Papers

Predicting observed dynamics does not establish recovery of the underlying physical mechanism. Can machine learning retrace the hidden-state reasoning behind the Hodgkin-Huxley (HH) model? We train structured latent models on simulated current and voltage, withholding gate identities and trajectories from training and model selection. We then test response prediction, state recovery, protocol transfer, and agreement with HH dynamics. Prediction error and its cross-seed spread both drop sharply at three latent dimensions under the tested protocols, while gate recovery under new protocols improves through five to six coordinates. State recovery depends on which observations the chart uses. Observed voltage improves current-clamp decoding relative to freely predicted voltage. Under voltage clamp, adding latent state to command voltage raises m-state $R^2$ from 0.976 to above 0.99, yet the transported field disagrees with HH on identical smooth samples. Known invertible HH coordinates achieve high fast-m field agreement under the same audit procedure. An exact HH identity decomposes the discrepancy into time-scale-weighted state error and a residual in the transported field; these terms can cancel or reinforce. These findings concern the tested models and charts. They support evaluating state and dynamics recovery separately, including chart inputs and transported-field agreement across interventions.

Latent visual reasoning (LVR) enables multimodal large language models (MLLMs) to perform intermediate computation in continuous latent tokens rather than expressing every reasoning step in words. However, unlike textual CoT, latent reasoning is not directly observable, making it difficult to supervise what latent tokens learn. In this work, we first conduct a thorough analysis of latent-token behavior and identify a latent evidence-credit gap: latent tokens respond only weakly to image perturbations that alter the correct answer. We hypothesize that this issue stems from the lack of explicit supervision during GRPO training. These findings suggest that a final-answer reward provides too little guidance on what visual evidence to preserve or how credit should be assigned across latent tokens. To bridge this gap, we propose ReaLVR, which brings visual-evidence supervision to the model's own free-running latent trajectories. ReaLVR contrasts correct and model-generated wrong answers to determine where stronger supervision is needed, and relevant and mismatched visual evidence to specify what to preserve. Across three model families, ReaLVR consistently outperforms evaluated LVR baselines, achieving the highest five-task average of 63.7% on Qwen2.5-VL-7B. Crucially, we are the first to scale visual reasoning in latent space, showing that our framework continues to deliver robust improvements at frontier model scales up to 235B. Further analyses show more question-sensitive latent-token positions, stronger alignment with relevant visual regions, and greater fixed-context dependence on the most attended latent tokens.

MeMo (Zanzotto et al., 2025) is a recent language-model architecture that stores associations between token contexts and next tokens in a correlation matrix memory. In this work, we study its single-layer form and show that its ideal retrieval rule is a multiclass classifier based on the positional Hamming kernel. The MeMo architecture represents both the sequence features and the output labels with Gaussian random codes. Its score is therefore a doubly randomized sketch of the ideal classifier. Under independent input and output codebooks, we bound the errors introduced by context sketching and output decoding, characterize their dependence on model and data parameters, and give a margin-based guarantee for recovering the ideal prediction. Controlled simulations support the trends predicted by the analysis. On a restricted WikiText-2 next-token task, we compare single-layer MeMo with classical baselines and show that it can offer a useful trade-off among predictive accuracy, memory, and throughput, particularly on a GPU, where its matrix operations can be parallelized.

Motor brain-computer interfaces (BCIs) aim to decode motor intention, enabling people with paralysis to control external devices. Neural motor decoding typically learns task-specific mappings from neural activity to kinematics, yet remains constrained by scarce paired neural-action data. We propose BrainVLA, a framework that enables neural motor decoding by drawing on a pretrained vision-language-action (VLA) model through language-mediated alignment. BrainVLA mitigates reliance on scarce paired neural-action data by leveraging VLA policies. We first construct VLA-compatible datasets including paired neural activity, action signals, language instructions, and rendered visual observations. Then, we adapt the OpenVLA-OFT policy to the target action spaces through LoRA fine-tuning. To establish an effective interface through which neural activity can convey motor intention to adapted VLA policies and guide action generation, we train a neural encoder via neural-language alignment, using language representations as semantic targets to capture latent motor intent from neural activity. The resulting neural representations serve as an endogenous intention signal to guide VLA policies to generate executable actions, while visual observations provide complementary information about the evolving task state. BrainVLA is evaluated on two neural motor datasets with different action dimensionalities using causal rollout decoding. It outperforms the evaluated baselines in cross-session decoding $R^2$ and task success rate, while demonstrating high training data efficiency. These results establish a route for neural motor decoding to draw on large-scale robotic priors through brain-conditioned VLA policies.

Transformers process tokens without any inherent notion of order, making positional encoding a fundamental requirement rather than an architectural refinement. Rotary Position Embedding (RoPE) has become the default positional encoding in modern language models, yet it is heavily biased toward nearby tokens. Existing alternatives have been evaluated under different settings, leaving the literature fragmented and without a clear replacement. We bring structure to this landscape by examining a specific weakness of RoPE: its slow frequency bands, whose wavelengths exceed the training context and expose models to unseen angles during extrapolation. We therefore introduce Data aware RoPE (DaRoPE), which preserves standard RoPE on the fast bands but replaces absolute position on the slow bands with bounded coordinates learned from contextual representations. Therefore, the slow-band geometry depends on the data rather than only on positional distance. We compare representative encodings under matched conditions across synthetic tasks, symbolic music, genomics, neural signals, and language models spanning 124M to 50B parameters. Across these experiments, DaRoPE leads on non-text benchmarks, mitigates recency bias, while remaining best or on par in language modeling and length extrapolation. Moreover, the learned coordinates also make the mechanism interpretable, revealing how attention layers leverage contextual information beyond token distance. Together, these results support DaRoPE as the best overall default among the evaluated methods, when there is no domain-specific reasons to prefer another.

Long-context LLM serving is increasingly bottlenecked by decode, where large KV caches limit batch size and underutilize GPUs. Sparse KV cache offloading expands effective capacity by storing most historical KV blocks in CPU DRAM and recalling only selected blocks on demand. However, we find that existing offloading systems shift the bottleneck to CPU-GPU recall I/O: recall volume varies widely across layers, decode steps and requests, while headwise sparse selection fragments recalls into many small PCIe transfers. This paper presents PulseInfer, an I/O-centric sparse KV cache offloading system. PulseInfer hides variable recall latency with interruptible layer-wise scheduling, adapts offloading decisions with IO-Adaptive Offloading Admission, and coalesces fragmented transfers using SoloHead sparse selection and a gather-scatter I/O engine. Implemented on SGLang, PulseInfer improves decode throughput by up to 4.7x over SGLang and 2.6x over the best existing offloading baseline, while reducing TPOT by up to 76% and preserving near-lossless accuracy.

Formal verification can play a key role in ensuring the reliability of Deep Neural Networks (DNNs) deployed in safety-critical systems. Modern DNN verifiers employ a branch-and-bound framework, which alternates between branching (splitting into smaller subproblems) and bounding (pruning subproblems) to efficiently explore the verification space. However, existing branching heuristics make greedy decisions based on static scoring functions. They do not anticipate long-term efficiency or leverage the growing availability of verification data to improve performance. This work introduces RSB, a reinforcement learning framework that learns to refine baseline branching heuristics. It trains an actor-critic architecture to maximize cumulative future rewards rather than immediate scores. The actor generates attention weights from observations of raw neuron features and learned graph embeddings, which rescale baseline heuristic scores to guide neuron branching. Evaluation on 600 challenging instances demonstrates that RSB consistently outperforms state-of-the-art branching heuristics, solving 11% more instances while reducing branch exploration by 50%.

Parameter space symmetries and conservation laws play an important role in understanding the loss landscapes and implicit biases of neural networks. Inspired by Noether's theorem in physics, prior works have sought to derive conservation laws under gradient flow from parameter symmetries, but the scope and limitations of this connection remain unclear. We develop a unified geometric framework that clarifies the precise relationship between the two notions, including the conditions under which symmetries correspond to conservation laws. We introduce a notion of compositional identifiability and use it to establish a general inheritance principle for complete characterizations of symmetries and conservation laws in multilayer networks. We apply the framework to multi-head and grouped-query attention, polynomial neural networks, and square deep linear networks.

Looped Transformers reuse a shared block across recurrent depths, making autoregressive decoding expensive because every generated token requires many sequential recurrent passes. Self-speculative decoders reduce this cost by drafting at an early depth and verifying at full depth, but typically bind draft computation to prefix representations from the same recurrent depth. We find that queries and keys approach their final-depth representations earlier than values, and controlled prefix-channel interventions show that mature values substantially improve shallow draft predictions. Motivated by this asymmetry, we introduce Depth-Asynchronous Self-Speculation (DAS), which decouples the depth of draft computation from the depth of verified-prefix representations it reads. Its Mature-V primitive lets shallow queries retrieve full-depth prefix values without additional recurrent computation. We further develop DAS-Wave, which combines depth-asynchronous prefix reads with carried parallel refinement, progressive block growth, and an independent full-depth verifier. Across four recurrent-model checkpoints and mathematics and code workloads, DAS-Wave achieves 4.00–6.96$\times$ mean throughput speedup over paired full-depth autoregressive decoding in the same inference stack. These results identify prefix-information depth as an effective design axis for recurrent self-speculation.

As large language models (LLMs) become increasingly widespread, preventing unsafe responses to harmful prompts is essential for their safe deployment. Activation steering offers an approach to improving LLM safety by modifying internal activations during inference without updating model parameters. However, a single prompt can involve multiple harm categories, and steering toward safety in one category may leave harmful content from another unaddressed. Despite advances in adaptive steering, existing methods do not explicitly coordinate steering direction and strength when multiple harm categories co-occur within a single prompt. To address this problem, we propose CAM-Steer, a Category-Adaptive Multi-category Safety Steering framework. Specifically, it estimates the risk associated with each harm category by comparing the current hidden state with safe and unsafe prototypes. The estimated risks are then used to combine the safety directions for different harm categories into a single steering direction and to determine the strength of the intervention. Finally, it rotates the hidden state along the composed steering direction, with the rotation angle determined by the estimated risks, while preserving the hidden-state norm. Experiments across three LLM backbones and seven harm categories show that CAM-Steer outperforms the evaluated baselines in average defense success rate, including when categories co-occur. Further analyses support its component designs and informative risk scores, with negligible inference overhead.

Most existing time series generators rely on a two-stage modeling paradigm: the first stage learns discrete latent representations of time series; the second stage performs autoregressive modeling on these discrete latents through next token prediction. However, this paradigm suffers from two stage-specific limitations: the first stage can lead to information loss when discretizing continuous time series, while the second stage is prone to error accumulation during autoregressive generation. To address these limitations, our core idea is to perform generative modeling in a continuous latent space with a more efficient autoregressive framework. We propose HALO, which enhances time series generation via Hyperspherical Latents and Masked Autoregressive modeling to achieve this goal by tackling two key bottlenecks: (1) variance and scale heterogeneity of continuous latent representations; (2) the difficulty of balancing generation efficiency with temporal correlation modeling. HALO first introduces a hyperspherical VAE that constrains continuous latents to a fixed-radius hyperspherical shell, effectively stabilizing the numerical fluctuations of continuous latent representations. Secondly, we develop a masked autoregressive model that balances parallel decoding and temporal correlation learning, substantially reducing the number of inference steps required for generation and improving generation stability. Our extensive experiments demonstrate that HALO achieves state-of-the-art generation performance while offering significantly improved inference efficiency over existing advanced baselines.

Masked diffusion language models support arbitrary-order generation, suggesting a natural way to produce diverse outputs. However, recent work argues that this flexibility reduces diversity by delaying high-uncertainty tokens that can lead to different generation paths. We trace this diversity loss not to arbitrary-order generation itself, but largely to low-confidence remasking (LCR), a widely used decoding rule. At each step, LCR samples a token at every masked position but commits only the sampled token with the highest probability, filtering out the rest. We show that this mechanism can exponentially suppress lower-probability tokens as more positions compete, and observe the same suppression in LLaDA. In contrast, top-probability position selection (TPP), which has often been conflated with LCR under the shared label confidence-based decoding, avoids this diversity loss. TPP first selects the position whose most likely token has the highest probability, then samples directly from that position's distribution. Replacing LCR with TPP restores diversity and yields Pass@$k$ comparable to left-to-right decoding, suggesting that the reported diversity loss stems largely from LCR's filtering rather than from generating high-confidence positions first. To further exploit order flexibility, we introduce Entropy-Guided Initialization (EGI), which samples the first token at the highest-entropy position and then follows TPP. This simple modification further improves rollout diversity and solution coverage beyond left-to-right decoding, with gains extending to downstream policy optimization, highlighting the potential of arbitrary-order generation for diverse rollouts.

Financial candlestick forecasting is fundamental to quantitative investment, yet it remains exceptionally challenging due to extremely low signal-to-noise ratios and vast heterogeneity across markets and instruments. Existing approaches have largely attempted to introduce deep learning to capture hidden temporal features, but most adopt an auto-regressive formulation, which leads to error accumulation during inference. Meanwhile, general-purpose time-series foundation models are not tailored to the unique structure of k-line data and yield unsatisfactory performance on downstream candlestick forecasting tasks. To tackle these problems, we introduce KiT, a K-line Diffusion Transformer foundation model, and reformulate future prediction as conditional path generation via flow matching: given a historical context window, the model generates an ensemble of plausible future OHLCV trajectories. We pre-train KiT at multiple parameter scales on billions of candlestick bars spanning multiple markets and timescales. Across three markets and seven resolutions, KiT attains a mean return RankIC of 0.057 and a mean volatility RankIC of 0.66, leading at every timescale and outperforming both task-specific financial forecasters and general time-series foundation models. Code will be available at: https://github.com/Luciferbobo/KiT.

Parameter-efficient adaptation enables continual learners to acquire task-specific knowledge through compact model updates while maintaining strong within-task performance. However, class-incremental inference requires each input to be classified among all classes seen so far without access to its task identity. For learners equipped with task-specific parameter-efficient modules, this introduces a critical task-routing challenge beyond catastrophic forgetting. We study post-hoc task routing without retraining the learner or introducing a separately trained router. Such training-free inference-time calibration remains comparatively underexplored in parameter-efficient class-incremental learning. We identify three sources of routing error (feature-level, task-level, and class-level misalignment) and propose Feature Distribution Calibration (FDC). Its three components address these misalignments: Task Subspace Filtering (TSF) suppresses feature components outside each task's principal subspace, Residual Likelihood Calibration (RLC) evaluates the typicality of its subspace residual, and Prototype Affinity Calibration (PAC) measures compatibility with the task's class prototypes. Experiments demonstrate plug-and-play applicability to eight parameter-efficient class-incremental methods using a shared encoder. With one component configuration selected per method across all five benchmarks, FDC improves final accuracy in all 40 method-dataset pairs by 4.39 percentage points on average. Enabling all components improves 35 of the 40 pairs, with an average gain of 4.45 points. When applied to a simple baseline, FDC achieves strong overall performance.

Graph neural networks (GNNs) excel at representation learning on Knowledge Graphs (KGs), achieving stateof-the-art performance on tasks like link prediction or entity classification. However, their high computational complexity, inherent to their user-defined message passing (MP) algorithm, still prohibits their widespread adoption, especially for large KGs. Current efforts to mitigate the scalability bottlenecks of GNNs on KGs, such as subgraph sampling, are often task- and model-specific, and do not reliably guarantee lossless (if applicable) runtime/space reductions. To address this, we extend Relational Sparse Matrix Multiplication (RSPMM), originally designed to losslessly lower the space complexity of composition-based MP with pointwise composition functions, to support more expressive functions (e.g., 2x2 block-diagonal matrix multiplication, Givens rotation, circular correlation). Our method delivers significant task-independent reductions in runtime and space for current GNNs on KGs and facilitates efficient re-implementations of GNNs that maintain near state-of-the-art performance on challenging KG tasks, for a fraction of computational costs.

Flow policies can model rich action distributions, but their iterative sampling limits decision speed. Adjoint matching uses the critic's action gradient to improve a flow policy without backpropagating through its sampling trajectory, yet its supervision is defined for instantaneous velocities. We propose QAMM, a method that turns the critic-derived adjoint signal into supervision for MeanFlow's average velocity. The resulting policy learns finite-interval transport directly and generates actions with few network evaluations. We derive the adjoint MeanFlow target, specify its gradient boundaries, and train it with an offline actor-critic. On ten HumanoidMaze tasks, QAMM produces effective two-call policies and achieves competitive performance against strong flow-policy baselines. These results show that adjoint-based Q optimization can be combined with average-velocity learning to obtain expressive offline policies with few-step action generation.

Explicit residual connections of the form (x+f(x)), often combined with normalization layers, have become a standard strategy for training very deep neural networks. However, residual addition primarily provides an algebraic shortcut for gradient propagation, while leaving the evolution of feature geometry across layers largely unconstrained. We introduce Learnable Lens Networks (LLN), a physics-inspired architecture that replaces direct feature-space residual accumulation with learnable optical transport in an augmented position-angle phase space. Each layer alternates between free propagation, which provides an implicit transport path, and a learnable lens field that performs nonlinear trajectory transformation and focusing. Theoretically, we establish that LLN transport is globally invertible and volume-preserving for any differentiable lens field, with the implemented coordinate-wise Gaussian transport further satisfying symplecticity. Importantly, these structural constraints do not limit expressivity: with unrestricted embeddings and readouts, LLN retain universal approximation of continuous end-to-end maps. Experiments across diverse dynamical systems demonstrate that LLN improves long-horizon prediction while using substantially fewer parameters than same-depth comparators. Further analysis reveals stable depth-wise gradient transport and interpretable learned dynamics under the coupled propagation and refraction design.

Small-molecule optimization integrates medicinal-chemistry reasoning and computational evidence through iterative, multi-objective decisions. When large language models (LLMs) reason over optimization histories stored primarily in conversational context, they must recover candidate identities, prior evaluations, and task constraints to guide subsequent decisions. We present M3OS, a multi-agent LLM system that decouples molecular-design reasoning from optimization-state management through Monte Carlo graph search. A persistent graph links evaluated candidates, parent-child transformations and evaluation evidence, while rewards and visit statistics guide LLM-assisted parent selection. Two branches combine tool-driven candidate generation with knowledge- and case-guided medicinal-chemistry editing. An execution harness controls graph updates through structured output extraction, molecular validation and task-bound evaluation. Agents receive role-specific contexts, while the graph preserves optimization trajectories beyond their active contexts. Across three molecular optimization benchmarks, M3OS achieves higher success rates than baselines, supporting the integration of persistent search state, specialized agents and controlled execution for multi-constraint optimization.

Data pruning reduces the training cost of knowledge distillation (KD). However, the preferred teacher capacity changes with the data budget: smaller teachers can outperform larger ones when limited training data are available. Understanding what drives this shift is important not only for teacher choice but also for identifying which samples are useful for distillation. We analyze teacher supervision by decomposing it into relational ordering—the ranking of classes—and score geometry—the magnitudes and margins of class probabilities—and show that the small-teacher advantage in the low-data regime arises not only from score geometry but also from relational ordering. Beyond understanding teacher capacity, our analysis reveals two properties of effective subsets: samples should match the difficulty appropriate for the available budget, and their relational signals should be diverse rather than redundant. Based on these findings, we propose DVA (Difficulty- and Volume-Aware data selection for KD), a training-dynamics-free method, which uses a small teacher as a proxy for budget-aware difficulty filtering and class-conditional relational volume maximization. Despite requiring no training dynamics statistics, our method remains competitive with training-dynamics-based methods while consistently outperforming training-dynamics-free baselines.

Looped architectures scale computation by reusing the same parameters across recurrent steps, and recent work shows that they substantially improve deep reinforcement learning policies on long-horizon tasks. Since recurrent depth directly controls computation, one may expect looped policies to naturally support elastic inference across recurrent depths. Surprisingly, we find that pretrained looped policies exhibit severe recurrent-depth specialization: reliable decisions are concentrated near the full trained depth, tying deployment computation to this depth even when less computation may suffice. Achieving depth elasticity, i.e., reliable decisions across recurrent depths with adaptive computation at deployment, therefore remains a key challenge. To address this, we propose FlexLoop, a novel post-training framework that converts pretrained fixed-depth looped policies into depth-elastic policies. FlexLoop keeps training on the original RL objective to preserve full-depth capability while performing adjacent-depth policy distillation to progressively transfer decision quality from deeper to shallower recurrent steps. The resulting policy supports reliable inference across recurrent depths and enables state-wise adaptive inference through recurrent-depth consistency. Experiments on $30$ online and offline long-horizon goal-conditioned environments show that FlexLoop preserves full-depth performance while making shallower depths effective. Keeping competitive performance, FlexLoop reduces average recurrent depth by up to $\bf{43\%}$ and achieves up to $\bf{1.34\times}$ wall-clock speedup in a stress test.

Progress reward modeling is the problem of estimating how a robot's behavior changes task progress over time. Reliable estimation requires distinguishing meaningful state changes from failed attempts and task-irrelevant actions. We introduce the Agentic Reward System (ARS), an inference framework for progress reward modeling with general-purpose vision-language models (VLMs), without additional reward-model training. Given an offline trajectory and a task instruction, ARS uses adaptive visual inspection for both event proposal and verification. A subagent proposes a task-relevant event timeline, which a primary agent verifies and revises before estimating per-frame progress. ARS can incorporate optional terminal outcome labels and visual references to inform its judgments. It can also audit progress estimates from external reward models. We evaluate ARS with a 27B VLM on a controlled semantic-mismatch benchmark and downstream policy learning in simulation and on a real robot. The benchmark reveals that several evaluated reward baselines assign spurious progress to wrong-object manipulation even in simple pick-and-place scenes. ARS better suppresses these errors and outperforms these baselines in simulation policy learning. We further demonstrate that ARS supports long-horizon policy learning from mixed-quality offline experience on real-robot multi-screw fastening in a full-scale laboratory replica of an industrial washing-machine assembly line. These results suggest that structured inference and verification can improve the usefulness of general-purpose VLMs for robot reward modeling. Code is at https://github.com/midea-ai/ars

Task-specific fine-tuning can rewrite a language model's answers beyond the training task, complicating updates that must preserve existing behavior. We introduce ATLAS, which turns retained-domain representations into an input-dependent rule for task adaptation. An activation atlas supplies local reference centers and directional filters to a shared low-rank residual. Target supervision learns the residual, while retained geometry shapes its action throughout training and inference. On Qwen3-8B, ATLAS achieves lower mean retained-output Kullback-Leibler (KL) divergence than all seven published baselines at shared coding-performance requirements, with consistent advantages across multiple training seeds. Structural comparisons identify the contributions of retained reference states and directional conditioning, and answer-level analyses show fewer rewritten mathematical answers and more stable commonsense choices. Experiments spanning five backbones and two retained domains further demonstrate coding gains with reduced retained-output movement. With compact storage and modest decoding overhead, ATLAS provides a practical mechanism for acquiring specialized skills while maintaining continuity in existing responses.

LLMs cannot forget the way we delete a file. Strangely, we are asked to remove something that was never put anywhere in particular. What the model took from a piece of text is now smeared across billions of weights. Existing methods rewrite all of them to change one thing, and none of them say which part produced that change. To address this, we introduce Causal Routing for Unlearning (CRU) by asking where the concept is expressed in the model and suppressing only that part. One untrained forward pass over the forget set ranks neurons by how their activations vary. Then, small routing modules on those neurons gate and suppress only the concepts that need to be forgotten. In CRU, the base model is frozen, and any change in behavior is caused only by the gated neurons; hence, why the routing is causal. Due to our parameter efficiency (only ~0.01% as many parameters as the base model), unlearning a concept costs 14 GiB, whereas the baselines require 71 GiB. On TOFU, CRU is indistinguishable from the retained model (p > 0.05, KS test) and is never Pareto-dominated, whereas every compared baseline matches its forgetting on the larger-forget batches only by collapsing utility. On RWKU, it achieves an adversarial-probe recall of 0.052, compared to 0.250 for the strongest baseline, meaning the knowledge is gone, not merely harder to reach. Thus, deciding on the intervention at query time, rather than fixing it beforehand, is the axis along which we argue that unlearning should proceed.

We introduce a deep kernel hedging framework that combines the flexibility of deep learning with the structural inductive bias of kernel methods. The hedging functional is restricted to a reproducing kernel Hilbert space whose kernel is parameterized through a neural network embedding of the input features. The framework minimizes a regularized empirical risk under convex loss functions and can accommodate path-dependent information through truncated time-augmented signature features. We derive a generalized representer theorem for the joint hedging problem, reducing the empirical optimization to a finite-dimensional problem. To further reduce the computational cost associated with large kernel matrices, we develop a scalable random Fourier feature approximation and establish convergence guarantees. The random Fourier parameters are sampled once and remain fixed throughout training, while the deep kernel adapts to market data through the learned neural representation. We evaluate the performance of the proposed deep kernel approach on both synthetic and real data and compare it with standard kernel methods and classical deep hedging architectures. Numerical results indicate competitive and robust hedging performance, particularly in low-data regimes, which highlights the benefits of combining expressive neural representations with the inductive bias of kernel methods.

Recent advances in Vision-Language-Action (VLA) models point toward general-purpose robotic intelligence by unifying perception, instruction, and control. Despite impressive progress, existing VLA models often adapt poorly due to tri-modal misalignment among vision, language, and action, which weakens action grounding and hurts generalization and fine-tuning efficiency. In this work, we present Alignment-Guided Flow Transformer (AGFT), a novel framework that explicitly enforces tri-modal alignment through a dedicated alignment loss, bridging the representational gap across modalities and enhancing task adaptation. While prior research has predominantly emphasized bi-modal vision–language alignment, we systematically formalize and study tri-modal alignment in VLA models, and provide both ablations and analysis to isolate its role in improving adaptation and robustness. To further accelerate deployment, we adopt a flow-matching objective, enabling substantially fewer inference steps than diffusion-based policies while maintaining accuracy. Theoretically, we establish a quantitative connection between the tri-modal alignment gap and the optimization tightness of flow matching; empirically, experiments on the extensive benchmark show that AGFT achieves superior success rates and lower inference latency compared to SOTA baselines, underscoring tri-modal alignment as a key ingredient for scaling robust VLA manipulation.

Physiological foundation models encode how a signal was recorded alongside the physiology it reflects. When recording conditions are associated with diagnosis, this acquisition provenance can become a shortcut, yet the usual evidence, shifted transfer and provenance decodability, does not show whether a predictor uses it. We introduce PhysioTRACE, a four-axis behavioral audit for frozen encoders that separates what a probe can decode from what a fixed task head relies on. Recover scores how decodable provenance is; Stress reverses only the provenance-target association on the same held-out records; Intervene removes a train-localized provenance component; and Verify certifies that removal only if it beats matched random projections within a declared utility margin. Each audit thus ends in one of three verdicts: no reliance, or reliance with the remedy certified or refused. Across EEG and ECG, five training objectives, and five frozen foundation models, the relation between Recover's calibrated score and out-of-distribution utility changes sign between datasets, so neither can stand in for a reliance test. On paired EEG views where the shortcut is known by construction, the audit detects it (the exposed head loses about 0.2 AUROC when the association is reversed, while a control head is unaffected) and certifies removal of a rank-two component that restores control-level behavior without measurable utility loss, for both encoder objectives tested. On real ECG device metadata it returns all three verdicts: it certifies a remedy that removes 91% of one model's excess vulnerability, finds no reliance where device and diagnosis are barely associated, and refuses the remedy for a second model whose localized direction also carries task signal. Robustness to how inputs were recorded therefore needs a behavioral test, and PhysioTRACE provides one that can pass, fail, or refuse a remedy.

Does structured mathematical knowledge help LLMs prove theorems in Lean 4? If so, for which models, and does the answer vary by problem? Formal libraries such as Mathlib encode 285,000+ verified theorems with syntactic dependencies, but the semantic layer mathematicians rely on for discovery (analogies, generalizations, cross-domain bridges) remains implicit. We introduce MathAgent, which builds this layer as a knowledge graph, MathKG, and uses it to augment LLM theorem provers. MathKG connects 364 Mathlib theorems and definitions by 9,434 typed semantic edges inferred via LLM-based relation extraction anchored to verified Mathlib declarations. We run a controlled ablation across four augmentation modes (no context, knowledge-graph context, Mathlib retrieval, both) and five models: Qwen3-8B/32B, their Lean-specialized derivatives Goedel-Prover-V2-8B/32B, and Claude Sonnet 4.6, on miniF2F, plus PutnamBench and MathOlympiadBench for Sonnet. Three findings emerge. (i) Specialization dominates augmentation: Lean fine-tuning adds 33-38 percentage points of solve rate in every mode, and a specialized 8B model beats a $4\times$ larger general one by 29-35 points, while no augmentation mode improves solve rate by more than 3 points. (ii) Augmentation is capability-conditioned: knowledge-graph context helps small models but hurts large ones, with the specialized model gaining more relative to its general base at every scale. (iii) Yet the augmentation modes solve different problems: an oracle selecting the best mode per problem solves 6% to 58% more than the unaugmented prover, a complementarity effect that strengthens on harder problems (32% more on PutnamBench). These results motivate adaptive strategies that select augmentation by model capability and problem. Code, data, and artifacts are available at https://github.com/sarehnabi/mathagent

Classical statistical theory is insufficient to explain the successes of general-purpose AI models, because it depends on handcrafted inductive biases that it cannot justify. No Free Lunch (NFL) theorems force any learner that beats chance on some environments to underperform on others. We might hope that past experience informs which environments to expect, but NFL applies equally to meta-learning. Thus, any method that makes meaningful predictions necessarily begins with an inductive bias external to the data. Choosing to bias toward short programs yields Solomonoff induction (SI), whose performance is competitive against all computable learners - albeit up to "constants" that become large when comparing against specialized methods that exploit background information. We therefore relativize SI to an information vantage point, biasing toward short programs with access to all preexisting information. This reframes the inductive bias: instead of seeking some absolute notion of simplicity, we favor accessibility with respect to our vantage point. An algorithm can only outpredict the relativized SI to the extent that its code contains additional information about the data, and no algorithm can generate such information. While SI is incomputable and hence not a practical algorithm, it provides a formal optimum for inference in the limit of infinite compute, and there is evidence to suggest that frontier AI systems roughly approximate it. Thus, the only known answer to meta-NFL is rooted in algorithmic information theory, which we should expect to play a fundamental role in explaining the generalization behavior of modern (and future) AI systems.

Transformer-based models are widely used for reasoning, coding, and multimodal agentic tasks. To provide formal assurance of desirable behaviors, such as robustness, safety, and fairness, neural network verification techniques prove required properties and provide auditable guarantees before deployment. However, prior work remains limited to small or restricted Transformers, and maintaining precision across deep models remains challenging. In this work, we introduce ZonoGpt, an abstract domain for verifying large transformers that maintains a space complexity independent of network depth. ZonoGpt uses a structured zonotope and a generator reduction mechanism to efficiently preserve correlations. To maintain precision, it introduces block-specific fused transformations for Attention and LayerNorm that retain feature relations, along with an affine transform for GELU that preserves generator relations. These mechanisms enable ZonoGpt to be the first approach to verify standard architectures, scaling to official HuggingFace models up to GPT-2 Medium (24 blocks, 300M+ parameters) and successfully verifying 1,339 instances across text and vision tasks.

This study addresses the catastrophic forgetting problem that occurs when sequentially learning successive tasks using Low-Rank Adaptation (LoRA) from a lifelong learning perspective. While existing approaches have primarily constrained parameter updates or learning subspaces to reduce interference with past knowledge, they have not fully considered additive interference. This occurs when a newly added residual adapter on top of a fixed past model generates non-zero responses along input directions important for old tasks, thereby altering previous predictions. To this end, we propose Subspace Protection with Allocated Capacity for Efficient Continual Adaptation (SPACE-LoRA). SPACE-LoRA directly suppresses the responses of the new residual branch along input activation directions that are important for old tasks and adaptively determines the protection coverage for each module based on past-task sensitivity estimated via a common Fisher sensitivity-based coverage target. Under a fixed LoRA rank, this approach adaptively adjusts module-specific protection coverage while suppressing interference along input directions sensitive to old tasks. We assess the effectiveness of activation-subspace protection in mitigating catastrophic forgetting and examine the role of sensitivity-guided protection in continual learning across diverse tasks. Code is available at https://anonymous.4open.science/r/SPACE-LoRA-7864.