, leaving active observability complexity strictly invariant while eliminating superfluous distinctions. In deterministic regimes, this complexity is characterized by an optimal adaptive distinguishing tree and Bellman recursion; in noisy regimes, it obeys a stopped-transcript relative-entropy lower bound and adaptive martingale certificates that compose without independence assumptions. We instantiate a prospective certified observer with staged recovery: a nominal verifier defers candidate compilation, triggering active probing only upon evidence, while a history-measurable score shell prunes hypotheses without sacrificing risk bounds. Stress audits across high-dimensional physical systems and thousands of operational trials demonstrate certified state recovery with zero false acceptances and substantial reductions in sensor reads and model steps.

Latent world models enable planning by predicting the effects of actions in a learned representation space, but their predictions can become unreliable when test-time conditions differ from training. Existing test-time adaptation methods address this by updating parts of the pretrained model, often modifying millions of parameters and requiring a choice of which internal components to adapt. We introduce Sandwich-Residuals, a lightweight alternative that keeps the pretrained world model frozen and learns only small residual corrections around the predictor. The residuals are optimized online using the model's self-supervised prediction error and require no rewards, labels, or source-domain data. Across 21 conditions on the AdaJEPA benchmark, our method achieves 1.3times the success rate of the frozen model while retaining 95% of the performance of the strongest AdaJEPA variant and adapting 97-99% fewer parameters. Under compound shifts, this advantage increases to 1.9times the success rate of the frozen model, while remaining comparable to internal block adaptation. We further demonstrate the same adaptation principle on a DINO-WM model for 3-D manipulation. These results suggest that effective test-time adaptation of world models does not necessarily require modifying their pretrained internal weights.

Autonomous research agents can already run machine learning experiments without human supervision, but many rely on a narrow search strategy: they repeatedly modify one program and keep changes only when they improve the current best result. This can cause them to discard useful partial ideas, alternative promising directions, and insights from failed or incomplete experiments. GEAR, or Genetic AutoResearch, replaces this single-path search with a population-based search over multiple research states. It keeps a set of strong candidate solutions, selects parents based on productivity, novelty, and coverage, and explores new ideas through mutation and crossover. Each research state stores its code changes, reflections, and performance data, allowing future decisions to build on past discoveries. The paper studies three versions of GEAR: one controlled through prompting, one using a fixed programmatic search controller, and one where the controller itself can evolve during the run. Under the same compute budget and environment, all three versions outperform the AutoResearch baseline. More importantly, while the baseline tends to settle into one local optimum, GEAR continues finding improvements over longer runs. Overall, the results suggest that autonomous research agents become more effective when they maintain multiple promising directions and can adapt their search strategy over time.

Test-time domain adaptation aims to adapt a source pre-trained model to a target domain without using any source data. Existing works mainly consider the case where the target domain is static. However, real-world machine perception systems are running in non-stationary and continually changing environments where the target domain distribution can change over time. Existing methods, which are mostly based on self-training and entropy regularization, can suffer from these non-stationary environments. Due to the distribution shift over time in the target domain, pseudo-labels become unreliable. The noisy pseudo-labels can further lead to error accumulation and catastrophic forgetting. To tackle these issues, we propose a continual test-time adaptation approach~(CoTTA) which comprises two parts. Firstly, we propose to reduce the error accumulation by using weight-averaged and augmentation-averaged predictions which are often more accurate. On the other hand, to avoid catastrophic forgetting, we propose to stochastically restore a small part of the neurons to the source pre-trained weights during each iteration to help preserve source knowledge in the long-term. The proposed method enables the long-term adaptation for all parameters in the network. CoTTA is easy to implement and can be readily incorporated in off-the-shelf pre-trained models. We demonstrate the effectiveness of our approach on four classification tasks and a segmentation task for continual test-time adaptation, on which we outperform existing methods. Our code is available at https://qin.ee/cotta.

In supervised learning, the question of data quality and curation has been over-shadowed in recent years by increasingly more powerful and expressive models that can ingest internet-scale data. However, in offline learning for robotics, we simply lack internet scale data, and so high quality datasets are a necessity. This is especially true in imitation learning (IL), a sample efficient paradigm for robot learning using expert demonstrations. Policies learned through IL suffer from state distribution shift at test time due to compounding errors in action prediction, which leads to unseen states that the policy cannot recover from. Instead of designing new algorithms to address distribution shift, an alternative perspective is to develop new ways of assessing and curating datasets. There is growing evidence that the same IL algorithms can have substantially different performance across different datasets. This calls for a formalism for defining metrics of "data quality" that can further be leveraged for data curation. In this work, we take the first step toward formalizing data quality for imitation learning through the lens of distribution shift: a high quality dataset encourages the policy to stay in distribution at test time. We propose two fundamental properties that shape the quality of a dataset: i) action divergence: the mismatch between the expert and learned policy at certain states; and ii) transition diversity: the noise present in the system for a given state and action. We investigate the combined effect of these two key properties in imitation learning theoretically, and we empirically analyze models trained on a variety of different data sources. We show that state diversity is not always beneficial, and we demonstrate how action divergence and transition diversity interact in practice.

State Space Models (SSMs) have recently emerged as efficient alternatives to Transformer-Based Models (TBMs) for long-sequence processing, offering linear scaling and lower memory use. Yet, how contextual information flows across layers and tokens in these architectures remains understudied. We present the first unified, token- and layer-level analysis of representation propagation in SSMs and TBMs. Using centered kernel alignment, stability metrics, and probing, we characterize how representations evolve within and across layers. We find a key divergence: TBMs rapidly homogenize token representations, with diversity reemerging only in later layers, while SSMs preserve token uniqueness early but converge to homogenization deeper. Theoretical analysis and parameter randomization further reveal that oversmoothing in TBMs stems from architectural design, whereas in SSMs it arises mainly from training dynamics. These insights clarify the inductive biases of both architectures and inform future model and training designs for long-context reasoning.

Controlling restricted knowledge in large language models is essential for model alignment and safe deployment. Test-time unlearning avoids costly retraining and parameter updates by intervening only during inference. However, existing activation-editing methods apply isolated pointwise corrections, overlooking how autoregressive generation continually reconstructs hidden states from the prompt, cache, and generated prefix. Consequently, later states may return to restricted knowledge regions after a locally successful correction, causing restricted knowledge re-entry. In this work, we propose Stateful Test-Time Unlearning via restricted knowledge boundary control (ST^2U), which formulates test-time unlearning as trajectory-wide boundary control. ST^2U first models restricted knowledge boundaries in low-dimensional invertible coordinates while leaving orthogonal non-target components unchanged. During inference, ST^2U monitors risk along the trajectory, applies minimal boundary corrections with contextual anchoring, and propagates historical correction states across tokens to mitigate knowledge re-entry. This trajectory-wide control enables more persistent forgetting while preserving non-target capabilities and limiting inference overhead. Across three benchmarks and three model families, ST^2U delivers the strongest overall balance, combining best or second-best retention with competitive forgetting and substantially less restricted-knowledge re-entry than test-time baselines (13.76%-19.84% versus 46.50%-59.10%).