LLM 理论进展

Large Reasoning Models (LRMs) have shown remarkable reasoning capabilities, yet they still suffer from overthinking, generating redundant reasoning steps which incur substantial token consumption. Existing methods, such as suppressing reflective keywords or forcing shorter reasoning lengths, attempt to mitigate this issue but inevitably truncate necessary steps and induce underthinking, thereby compromising performance. To address this dilemma, we investigate the latent representations and observe that efficient reasoning steps naturally cluster into a concentrated region in latent space, while those deviating from this region tend to produce verbose sequences. To leverage this, we keep reasoning focused within this region via a quadratic program which projects deviating hidden states back into the region. Then we propose a novel training-free framework to achieve efficient reasoning that reduces token generation costs without sacrificing performance. Extensive experiments conducted on four models ranging from 1.5B to 14B, and across six benchmarks in math reasoning, coding, and scientific QA, validate the effectiveness of our method, up to a 12.1% improvement in accuracy while reducing generated tokens by 11.8% to 52.8%. Codes are available at \href{https://github.com/hzn18/Opt4Reasoning}{https://github.com/hzn18/Opt4Reasoning}.

We introduce GlyphBench, an environment suite for reinforcement learning (RL) post-training of language-model agents, with over 360 tasks spanning diverse games. GlyphBench renders spatial observations as two-dimensional Unicode grids and connects training, evaluation, and trajectory replay through a unified interface designed to support efficient and reproducible research. We use GlyphBench to study how observation interfaces, reasoning effort, and agent harnesses affect performance, and how RL configurations shape learning dynamics. Our results show that glyph observations outperform native text and pixels in our Craftax experiments, with further gains on several BALROG environments. RL on 100 GlyphBench tasks improves Qwen3.5-4B on held-out Reasoning Gym problems, reaching 63.48% accuracy and outperforming the base model, a math-trained baseline, and a code-trained baseline. These experiments provide empirical evidence that reasoning gains from gameplay can yield stronger transfer than math or code. Together, these results highlight GlyphBench's value as a testbed for systematic research on how language-model agents learn, interact, and generalize.

Reinforcement learning (RL) has become a key paradigm for enhancing the reasoning of large language models, yet the high dimensionality of parameter updates makes its training dynamics hard to analyze. We study reinforcement learning with verifiable rewards (RLVR) and use vector steering to identify a low-dimensional effective manifold in activation space associated with RL-induced gains. We uncover two geometric properties. (1) Effective Manifold Capacity: the capacity needed to reproduce RL gains can be very small but is not infinitely compressible; at extremely low capacity, intervention dimensionality and input-dependent expressiveness become key constraints, and this requirement varies with injection depth. (2) Control Manifold Separation: effective control directions lie mainly in the low-variance complement of the activation principal subspace. Within a task and base model, the learned geometry stays largely consistent across training configurations, and across tasks geometric alignment correlates with capability transfer. Experiments on 5 LLMs and 6 verifiable-reward tasks support these findings. We then propose Alpha-Stabler, a plug-and-play framework with a Predictor that monitors principal-subspace intrusion for early collapse warnings, and a Controller that removes the principal-subspace component of activation gradients during backpropagation while preserving the orthogonal complement. Alpha-Stabler stabilizes training for 2,000 steps and consistently improves RL gains, offering practical insights for robust post-training. Code: https://github.com/caiyuchen-ustc/On_Policy_Vector_Training

Physical interactions can create future hazards that are not apparent from the robot's current geometric surroundings. We present a framework termed Predictive Semantic Safety (PSS), which connects visual physical reasoning to backup-based safety filtering. A vision-language model (VLM) predicts physical events and their timing or directly predicts object displacements. An explicit motion model converts event hypotheses into object trajectories. Split conformal prediction calibrates position errors jointly across specified objects, observation times, and future times; geometric shape bounds convert the resulting position regions into predicted object occupancy. PSS evaluates a prescribed backup maneuver against this occupancy and derives input-affine constraints for minimally modifying the nominal input while preserving backup feasibility under the robot dynamics and input limits. MuJoCo experiments with a Unitree Go1 consider falling fixtures, impact-driven support loss, and contact propagation. PSS achieves a safe episode rate of 99.3%, compared with 43.3% for a Backup Control Barrier Function baseline that only uses current obstacle geometry.

In agentic AI systems, frozen foundation models are increasingly deployed as closed-weight API endpoints, making downstream adaptation possible only through the inputs and inference procedures surrounding the model. As a result, for each input query, two coupled decisions largely determine both answer quality and token cost: what evidence to provide and how much reasoning budget to allocate. Fixed defaults along these axes are often suboptimal, misallocating support form or reasoning depth on roughly 80% of queries in our analysis. To address this challenge, we propose FORGE, a unified framework for adapting frozen models through per-query routing over a joint action space that spans both support form and thinking depth. Under an entropy-regularized, cost-aware utility objective, we derive a closed-form Boltzmann routing target and instantiate the policy as a lightweight 269K-parameter factorized router. The routing policy is trained around the frozen host, without any weight access, through a three-stage pipeline: offline arm enumeration, supervised Kullback-Leibler (KL) distillation from the Boltzmann target, and Group Relative Policy Optimization (GRPO) refinement with host feedback. Across 5 knowledge-intensive benchmarks and 8 frozen backbones ranging from 7B to 671B parameters, FORGE improves accuracy at 42-45% lower token cost on both main hosts, transfers zero-shot across hosts at lower token cost, and composes with intrinsic thinking budgets where available.

Large language models receive limited explicit training in reasoning about runtime program states. We study whether training models to reason about runtime program states improves downstream software-engineering capabilities. We introduce two complementary program-state reasoning tasks. Buggy input-output reasoning requires a model to generate a concrete input that exposes a behavioral difference between a buggy program and a hidden correct implementation and to predict the resulting execution behavior. Precondition-postcondition reasoning requires an agent to symbolically characterize a bug-triggering precondition, predict the expected postcondition, explain their causal connection, and instantiate this reasoning as an executable regression test. By incorporating these two tasks into a staged post-training pipeline, we develop Comet-9B, a 9B language model based on Qwen3.5-9B Base. We evaluate the resulting checkpoints on repository-level patch generation, regression-test generation, and security PoC generation. Adding both program-state reasoning tasks to supervised fine-tuning (SFT) on issue resolution improves success rates by 7.25 percentage points on SWE-bench Pro and 9.70 points on SWT-Bench Verified. Sequential reinforcement learning on the two tasks yields further gains of 7.25, 26.79, and 4.67 percentage points on SWE-bench Pro, SWT-Bench Verified, and CyberGym, respectively. Despite having only 9B parameters, Comet-9B achieves a score comparable to the reported GPT-5.2 result on SWE-bench Pro and matches the reported success rate of a GPT-4o-based agent on SWT-Bench Verified.

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.

Controlling persona in large language models (LLMs) at inference time is important for role-playing, personalized dialogue, and social simulation. Recent methods extract persona vectors from the model's activation space and apply Euclidean operations---addition, scaling, and linear interpolation---under the linear representation hypothesis. However, these methods themselves report systematic failures: non-orthogonal trait dimensions, asymmetric ceiling and resistance effects, and significant deviations in multi-trait composition, suggesting that the linear isotropic assumption does not hold. We propose PersonaManifold, a framework that models persona representations as points on a curved, low-dimensional Riemannian submanifold in activation space. We estimate the manifold's intrinsic geometry---local metric tensors, geodesic distances, and Ollivier-Ricci curvature---and introduce geodesic steering, which interpolates between personas along manifold geodesics rather than Euclidean straight lines. We also propose the Behavioral Similarity Triplet (BST) benchmark, which automatically generates situational questions grounded in six established psychological constructs and defines persona similarity through behavioral responses rather than self-report questionnaires. Experiments on three open-source LLMs show that persona activations form a manifold with heterogeneous curvature, geodesic distance predicts behavioral similarity more accurately than Euclidean alternatives with independent contributions from anisotropy and curvature, and geodesic steering produces more coherent intermediate personas on both our BST benchmark and external evaluations, with the advantage concentrated in high-deviation regions where the manifold deviates most from flatness.

Misinformation on social media remains a critical problem, and more and more people settle it by asking a language model instead of a fact checker. Whether models judge such claims reliably is debated; whether they judge them equally well in every language people ask in has gone almost unasked. We test eight models from five families, 3B to 70B, on 1,500 encyclopedic factual claims that exist in identical form in eight languages. English is judged better than every other language on every model, and the gap is widest on the smallest ones, where Llama-3B on Arabic is no better than guessing. Existing remedies retrain on more multilingual data or fit an unconstrained map between language representations, and neither asks whether the model already holds the answer and simply fails to say it. It largely does: a linear probe recovers the truth from the very activations the model fails to express. We propose RoSh, a per-language shift and rotation of the residual stream, computed in closed form at three layers, with no training and no weight modified. It improves every model and closes 75% of the gap on average, helping most where the model was worst: Arabic on Llama-3B goes from chance to nearly the English level, and a fifth fewer of the claims answered correctly in English are lost in translation. What remains is no longer a read-out failure: afterwards the head recovers as much of what is encoded outside English as it does in English. An unconstrained map fitted on the same pairs falls below the untouched baseline, so the orthogonality constraint is doing the work, and every model clears a scrambled-correspondence control and ten further controls. On the two benchmarks of the closest inference-time method, latent-space intervention, run with its own data and metric code, RoSh's gains are five to thirteen times larger.

We develop an information-theoretic framework for generalization in next-token prediction under temporally dependent data. We consider independent trajectories generated by finite-memory Markov processes and distinguish algorithmic dependence, quantified by mutual information, from temporal dependence, characterized by mixing. For cross-entropy loss, we derive an expected generalization bound using the Donsker--Varadhan variational representation and a McDiarmid-type concentration inequality for Markov chains. A refinement captures the joint effect of context length and temporal mixing through the mixing properties of the history-state process. We then extend the bound through a rate--distortion formulation, replacing mutual information with the minimum information rate required to represent the learned model within a prescribed distortion in the generalization gap, yielding informative guarantees for deterministic algorithms over continuous hypothesis spaces. For margin-based prediction, we derive explicit bounds for linear and self-attention next-token predictors via noisy low-dimensional compression, revealing the roles of context length, model complexity, sample size, margin, and temporal mixing. Experiments on TinyStories and ETTh2 show that longer contexts can reduce both training and test losses, but typically reduce training loss more, enlarging the generalization gap. A complementary ETTh2 analysis identifies an effective predictive-memory scale near 24 hours, with no statistically supported improvement beyond this scale, offering a plausible explanation for test-performance saturation at larger contexts.

Recent studies suggest that large language models encode emotion concepts as structured internal representations, but most existing work focuses on text and a single architecture. Therefore, we ask, do emotion concepts generalize across sources, modalities, and architectures in vision--language models (VLMs)? To address this, we construct CMES (Cross-Modal Emotion Stimuli), a multi-source collection of emotion-conditioned stories, real facial expressions, synthetic portraits, and synthetic emotion-evoking scenes. For each stimulus source, we extract a separate set of six Ekman emotion vectors from each of three VLMs. We report four main findings as follows: 1) Image-derived emotion vectors form a low-dimensional geometry similar to that of text-derived vectors. Valence is relatively stable across sources, while arousal varies more. 2) Text- and image-derived emotion vectors have modest cosine similarity but still show held-out cross-modal correspondence. Text-derived vectors can also steer image interpretation. 3) Cross-architecture correspondence remains even when native cosine is near zero. Transformations estimated from generic ImageNet activations recover both correspondence and causal transfer without using the six emotion vectors or their labels. 4) After aligning representations across architectures, we construct a shared emotion subspace that preserves affective geometry and selective steering effects. The corresponding consensus emotion vectors also generalize to a held-out fourth architecture at two model sizes. These results suggest that emotion representations can share relational structure and causal effects across sources, modalities, and architectures, even when individual vector directions differ.

Vision-language models (VLMs) can answer simple visual questions, but often struggle when one question requires several visual judgments. We study this gap with controlled tasks for feature binding, numerosity, spatial relations, and amodal completion, together with a Composite task that combines them. Matched counterfactual image pairs isolate changes in the visual evidence needed to answer. Across four models, direct answers, hidden-state readouts, and state interventions show that the individual judgments can be made without explicit reasoning and that intervening on the corresponding states can affect the answer. During reasoning, the Composite answer becomes decodable from hidden states and usable from shortened traces, often before the model stops on its own. We train a small detector to predict this readiness and stop reasoning at that point. On MMStar and RealWorldQA, this reduces mean reasoning tokens by 79.1% and 74.5%, while average accuracy rises by 3.13 and 3.30 percentage points, respectively. These findings connect the internal development of answer readiness to a practical rule for allocating reasoning computation.

Humans often solve spatial problems by mentally simulating visual transformations. In contrast, conventional vision-language models (VLMs) reason primarily through language. We investigate whether VLMs can solve spatial problems by reasoning with both text and generated visual states. To this end, we introduce WM-VLM, which equips a pretrained VLM with a lightweight world model branch for generating intermediate visual states. Our two-stage training first teaches the model to generate the next visual state and then to use that state for reasoning. We programmatically construct spatial reasoning tasks with verifiable intermediate visual states. These tasks allow us to evaluate how well the model generates visual states and how much it relies on them to answer the question. On 2D and 3D mental rotation tasks, WM-VLM consistently outperforms the supervised fine-tuned backbone, with gains of up to 39.25 percentage points. Ablations suggest that these gains depend on the generated visual states, as removing or corrupting them sharply reduces performance. Together, these results suggest that internal world models offer a promising path toward VLMs that reason in both language and visual space.

Reinforcement learning with verifiable rewards (RLVR) improves the reasoning capabilities of large language models but incurs substantial costs from rollouts and policy updates. Online prompt selection improves efficiency by using per-prompt Bayesian posteriors to predict difficulty and prioritize informative prompts. However, existing methods overlook how reliably learning signals are extracted from sampled responses. In GRPO, a response's advantage depends on both its own outcome and the randomly sampled outcomes of its peers through group normalization. Our theoretical and experimental analyses show that uncertainty in group composition introduces composition noise, a non-vanishing variance component that imposes an irreducible lower bound on gradient estimation error and impairs downstream prompt selection. We propose MaPP (Marginalized Posterior-Predictive), a unified framework for data-efficient RLVR that denoises response-level advantage estimation and improves prompt selection using a shared Beta posterior. For each response, MaPP replaces the standard group-relative advantage with a composition-invariant intrinsic advantage through closed-form Beta-Binomial marginalization. The resulting posterior-predictive estimator has an error that provably diminishes as the posterior concentrates. Using the same posterior, MaPP derives an uncertainty-aware prompt selection score to improve data efficiency without additional rollout cost. Experiments on mathematics, planning, and visual geometry across five model backbones show that MaPP consistently outperforms GRPO and strong selection baselines, achieving up to +2.45 average accuracy improvement over the strongest baseline under the same rollout budget and setting a new state of the art.

Despite substantial progress across downstream applications, vision-language models (VLMs) remain susceptible to language bias, often prioritizing linguistic cues over visual evidence and consequently producing incorrect predictions. Prior studies have proposed various approaches to understanding and mitigating language bias in VLMs, yet their findings often conflict due to the difficulty of tracing how language bias propagates within black-box VLMs. Building on the word completion task, we trace how language bias propagates through VLM inference by (1) proposing a diagnostic framework that decomposes the inference process into four distinct yet interdependent stages to trace the propagation of language bias; and (2) examining how two key factors underlying language bias, i.e., linguistic priors and cross-modal coverage, evolve across these stages and ultimately give rise to incorrect predictions. The linguistic prior captures the strength of statistical bias induced by the language model component of a VLM and represents the origin of language bias, whereas cross-modal coverage measures the extent to which linguistic cues cover the visual content. By decomposing inference into four stages and characterizing the interplay between linguistic priors and cross-modal coverage across these stages, we propose a systematic framework for tracing the propagation of language bias throughout the inference process; and uncover the underlying mechanism of language bias by revealing the interplay between linguistic priors and cross-modal coverage.

While Large Reasoning Models (LRMs) excel at complex reasoning, alignment through reinforcement learning often induces systemic overconfidence. In production environments, where logits may be unavailable, robust black-box uncertainty quantification (UQ) is essential for trustworthiness and safety. Focusing on question-answering for LRMs, we show that existing black-box methods, such as paraphrase-based self-consistency and confidence verbalization, offer little to no improvement over simple repeated sampling, suggesting that alignment suppresses useful output variability. We introduce prompt-level relaxation operators that broaden the model's effective output distribution by approximating the effect of an optimal policy obtained with a stronger KL-regularization parameter, hence closer to the reference model. Theoretically, we demonstrate that relaxation improves calibration. We propose Jailbreak for Uncertainty (J4U), a jailbreak-derived technique for UQ that empirically reproduces the behavioral signatures predicted by our relaxation theory. Across 3 datasets and 4 LRMs, including a closed-source production model, J4U's improvement over repeated sampling achieves statistical significance in up to 6 times more LRM-dataset-metric settings than the strongest black-box UQ state-of-the-art baseline we evaluate, with average ECE reductions up to 5 times larger. These results provide a practical tool for UQ in black-box LRM deployment.

Sparse autoencoders (SAEs) are an important tool for mechanistic interpretability, but interpreting their many features remains challenging. Existing methods characterize input-side activation patterns and output-side intervention effects, yet often leave their functional connection implicit, while input-side evidence collection typically relies on costly large-corpus scans. We introduce functional interpretation, which characterizes an SAE feature as a mapping from its activating input semantics to its output effects under intervention, and present Dual-End Agentic Feature Interpretation (DAFI), an agent that actively gathers evidence and refines input-side, output-side, and functional interpretations through component-specific feedback. Its short-context token probing enables on-demand activation evidence collection without a full corpus scan. On GemmaScope, DAFI improves Input score by 13.1 percentage points over SAGE and Output score by 38.9 points over Token Change, while being substantially more token-efficient than a general-purpose coding agent. Skills distilled from successful refinements raise the held-out joint pass rate from 58.0% to 92.0% and improve both interpretation quality and efficiency when transferred to a new model-SAE setting. Across features with reliable endpoint interpretations, 70.7% exhibit non-equivalent input and output semantics. On AxBench, DAFI also improves steering-feature selection over output-score filtering. Code is available at https://github.com/THUAIS-Lab/DAFI.

Language models sometimes produce correct outputs even when their inputs are corrupted by deletion, replacement, or misspelling. We study the internal processes accompanying this behavior, which we call context restoration, in controlled attention-only transformers and five pretrained LLMs (1B-32B parameters) across arithmetic, reading comprehension, and multiple-choice reasoning tasks. In the attention-only transformers, restoration emerges spontaneously despite training exclusively on clean sequences, without corruption training or an explicit denoising objective. We find that context restoration follows a two-phase process: early layers localize effects associated with repair at corrupted positions, while later layers accumulate these effects at uncorrupted positions through the residual stream and ultimately concentrate them at the output position. Repair outcome is predictable from hidden states: cosine alignment with the clean state is highly predictive in attention-only models, while linear probes recover additional information in pretrained LLMs. A linear probe using only the corrupted prompt's first-block hidden state predicts failure with mean ROC-AUC 0.78. This enables failure triage under matched or even partially shifted deployment conditions and may reduce unnecessary verification or computation. Failed examples also show substantially greater nonlinearity along corruption directions. Moderate-corruption finetuning increases corruption tolerance while simultaneously reducing displacement-normalized linearization error, associating improved robustness with a more nearly linear response to corruption.

Reliable refusal of harmful requests is essential to the safe deployment of language models. Because excessive eagerness to please users may undermine existing refusal capabilities, reducing sycophancy offers a potential route to stronger refusal beyond the harmful scenarios covered by safety training. We investigate this possibility using compensatory feature injection (CFI), a training technique designed to limit the acquisition of a target concept by supplying its associated activation during learning. Across three Qwen3.5 base models, we use sparse autoencoders (SAEs) to identify the top-ranked sycophancy feature from paired sycophantic and independent responses, then validate its behavioral influence through inference steering. We subsequently inject the selected feature during supervised fine-tuning on sycophantic targets. Positive injection reduces learned sycophancy after removal (by 62.0% relative to ordinary fine-tuning in 35B-A3B), whereas modest negative injection increases it. Unexpectedly, these reductions in sycophancy do not consistently improve direct refusal of harmful requests, motivating a narrower evaluation of the same harmful intents under user pressure. In this setting, ordinary fine-tuning on sycophantic responses substantially weakens refusal, while selected checkpoints trained with positive injection recover part of the loss, including approximately 95% in 35B-A3B. These findings show that persistent sycophancy reduction does not guarantee stronger direct refusal, while identifying recovery under user pressure as a distinct, conditional benefit of training intervention.

Residual stream pruning methods reduce inference cost by shrinking the model's hidden dimension, but existing approaches typically choose these dimensions by minimizing activation reconstruction error. This criterion implicitly treats all perturbation directions as equally important, ignoring the sensitivity of downstream layers. We introduce a sensitivity-aware approach to residual-stream pruning that directly accounts for this direction-dependent sensitivity. Using a second-order approximation to the output KL divergence, we characterize the effect of a residual-stream perturbation through both its activation covariance and the local sensitivity of the model output. The resulting subspace selection objective couples these two quantities, but is difficult to optimize directly. We derive a tractable spectral upper bound that reduces subspace selection to an eigendecomposition of a sensitivity-weighted covariance matrix, retaining the efficiency and structural simplicity of rotation-based pruning methods. Across several instruction-tuned language model families, our method consistently reduces calibration KL divergence relative to activation-only pruning and improves perplexity and downstream task performance over a range of compression levels. Our results show that preserving activation energy alone is insufficient for residual-stream pruning, and that explicitly accounting for how perturbations propagate to the model output provides a more effective criterion for selecting dimensions to remove.

Gated Linear Attention (GLA) Transformers advance linear recurrent models through data-dependent gating, but face a core limitation: the fixed-capacity memory matrices across all heads operate at a single temporal resolution, where each token is processed individually, forcing them to simultaneously encode local syntactic patterns and long-range semantic structure, creating a representational bottleneck that gating alone is insufficient to resolve. We introduce Multi-Scale Gated Linear Attention (MS-GLA), which addresses this by distributing attention heads across multiple temporal resolutions. Coarser resolutions pool longer token spans naturally specializing toward long-range dependencies, while finer head groups retain sensitivity to local syntactic structure. A learnable, input-dependent fusion layer dynamically recombines head group outputs at each timestep, expanding effective memory capacity without increasing per-head state size. This multi-resolution decomposition draws on principles from Multi-Scale State-Space Models (MS-SSM), adapting them to the gated linear attention setting. We evaluate MS-GLA on language modeling, recall-intensive tasks, and long-context generalization. Across all settings, MS-GLA consistently achieves higher accuracy and lower perplexity than GLA at matched parameter counts, with up to 18.9% improvement on recall-intensive tasks and 9.5% lower average perplexity on language modeling benchmarks, validating multi-temporal resolution decomposition as a principled and effective extension of Gated Linear Attention.

Recent progress in machine learning is driven by large-scale foundation models, where scaling laws and finding optimal scaling prescriptions for architecture, data, and hyperparameters are key in advancing the state-of-the-art. Therefore, it is surprising that no systematic study evaluates the methodology to obtain scaling laws and prescriptions across different model types. To shed light on this crucial blind spot and facilitate future research, we introduce the surrogate benchmarks ScAn-Bench-LLM and ScAn-Bench-VLM based on 4524 and 8024 checkpoints of language and vision-language model pipelines. On our benchmarks, we perform the first systematic evaluation of both data acquisition and extrapolation methodology for scaling analysis across different data modalities.

Adapting large language model agents during deployment requires not only retaining past experience, but also turning new observations into timely guidance. Many test-time learning methods, however, acquire knowledge from completed episodes. Feedback from an ongoing interaction may therefore not be distilled into knowledge soon enough to help the next decision. Acquiring knowledge at the granularity of individual transitions could reduce this delay, but raises a separate challenge: a rule that is useful within one episode may not be reliable enough to guide future episodes. Waiting for validation can forfeit immediate benefits, whereas unrestricted reuse can propagate accidental or misattributed guidance. We introduce StepLearn, a nonparametric framework that separates immediate use from persistent trust. It turns informative transitions into hypotheses that can guide the next step, while requiring prospective validation before reuse across episodes. Their predicted effects are checked against subsequent observations outside the source episodes, and only sufficiently supported hypotheses become available for persistent guidance. This process updates external knowledge while keeping all model parameters fixed. Over five rounds on WebArena-Lite and ALFWorld, StepLearn achieves average success rates of 59.9% and 84.0% with GPT-5-mini, and 57.8% and 88.1% with Qwen3.5-35B-A3B, respectively. It outperforms EvoTest, the strongest baseline, by 2.2-12.7 percentage points across the four settings. Learning dynamics further shows that these gains are not restricted to the final repetition, with advantages already present on first task attempts in most settings.

Code large language models acquire programming capabilities from large code corpora, but can also memorize implementations that later require removal. Code unlearning is needed to control their continued reproduction when copyright or security concerns arise. However, targeted and retained code share computational patterns, creating a tension between forgetting specific implementations and preserving general programming ability. We propose UNBIND, a code unlearning framework that separately considers which hidden states correspond to the target code and how to suppress its reproduction. By constructing separate directions for these objectives, UNBIND achieves selective unlearning at inference time while keeping model weights fixed. Our evaluation covers fourteen baselines across two code models and two corpora. UNBIND achieves the highest joint forgetting and utility score in every setting. It reduces target code reproduction by 97.3% to 99.1% as measured by F-BLEU, with at most two fewer HumanEval+ and six fewer MBPP+ problems solved than the original models. In repeated extraction tests under a fixed budget, the number of targets yielding exact spans of at least 50 tokens falls from 188--262 to 0--2 out of 300 per setting. No extracted span reaches 100 tokens, and the mean best recovery ratio ranges from 0.43% to 6.45%. Multilingual and related-code evaluations further show effective forgetting with limited impact on useful programming capabilities, supporting UNBIND as a practical approach to selective code unlearning.

We introduce Solver Agent, an AI framework based on large language models for calculations and proofs in mathematics and theoretical physics. The solution process is tracked through a persistent ledger that records assumptions, derivations, and computations. A central agent delegates tasks to specialized sub-agents, while independent agents verify both intermediate steps and the final result. This setup improves the traceability, reproducibility, and verification of computer-assisted calculations. Applying Solver Agent, we study global F-theory uplifts of Type IIB orientifolds and their S-fold generalizations. We establish sufficient conditions for Weierstrass models over projective threefolds with terminal $\mathbb{Z}_k$ quotient singularities ($k\in\{2,3,4,6\}$) to give $\mathbb{Q}$-factorial projective elliptically fibered Calabi-Yau fourfolds with isolated Gorenstein terminal quotient singularities. These geometries realize O3-planes and S-folds, where local D3-brane probes of the latter yield four-dimensional $\mathcal{N}=3$ superconformal field theories. Using stringy invariants, we derive fixed-point contributions to Hodge data and Euler characteristics, and show that these Euler corrections determine the localized D3-brane charges required for tadpole cancellation. We illustrate these results using toric hypersurface constructions, where a single three-dimensional polytope determines both the Type IIB Calabi-Yau threefold and the F-theory base; here, the orientifold double cover naturally forms a bisection of an alternative genus-one-fibered uplift with discrete $\mathbb{Z}_2$ gauge symmetry. Finally, we provide methods for toric computations and four-form flux analysis in four-dimensional $\mathcal{N}=1$ compactifications with non-abelian gauge sectors.

General-purpose robots must infer what a new task requires and translate that understanding into appropriate physical action. In-context learning (ICL) for robots supports this process by using demonstrations and interaction to direct existing competence with neural parameters held fixed during deployment. We organize this literature review around the interfaces connecting contextual evidence to execution, distinguishing four families: context-conditioned policies, geometric demonstration transfer, world-model-based control, and skill- and agent-based execution. Comparing these interfaces clarifies their transfer assumptions and the roles of training, correspondence, and memory in making context useful. Across manipulation and navigation, we examine how these mechanisms preserve taught requirements as objects, environments, and execution conditions change. This analysis links method design to evaluation practices that distinguish responsiveness to teaching, physical transfer, and benefits from retained experience. The resulting agenda connects compositional task acquisition and faithful transfer with physical recursive self-improvement, in which experience improves the ability to learn subsequent tasks.

We study how to build more capable general-purpose agents by extending large language models (LLMs) with native typed decision-making. We introduce Dyad, an architecture that augments a pretrained LLM with an environment-conditioned action encoder that embeds each candidate action description in parallel, then scores these embeddings against the LLM's internal state to yield a distribution over typed actions. By factorizing decision-making into representations of the evolving interaction state and environment-specific action semantics, Dyad introduces an inductive bias for learning reusable representations while keeping action scoring efficient even as the action space grows. We investigate two complementary reinforcement learning settings driven by environment interaction. With the LLM frozen, training the action encoder alone achieves consistent gains across four unseen environments, enabling modular adaptation without modifying any LLM parameters. Jointly optimizing both components outperforms conventional RL post-training across diverse interactive tasks and model scales, including a 3.80% average absolute gain on ALFWorld with a 9B model, while improving general knowledge, reasoning, and coding.

Large language models can reason in continuous space instead of decoded text, by recurring on their own hidden states or by passing those states between agents, while training supervises only the Cross-Entropy (CE) of the final decoded answer and does not constrain the thought. Theoretical and empirical analyses establish and confirm four failures of CE-only training that lead to a lower probability of the correct answer such as collapsing thoughts across distinct questions and retaining irrelevant information. We introduce REST (REpresentation-Supervised Thoughts), a training objective that turns four properties of a valid thought representation (causality, minimality, separability, and stability) into differentiable losses added to CE. We instantiate it in latent single-agent and multi-agent systems, without architectural changes or added parameters at inference. Across 7 benchmarks spanning mathematics, science, medicine, and code generation, with the same training data, compute, and latent budget, REST increases accuracy over CE-only training across agent settings and model sizes by up to 7.5 percentage points and convergence on a final answer by 30%. Furthermore, REST thoughts encode more of what is required to achieve the correct answer, and decoding them better recovers the intended output of the agent, which makes latent communication easier to interpret. Project Website: https://fard-lab.github.io/REST

The way a model distributes activity over each layer's attention heads offers a coarse view of how it routes information through depth; how this changes with the task is part of what a mechanistic account must explain. Holding prompt length fixed, we vary how many serial steps a task demands and measure, in every layer of 17 open-weight models, whether activity concentrates on a few heads or spreads across many as demand rises. Both occur: in most models, layers just before mid-depth concentrate activity and later layers spread it. Models differ in where and how strongly this happens. The Qwen2.5 base models from 0.5B to 7B, for example, spread less than the average model in every task and concentrate activity in parts of their second half, where Llama models from 1B to 8B and OLMo-2 spread; the contrast largely holds between Llama-3.1-70B and Qwen2.5-72B, which have the same number of layers and heads. These differences are reproducible, and post-trained models keep much of their base model's pattern. An ablation study suggests that, within a task, models whose activity is more concentrated on their top heads also depend more on those heads for the answer. Concentration and spreading across layers thus offer a new way to compare models, by how they route information through depth. Code is available at https://github.com/johnnyjli/serial-demand-heads.

Large language models (LLMs) show considerable potential in simulating human attitudes and preferences. Prior work finds that LLM-generated responses can compress the range of attitudes found within populations and misrepresent particular subgroups in ways that vary across models and topics. We introduce Population Fidelity, an evaluation framework that distinguishes key conditions required for a set of LLM-generated responses to represent a population. It incorporates three dimensions: group-level accuracy, the amount of between-group variation, and the structure of that variation. We demonstrate the framework's utility in two ways. First, we reproduce a prior study of "machine bias" in LLM survey responses and apply the framework to its models and more recent ones, showing that poor representation reflects not only insufficient between-group variation but also variation assigned to the wrong groups. Second, we evaluate one proposed approach to improving models' population representativeness: cultural fine-tuning. We find that cultural fine-tuning can improve alignment with the survey center without improving the representation of within-population differences, a distinction that measures of aggregate agreement do not capture. We argue that representing a population requires models to reproduce several features of human attitudinal variation simultaneously. Our framework organizes these features and provides reusable code, data, and trained models for evaluating population fidelity across substantive domains and assessing proposed alignment methods.