LLM 理论进展

Autonomous agents increasingly rely on memory to generalize beyond their training environments. However, agents are bounded by what they have seen and believed, and leveraging such memories in unseen environments can introduce biases into their internal beliefs. We formalize this phenomenon as false memory, which can arise from spurious correlations, environment shifts, and knowledge conflicts. Despite its importance, false memory is difficult to evaluate because it stems from agent internal beliefs and is easily confounded with ordinary generalization failures. Therefore, we propose FAME, a training-free framework that evaluates false memory through the evolution of agent beliefs under counterfactual reasoning. Specifically, counterfactual scenarios reveal how beliefs change as the latent concept of memory shifts under hypothetical interventions; thus, measuring the resulting concept drift provides a signal for distinguishing faithful versus false memory. Such concepts can be estimated from agent hidden states before answer generation, avoiding the need for reward design or answer sampling. Empirical experiments reveal that simply monitoring answers often fails to detect false memory, while FAME achieves AUROCs of 76.2% - 96.7% across false-memory settings, and outperforms the best baseline by 3.4% - 23.3% across realistic benchmarks, spanning math reasoning (GSM-Symbolic), code generation (GitChameleon), and complex reasoning (BigBench-Hard). We further release corresponding counterfactual templates and facilitate future research on false memory.

LLM agents often admit multiple high-quality solutions to the same task, differing in reasoning structure, tool-use pattern, or interaction trajectory. Yet existing notions of diversity in LLM post-training are mostly implicit, arising from general stochasticity and regularization mechanisms rather than explicitly targeting task-relevant behavioral variation. While such implicit diversity can be useful, it does not directly specify which forms of behavioral variation should be encouraged for a given task. In this work, we study explicit trajectory diversity in RL-based post-training for LLMs. Our key idea is to define diversity through user-specified, task-specific trajectory descriptors, which map each sampled trajectory to an interpretable behavioral representation, and then measure diversity as a set-level functional over the resulting descriptor matrix. Building on this formulation, we introduce Trajectory-guided Joint Policy Optimization(TJPO), a single-policy framework that optimizes explicit diversity over sampled trajectory groups, avoiding the need for population-based policy training, and instantiate it within group-based policy optimization through trajectory-level learning signals. This design makes the diversity objective both interpretable and controllable. Experiments on Sokoban and ALFWorld show that TJPO improves task-specific trajectory diversity while maintaining competitive task performance. Descriptor and trajectory analyses show that the learned variation follows the specified behavioral dimensions and includes distinct successful strategies. Extra experiment results suggest that explicitly shaping trajectory diversity can help LLM agents satisfy user requirements and remain effective when task conditions change.

Production LLM serving stacks combine an inference engine's local prefix cache with a shared KV-cache tier for fleet-wide reuse. The local cache distinguishes requests by adapter, weight configuration and sharing domain, but the shared tier may key entries only by token content and coarse model metadata. This boundary erases provenance and lets identical tokens under incompatible computational or sharing contexts collide. We call this composition gap provenance-blind reuse and present its first systematic study. A source audit of three vLLM connectors confirms the structural omission, while runtime experiments reproduce it across vLLM and two SGLang releases, 12 models from 7 families (0.5 B-32 B), and over 160 configurations. Cross-adapter collisions reduce accuracy from 0.94 to 0.64, incompatible KV representations reduce reasoning accuracy to zero, and salt omission enables 93% prompt identification from timing. We formalize the missing guarantee as the KV provenance contract: for a declared dimension registry, shared keys must be injective over computational and sharing provenance, with identities stable across workers. Any dimension with a stable identity can therefore be added without connector-specific key logic. A canonical descriptor binds per-request and per-worker provenance into lookup and store keys, while a differential checker detects dimensions that change KV state without changing the key. Implemented in vLLM and SGLang 0.5.20 across three cache paths, provenance binding eliminates unsafe reuse while preserving legitimate sharing. Hit-path latency changes remain within 0.34 ms and below run-to-run variation; retention grows with provenance diversity.

The scale and expense of pre-training language models make efficient hyperparameter tuning essential, yet a principled guidance is still missing. In this work, we analyze language model pre-training dynamics from a local landscape geometry perspective. Our study reveals two distinct phases. In Phase I, sharpness of the local landscape is initially high, leading to instability and loss plateaus under large learning rates (LRs). The landscape shifts from sharp to flatter regions early in training. This dynamic explains the necessity of LR warmup and further suggests that larger peak LRs require proportionally longer warmup periods. In Phase II, the local landscape is governed by the gradient noise scale. Our theory identifies a depth flatness trade-off: high noise from smaller batches widens the loss basin, whereas reduced noise from larger batches deepens it. This theory motivates a dynamic batch-size (BS) scheduler that begins with a small BS and increases it late in training. Together, we provide a unified view of loss landscape evolution, which translates into actionable tuning strategies for large-scale pre-training.

Predicting molecular properties for compounds that differ structurally from labeled training molecules is important for drug discovery and materials design. Tabular foundation models (TFMs) offer a promising approach through in-context learning, but their performance under structural shifts and the value of molecular comparisons in this setting remain underexplored. We study structural generalization in molecular property prediction and introduce MolPAIR (Molecular Pair-Augmented In-context Refinement), a framework that combines molecule-level and molecular-pair contexts without task-specific parameter updates. A global tabular foundation model (TFM) first predicts a query's property from labeled molecular examples. A second frozen TFM predicts differences in prediction errors between the query and labeled reference molecules, using these comparisons to refine the initial prediction. Across 58 MoleculeACE and Polaris tasks, CheMeleon representations combined with TabPFN-3 already outperform each evaluated baseline on a majority of tasks. MOLPAIR further improves this predictor on 46 of 58 tasks, with gains across four molecular representations and three TFM backbones. These results show that explicit molecular comparisons can strengthen tabular in-context learning for structural generalization while keeping the molecular encoder and pretrained model weights fixed. The code and datasets are available at https://github.com/nums-ai/MolPAIR.

Causal AI is a branch of Artificial Intelligence which helps understand and reason about cause and effect relationships, not just patterns or correlations. Causal discovery aims to infer elements of the underlying causal structure--often represented as a directed graph--from observational and, when available, interventional data. While causal discovery is the fundamental step for moving beyond mere associations toward genuine understanding, and thus the basic building block of causal AI, it becomes intrinsically difficult when causal relations must be inferred from single observations. In such situations, standard causal discovery methods cannot be used and one has to identify causal relations from limited amount of information. This is typically the case for, e.g., sequences of events produced by different alarms which need to be analyzed on the fly to detect abnormal phenomena, which are usually rare. We show in this study that it is possible to leverage the predictive power of Large Language Models (LLMs) to infer causal relations between only two sequences of events. This approach, which is validated on both synthetic and real data, provides better results than standard causal discovery algorithms on several time series data, even though these data were converted into smaller, single observed sequences.

Power-law learning curves are often treated as fixed properties of a model and its data, although learning-rate and batch-size schedules can change the observed loss. We study this dependence in noisy online SGD with linear random features. Conditional on the representation, an exact Volterra equation separates two response components: a forcing term that propagates unresolved target error and a memory kernel that propagates stochastic-error injections. We prove that either component follows a power law if and only if its cumulative weighted spectral mass has the corresponding low-spectrum scaling; individual eigenvalues and target coefficients need not obey coordinatewise power laws. Under a joint schedule, intrinsic time $T_t=\sum_{s<t}η_s$ controls optimization progress, while $r_t=B_t/η_t$ controls noise injection. Their interaction yields sharp conditions under which a schedule preserves, changes, or destroys the clean power law, together with a memory ceiling on noise reduction. The power-law random-feature model realizes this mechanism in $3+3(+2)$ propagation regimes with phase-dependent compute rates. Controlled nanoGPT experiments show that (1) learning-rate and batch-size schedules with matched $B/η$ paths are nearly equivalent in intrinsic time, (2) a forcing-memory surrogate accurately predicts loss across schedules, and (3) its fitted exponents across real-world datasets identify the regime of LLMs in $3+3(+2)$ map.

Steering large language models typically relies on linear, context-independent interventions in activation space, an assumption that recent work has challenged and that can induce an information bottleneck when a fixed representation must encode many behavioral distinctions. We introduce MetaSteer, a method that learns nonlinear interventions with context-dependent effects and applies them to attention projection matrices, producing activation effects that vary with the input context by construction and requiring no linear concept-geometry assumption. Framed as preference-based optimization, MetaSteer is trained once on a pooled preference corpus and transferred zero-shot to unseen concepts and out-of-distribution contexts. We find that, despite using low-rank adapters, MetaSteer induces structured, context-dependent changes in hidden-state trajectories while partially preserving aspects of their local trajectory dynamics, including velocity and curvature. We evaluate MetaSteer on three controlled text-generation benchmarks and three agentic settings across multiple model families and scales. MetaSteer matches or outperforms strong task-specific steering baselines on most aggregate comparisons in the zero-shot regime. Across the evaluated settings, stronger text-generation steering is associated with stronger agentic steering performance. We further discuss geometric trajectory effects, capability retention, and safety considerations raised by transferable steering.

Next-token prediction has driven remarkable progress in large language models, yet a growing body of evidence suggests that they can struggle on problems governed by complex global constraints. In this work, we focus on this regime and ask whether some of these limitations arise from the inference interface induced by next-token prediction itself. We study this question through blackboard intelligence: an inference-time perspective in which a model works on a fixed, revisable canvas and searches over candidate solution states rather than committing to a causal, left-to-right trajectory. We instantiate this idea with diffusion language models, whose any-order prediction interface naturally exposes predictions over partially filled solution states. Our key observation is that mean confidence, a simple model-internal quantity available from the standard masked diffusion objective, provides a useful proxy for global coherence and can guide inference-time search and revision. Empirically, across ZebraLogic, Nurse Rostering, and Job-Shop Scheduling, Blackboard consistently improves inference while holding the fine-tuned LLaDA-8B-Instruct checkpoint fixed and substantially outperforms same-scale autoregressive baselines, reaching 90.4% accuracy on ZebraLogic-Hard, 76.4% exact feasibility on Nurse Rostering, and 80.2% optimality on JSSP. Stronger autoregressive search and refinement also fail to close the gap on ZebraLogic-Hard, while Blackboard surpasses tested frontier LLMs there and on JSSP despite their substantially greater scale and strong test-time reasoning. We open-source our codebase at https://github.com/jwoosang1/blackboard-intelligence.

Learning from human preferences is central to large language model (LLM) alignment, but human preference annotation is costly. Active preference learning reduces this cost by selecting informative comparisons, and LLM judges can provide additional scalable feedback. However, the preferences of the judges may deviate from those of the target human population. Even after calibration on trusted reference data, active acquisition can shift the comparison distribution and expose residual judge bias. We therefore incorporate judge deviations into the acquisition design rather than relying on a separate calibration stage. Under joint estimation, comparisons that appear highly informative about the reward may also reflect judge bias and therefore provide less information about human preferences. To address this issue, we propose Nuisance-Adjusted Optimal Design (NAOD), a comparison-selection strategy that prioritizes policy-relevant target information after nuisance adjustment and uses the Frank-Wolfe algorithm for optimization. Theoretically, we establish a sharp conditional local asymptotic minimax lower bound on policy risk and construct an estimator that attains it. We further characterize the finite-sample cost of learning the nuisance representation and show that representation error can reverse an oracle design advantage. Finally, we validate these predictions experimentally and evaluate NAOD on Chatbot Arena data across 17 judges, 15 budget configurations, and 15 random cluster-level splits. NAOD reduces the mean regret of proxy policy by 29.1% relative to a matched target-information design, outperforms existing methods, and improves human-preference prediction on held-out data.

Machine unlearning has emerged as a crucial mechanism for removing hazardous knowledge and enforcing safety alignment in Large Language Models (LLMs). However, recent studies reveal a persistent security risk: unlearned models remain highly vulnerable to retraining attacks, where suppressed malicious behaviors rapidly resurface after benign fine-tuning. In this work, we investigate the optimization dynamics of unlearning and identify that this vulnerability stems from shallow alignment. Rather than effectively erasing target knowledge, models often exploit a shortcut by activating previously dormant parameters to act as spurious suppressors, forming a fragile inhibitory shell over intact malicious representations. To address this issue and enforce authentic memory deletion, we propose FDCU, a novel dual-constrained subspace projection framework. FDCU restricts parameter updates through a highly scalable, element-wise dual-masking rule: it preserves general knowledge manifolds via Fisher Information and strictly prohibits the abnormal activation of spurious suppressors via the Principle of Minimal Functional Intervention (PMFI). By reliably blocking the model's ability to superficially hide knowledge, FDCU promotes the authentic dismantling of target representations. Extensive experiments across specific knowledge erasure and safe output control tasks demonstrate that FDCU achieves state-of-the-art robustness against retraining attacks while maintaining near-lossless general utility, ensuring durable safety for LLMs.

Recent work on hallucination detection in large language models has shown that, for a fixed pre-trained model and reasoning task, it is possible to estimate the model's confidence in the correctness of its outputs. Such uncertainty estimates have primarily been used to improve truthfulness by detecting or filtering confabulations. In this work, we ask whether these signals can instead be used more proactively to directly improve the accuracy of model-generated answers. We propose USteer, a simple, training-free steering mechanism that adjusts a model's layer-wise activations during inference using the gradient of a confidence measure with respect to the activations. This procedure nudges generation toward outputs with lower uncertainty at inference time, without modifying model parameters or requiring additional supervision. We show that this approach consistently reduces hallucination across a range of tasks, demonstrating that confidence signals can be leveraged not only for detection, but also for effective inference-time control of model behavior.

Does a language model merely predict tokens, or does it understand what it says? We make this question measurable by defining "understanding" through the lens of no-arbitrage. A model understands a vocabulary to a certain degree if a computationally bounded trader cannot extract guaranteed profit by betting against the model's probabilities on logically related claims (a "Dutch book"). We establish three theoretical results: first, because full logical coherence is computationally intractable, understanding is inherently graded, not absolute. Second, we prove that the exact optimum of standard next-token prediction is inherently incoherent across different question formats; the flaw lies in the training objective, not the architecture. Third, we show that uncertainty accumulates predictably along reasoning chains, making unjustified overconfidence an arbitrage opportunity in itself. To address this, we introduce Arbitr, a training framework where an adversarial trader penalizes the model for logical inconsistencies, paired with a calibration anchor to prevent uninformative collapse. Across five pre-registered experiments on Qwen2.5 and Phi-3.5 models, we demonstrate that standard models are highly exploitable across different phrasings. Arbitr reduces this exploitability by orders of magnitude without sacrificing task accuracy, and the effect successfully transfers to unseen logical patterns and new model families. Crucially, we uncover a scaling illusion: at 7B parameters, near-zero measured incoherence often coincides with extreme, unjustified confidence. We conclude that while Arbitr enforces rigorous logical consistency, coherence is a necessary condition for knowledge, but not a sufficient one

Recursive reasoning models apply a small shared Transformer block many times to refine a latent state. This gives them large effective depth with few parameters and makes them strong on algorithmic tasks. Such compact solvers are natural candidates for tools that an LLM can call on narrow algorithmic subproblems. However, existing models such as HRM, TRM and URM differ in architecture, gradient propagation and training procedure simultaneously. This makes it hard to tell what drives their performance, and their optimization is still poorly understood and often unstable. In this work we address both of these gaps. First, we study these questions under a unified experimental pipeline spanning six algorithmic domains. Individual controlled ablations are performed on representative domains, while the resulting recipe is evaluated across the full suite. The study reveals a surprisingly simple recipe for stable and generalizable recursive reasoning: an intermediate gradient horizon, large physical batches and controlled updates of the recurrent state. An explicit hierarchical architecture is not needed. Second, we combine these findings into a stable 13.6M-parameter model that achieves the strongest overall performance among the evaluated recursive baselines, with particularly large gains on out-of-distribution generalization. It raises Arithmetic OOD accuracy to 71.2%, from 36.2% for the strongest baseline, while reaching 98.41% on Sudoku and 59.5% pass@2 on ARC-AGI-1. Our results show that, within the recursive architectures studied here, performance depends strongly on how recurrence is optimized and stabilized. More broadly, it shows how AI systems can be improved by optimizing their components one at a time.

While Abstract Meaning Representation (AMR) has historically improved performance on a range of NLP tasks, the benefit---or lack thereof---of AMR augmentation for modern LLMs is thus far unclear. In this paper, we attempt to reproduce recent work that reported substantial downstream gains from AMR augmentation, finding that these are likely due to specific choices in the experimental settings used: using a consistent and unified protocol for hyperparameter selection, we observe that text-only baselines consistently match or exceed the performance of AMR-augmented models. To investigate this null result, we introduce a perplexity-based probe measuring the degree to which AMR provides an LLM with supplemental relational knowledge not already available to the model. We find that AMR augmentation does not help LLMs improve their understanding of relational content in the sentence, indicating that augmenting these models with AMR offers no clear benefit on downstream tasks.

Large language models have achieved remarkable capabilities across diverse domains, yet their safety alignment remains vulnerable to jailbreak attacks. In this work, we identify a previously underexplored failure mode - safety generalization lag - where alignment trained predominantly on natural language fails to transfer to the code domain. We show that this lag induces a code-completion blind spot, allowing malicious intent embedded within syntactically valid code to evade safety mechanisms. To exploit this vulnerability, we propose CodeMimicry, a fully automated black-box jailbreak framework that generates structured, object-oriented code prompts to induce harmful outputs via code completion. Experiments on 8 state-of-the-art commercial LLMs demonstrate that CodeMimicry achieves a 96.25% attack success rate with 1.51 queries on average, significantly outperforming both template-based and optimization-based baselines. Beyond empirical performance, we provide a mechanistic analysis of code-based jailbreaks through latent space representations, including projection onto refusal-related directions and activation steering. This analysis offers an explanation of how CodeMimicry bypasses safety mechanisms in code-related domains. Our findings reveal a weakness in current safety alignment and highlight the need for robust alignments in structured domains such as code.

Chain-of-thought (CoT) traces often serve as a proxy for how Large Language Models (LLMs) arrive at their answers. However, growing evidence shows that models' CoT often fails to reflect their internal computations and can be changed without affecting their final answers. In this work, we measure and improve the alignment between the reasoning described in an LLM's CoT and what it computes internally. We propose CoT-Interpretability Alignment (CIA), a metric that measures the agreement between a model's CoT traces and its internal reasoning strategies as detected by interpretability tools. We evaluate CIA on three tasks (two-hop question answering, hint intervention, and integer multiplication) across three LLMs, finding that LLMs exhibit limited alignment across all tasks (44.8-75.9%). We then experiment with improving CIA via post-training, setting both the task accuracy and parametric faithfulness signals as a reward. Experiments show that we can substantially improve CoT parametric faithfulness while maintaining or improving the task accuracy. We provide rich analysis, such as their generalization patterns. Our work provides both a framework for auditing CoT parametric faithfulness and a pathway toward making models' explicit reasoning more trustworthy. Code and data are available at https://github.com/yihuaihong/CIA-minimal-repro.

Large language models (LLMs) have been rapidly improving in long-context tasks, powered by Chain-of-Thought (CoT) reasoning. However, the internal mechanisms underlying this improvement remain unclear. We investigate these mechanisms through a needle-in-a-haystack (NIAH) counting task, where an LLM is asked to count the number of records dispersed in a long text. Across twelve model comparison groups, Thinking (or reasoning) improves counting accuracy over Non-thinking, with pronounced gains at larger counts. This motivates our mechanistic analysis, which identifies two contrasting mechanisms: (i) broad retrieval, where Non-thinking models broadly attend to multiple needles; (ii) targeted retrieval, where Thinking models use enumeration in CoT traces to successively retrieve needles. Targeted retrieval concentrates attention on individual needles and is accompanied by more compact internal representations. Moreover, causal intervention analysis suggests that Thinking models use the CoT trace to maintain and update an internal counter as needles are successively retrieved, even without explicit numbering. In small controlled experiments, both retrieval mechanisms and counter states emerge under standard autoregressive training. Together, our results connect long-context retrieval with representation geometry of counting, supporting a state-tracking account of CoT reasoning.

Role-playing prompting has become a popular yet simple technique for improving LLM reasoning and output quality. However, whether it consistently boosts performance across diverse domains remains unclear, as systematic validation is lacking. To fill this gap, we run multi-model, cross-domain, and multilingual experiments on MMLU and MMLU-Redux. We find that gains from role-play prompting depend heavily on model capacity, knowledge domain, and prompt language. Drawing on metacognition theory, we propose the persona-related cognitive alignment hypothesis: role-play works only when the LLM correctly grasps the designated persona and its associated knowledge domain. We test this hypothesis through persona information richness ablation, layer-wise entropy divergence analysis, and latent thought-space deflection observation. To reduce persona cognitive bias and stabilize role-play performance, we propose Mixed-Language Concatenate Prediction (MLCP), a simple, training-free, and efficient multilingual prompt concatenation strategy. It aggregates semantically equivalent role prompts to enrich complementary representational cues. Extensive experiments show that MLCP consistently outperforms vanilla role-play prompting across all tested LLMs.

Chemical reaction-condition optimization — choosing the catalyst, ligand, solvent, reagent, temperature, time, and atmosphere that jointly maximize yield and stereoselectivity — is a central, judgement-laden subtask of organic methodology research that large language models are increasingly expected to support. Yet existing chemistry benchmarks evaluate reaction-class labelling, retrosynthesis, or SMILES manipulation, and do not ask models to read a real condition-screening table and pick the best set. We introduce RxnOptBench, a benchmark whose every option and precedent is a real wet-lab entry mined from the optimization tables of organic-methodology papers published in 2025, graded by a continuous relative score derived from a declared headline utility that combines reported yield with enantiomeric excess (ee), diastereomeric ratio (dr), and regioisomeric ratio (rr), and equipped with a paired precedents-vs-no-precedents design that isolates in-context use of literature evidence from parametric memorization. Across nine frontier LLMs and three Chemistry LLMs, even the best models leave substantial headroom: chemistry-specialized models fall to the random-baseline floor on multi-axis selection, while open-weight models have closed most of the gap to proprietary frontier models. We release the final human-reviewed benchmark test set and evaluation code.

Maximum Likelihood Reinforcement Learning (MaxRL) targets prompt-wise log-success and has shown strong performance on reasoning tasks. Under finite rollout budgets, however, the estimator used by MaxRL attenuates each prompt's likelihood gradient by a factor that depends on its success probability and rollout count. Under uniform rollout allocation, the common rollout count fails to compensate for success-dependent attenuation, leaving low-success prompts more strongly attenuated and distorting their relative contributions to the expected aggregate gradient. We introduce SERA (Scale-Equalized Rollout Allocation), which redistributes a fixed rollout budget to approximately equalize these finite-rollout scaling factors. Building on our theoretical analysis of how finite rollouts distort prompt-wise likelihood gradients, we formulate the allocation as a fixed-budget max--min problem, derive a waterline solution to its continuous relaxation, and introduce a multiplicity correction to remove the additional prompt weighting induced by heterogeneous rollout counts. Experiments show stronger alignment with exact likelihood gradients in a controlled ImageNet setting and improved multi-sample solution coverage over MaxRL on maze navigation and mathematical reasoning under matched training rollout budgets.

The strong generalization performance of on-policy post-training paradigms has motivated studies of their parameter update behaviors. However, these studies treat the observed behaviors only as byproducts in on-policy training, overlooking their potential to serve as optimization principles for improving the generalization of other paradigms such as supervised fine-tuning (SFT). To address this limitation, we investigate whether there exists a specific on-policy update behavior that can achieve such improvements. First, our analyses reveal that SFT updates parameters along consistent directions, while the on-policy paradigm continuously adjusts the direction during training. This difference inspires us to focus on the cumulative update direction of each parameter as a promising behavior. Then, we evaluate its effectiveness for improving generalization by proposing On-Policy direction-constrained Supervised Fine-Tuning (OPSFT), which constrains SFT updates to the direction identified by on-policy paradigms. The strong performance of OPSFT indicates that the generalization advantage of on-policy paradigms can be transferred to SFT through the parameter update direction. Once such a direction is identified, even SFT can generalize with its updates constrained to this direction. This finding offers two practical benefits by combining the strong generalization of on-policy paradigms with the advantages of SFT, including the high training efficiency and ability to leverage high-quality trajectories. For efficiency, we identify update directions that support strong generalization using a few on-policy training steps, and subsequently apply OPSFT to achieve high training efficiency. For leveraging high-quality trajectories, OPSFT can utilize these trajectories to continue improving a post-trained model along its update direction without disrupting the ability learned from on-policy training.

Large language models (LLMs) exhibit strong general capabilities that mechanistic interpretability has attributed to sparse computational circuits. However, existing circuit studies emphasize preserving functionality or explaining safety, leaving the mechanisms underlying failures across a broader range of tasks largely unexplored. Extending circuit analysis from abilities to errors, we explore the perspective that such failures may likewise arise from erroneous internal computations and that targeted tuning of the corresponding parameters can correct such errors while largely preserving other capabilities. Motivated by this insight, we introduce RESCUE (Reasoning-Error Sparse-Circuit Uncovering and Editing), a framework that localizes error-associated circuits and surgically repairs them for performance enhancement. General tasks typically involve multi-step reasoning and long-form generation, where early deviations can cause prefixes to drift from supervised references, leading SFT-based mask optimization to overlook circuits involved in generation-time errors. RESCUE therefore refines these masks through reinforcement learning with multiple masked-model rollouts, improving their relevance to observed task failures. Finally, RESCUE introduces a pruning technique and precisely fine-tunes error circuits to correct task failures, thereby translating error localization into a sparse and targeted model update. We validate RESCUE on heterogeneous repair sets across two domains: (1) mathematical reasoning, identifying a math error circuit of 1.40% density whose repair raises accuracy from 6.0% to 75.5%; and (2) medical QA, where a similarly compact 1.44% circuit improves repair-set accuracy from 0% to 81%. Our code is available at: https://github.com/chuanpupig/RESCUE.

Video generation models have demonstrated emerging zero-shot capabilities for visual reasoning, perception, and other vision tasks. However, diffusion-based video generation is inherently stochastic, while many downstream vision tasks are deterministic. Motivated by the effectiveness of self-consistency in chain-of-thought reasoning for large language models, we investigate whether self-consistency can similarly improve diffusion-based video reasoning. We first introduce a training-free test-time scaling method that samples multiple video generations and aggregates their predictions through self-consistency. Specifically, we aggregate extracted paths, locations, or masks from multiple rollouts into a consensus prediction. To reduce the inference overhead of multi-rollout generation, we read out predictions early in the denoising trajectory, which preserves consensus quality while reducing denoising steps by more than half. We further propose Rejection Fine-Tuning (RFT) to distill consensus predictions into the video generation model. The resulting model internalizes the benefit of multi-sample consensus and requires only a single generation at inference time, while substantially outperforming the original model. Experiments on three tasks, including maze solving, visual search, and referring segmentation, show that both our self-consistency inference and consensus distillation dramatically improve video-based perception and reasoning, without requiring ground-truth videos or task-specific verification. For visual search, self-consistency raises task accuracy from 48.4% for a single generation to 99.0%. The distilled model retains much of the consensus benefit with a single rollout. For 4-by-4 maze solving, consensus-based training improves the single-generation strict success rate from 72.0% to 84.0% with the same inference latency.

We study the learning dynamics of fine-tuning a policy model on self-generated and reward-weighted data, with particular focus on a generalized version of REINFORCE — referred to as RE(S) — that updates the rollout distribution once every $S \ge 1$ gradient steps. Prior work in bandits and reinforcement learning has developed rich theory for policy gradient methods, and on-policy sampling (i.e., a small $S$, ideally $1$) is often viewed as crucial to their success; yet in prominent application like post-training large language models, reward-guided self-training has proved to be effective even when the rollout distribution is updated infrequently, but theoretical understanding remains limited for the convergence properties of these off-policy methods. To bridge these gaps, we develop a unified theory for RE(S) that covers the full spectrum of $S \ge 1$: it can be interpreted as a stage-wise optimization process, where each stage takes $S$ gradient steps for minimizing the Kullback-Leibler distance to a fixed reward-weighted rollout distribution. For multi-arm bandits with softmax policies, our in-depth analysis and numerical experiments reveal three key findings: (1) for any fixed $S$, RE(S) enjoys global convergence to the optimal policy as the number of rollout distribution updates $B = \lfloor T / S \rfloor \rightarrow \infty$, where $T$ denotes the number of gradient steps; (2) we prove tight two-sided bounds showing that the suboptimality gap of RE(S) achieves an asymptotic $Θ(1 / T)$ convergence rate, while $S$ only affects the length of a burn-in phase; (3) when initialized at a weak policy with a small optimal-action probability, RE(1) gets trapped around suboptimal policies for a long period, whereas RE(S) with a suitable $S$ avoids the detour and achieves significantly faster convergence to the global optimum, highlighting the benefits of off-policyness in this case.

Unsupervised tabular anomaly detection (TAD) aims to identify anomalous rows in tabular data using normal training samples. While conventional methods rely on dataset-specific training and configuration search, recent tabular foundation models (TFMs) enable zero-shot anomaly detection on unseen datasets via in-context learning. Most TFM-based approaches, however, require anomaly-specific pretraining from scratch, making detection inherently dependent on synthetic TAD-specific priors and costly to update. Some approaches instead repurpose pretrained general-purpose TFMs for TAD to avoid this burden, but rely on computationally expensive formulations with restrictive anomaly inductive biases. In this work, we introduce TaskBridge, a new framework that efficiently repurposes pretrained general-purpose TFMs for unsupervised TAD by constructing virtual supervised tasks that directly recast anomaly detection as supervised in-context inference of TFMs. The resulting virtual tasks induce predictive structures under which normal queries and their target pairs receive high support, whereas anomalies tend to violate the induced structures and receive lower support, providing direct anomaly evidence. Across 790 real-world datasets, TaskBridge consistently outperforms 30 baselines, including state-of-the-art TFM-based approaches, without anomaly-specific TFM pretraining or dataset-specific model optimization.

Achieving strong performance with graph neural networks (GNNs) typically requires training and hyperparameter tuning for each dataset, incurring repeated costs and effort. Graph in-context learning (ICL) avoids this by using a single pretrained model to predict unknown node labels directly from labeled context nodes. Existing approaches, however, rely on dense attention across nodes, making inference increasingly expensive as graphs grow. In this work, we present Ephris, a new graph in-context learner built on sparse message passing, scaling linearly with the number of node-feature entries and graph edges. Ephris is pretrained entirely on synthetic graphs generated from structural causal models with diverse graph structures and relational dynamics, exposing the model to varied dependencies among topology, features, and labels. We evaluate Ephris on 51 node-classification datasets against 15 extensively tuned GNNs and existing graph ICL methods under both high- and low-label train/validation/test splits. Across both settings, Ephris ranks first on all four aggregate measures: Elo, improvability, average rank, and accuracy. Its inference cost remains comparable to training a single GNN once, while being over 10 times faster than previous graph ICL models. Together, these results advance the performance-runtime Pareto frontier, demonstrating that strong graph ICL does not require dense attention. Code and model weights are available at https://github.com/nums-ai/ephris.

Multimodal Large Language Models (MLLMs) consistently struggle with fine-grained visual counting, yet the underlying causes remain poorly understood. In this work, we present a mechanistic analysis of this failure mode, identifying two critical bottlenecks inherent to the global attention pipeline of MLLMs. First, we reveal an individuation bottleneck stemming from image patchification: because Vision Transformers process patches independently, they struggle to group fragmented geometric features across boundaries into distinct object representations. Second, we identify a collapse in the subsequent counting aggregation process, where representation separation rapidly diminishes as numerosity increases due to attention compression. Identifying and formalizing these twin bottlenecks constitutes our first major contribution. To overcome them, we propose ConvStack, a lightweight architecture that operates directly in the visual token space to explicitly aggregate and inject local spatial structures via zero-initialized residual connections. By explicitly addressing the individuation bottleneck, ConvStack provides unambiguous geometric evidence for downstream aggregation. Remarkably, by fine-tuning exclusively on counting tasks, the model achieves substantial improvements in dense object counting and broader spatial understanding benchmarks, without compromising on general visual capabilities.

Handwritten Text Recognition (HTR) systems have become an indispensable tool for the digitization of historical documents. Not only do they cut down time and cost, but they also allow democratizing access and processing of their contents by generating their transcripts. However, literature in HTR currently focuses mostly on specialized models that require large amounts of annotated samples to achieve satisfactory performance. We explore the use of In-Context Learning with pre-trained Vision-Language Models (VLMs) to create a transcription pipeline without updating the model's parameters. We then evaluate this pipeline across multiple collections and models, and demonstrate that general-purpose VLMs can be effectively taught how to transcribe handwritten text from images. To assess how our observations may translate to practical applications, we evaluate the performance in a Cross-Domain (CD) scenario, where context examples are drawn from a different collection than the query image. Results in both the controlled In-Domain (ID) scenario and the realistic CD scenario follow the same patterns. First, as context size grows, the error range is expected to narrow towards the average performance. Thus, larger context sizes sacrifice the performance of the oracle-best sampling for lower expected error rates. The results obtained show that, without any parameter updates, this methodology has strong potential to compete with traditional HTR in the presence of domain shift. Moreover, we show and argue that some context samplings work better than others and suggest more effort should be put into finding an ideal sampling method in future work.

Test-time compute scaling has emerged as a cornerstone of advanced machine reasoning, yet performing iterative deliberation directly within continuous latent representation spaces reveals a catastrophic pathology: the Deliberation Drift Cliff. While unconstrained recurrent latent models achieve initial reasoning gains at short horizons (K <= 4), their reasoning collapses when extrapolated to deeper thinking steps (K >= 16), dropping by 22% to 62% across standard logical benchmarks. We resolve the trilemma among expressivity, Lyapunov stability, and computational efficiency in test-time latent reasoning through a 22-round empirical and theoretical investigation. We demonstrate that strictly conservative scalar potential gradient flows suppress long-range drift (cliff 3.40%) but bottleneck peak reasoning accuracy at 32.73%, whereas unconstrained rotational flows achieve high symbolic expressivity (82.33%) but suffer a severe 36.87% drift cliff. To resolve this geometric duality, we establish Port-Hamiltonian Latent Deliberation (PH-LD) and propose the Direct-Gradient Pure-Tensor Helmholtz-Hodge Decomposition (DG-HHD). DG-HHD parameterizes the attracting flow as a tangent projection tensor network while orthogonally decoupling non-zero circulation (Hodge machine error 1.65e-17, contraction error 5.55e-17), eliminating runtime autograd dependencies to achieve 1.84x vector field and 2.09x RK45 rollout speedups. In a 15-arm symmetrical Pareto benchmark, DG-HHD achieves 58.67% peak accuracy (+25.94% absolute gain over conservative HHD) and retains 35.27% at K=32. Transferred to small language model (SLM) multi-hop causal reasoning, DG-HHD delivers monotonic compute scaling (49.33% to 51.56%) and suppresses out-of-distribution drift (cliff -0.66%). All 30 Level 0 deterministic invariants are certified.