LLM 理论进展

Influence functions estimate how individual training examples affect the behavior of large language models (LLMs). Analyzing how training data influence different behaviors of an LLM involves repeated influence computation. Reusing stored training gradients reduces the computational cost, but storing full gradients is prohibitively expensive at LLM scale. We study how to compress these gradients while preserving influence estimates for future queries that are unknown at storage time. Through a worst-case analysis, we characterize the optimal fixed-dimensional linear representation and propose eigenbasis-corrected one-bit gradient projection (EOGP) to approximate it at scale. Specifically, EOGP uses EK-FAC to reduce gradient dimensionality, then applies PCA within the retained subspace to learn compression directions from the training gradients. We then apply one-bit quantization to the resulting coordinates, allowing more coordinates to be retained within a fixed storage budget. On GPT-2, EOGP predicts retraining outcomes more accurately than the evaluated compression baselines while using one-sixteenth of their per-example storage. On OLMo 2 SFT models from 1B to 32B parameters, EOGP remains competitive with the baselines allocated over 100 times as much storage per example.

Decoder-only transformers are trained only through a terminal next-token prediction loss, yet this loss constrains every intermediate hidden state through the fixed downstream computation. We formalize this constraint by studying layerwise loss-to-go functions: the terminal loss obtained by continuing a candidate hidden state through the remaining transformer blocks. Around successful validation trajectories, we show that the local second-order geometry of these functions is governed, up to low-loss residual terms, by a pullback Fisher operator on hidden-state space. Its spectrum identifies output-sensitive directions and approximately prediction-null directions, yielding a local observable subspace of the residual stream. For causal transformers, the same geometry induces a tokenwise curvature score: a Fisher-weighted sensitivity of the target logits to perturbations of each token's hidden state. This score vanishes outside the causal ancestor set of the target and is controlled by downstream Jacobian couplings, making it a loss-aware alternative to attention magnitude. We estimate these quantities using matrix-free Jacobian-vector and vector-Jacobian products and evaluate them across decoder-only language models on WikiText, OpenWebText, and FineWeb. Empirically, the induced geometry predicts perturbation sensitivity, supports nonuniform layerwise rank allocation, yields competitive structured token-pruning signals, and improves low-rank student recovery when added to stronger autoregressive distillation objectives such as reverse KL and skew KL. These results support a predictive-geometric view of transformer computation: near successful trajectories, the terminal loss induces a thin, anisotropic set of output-relevant hidden-state directions that can be measured and exploited for compression and distillation.

Running a language model locally offers advantages in privacy, latency, and cost, but local hardware fits only small models, which are less capable than frontier models. The usual remedy for a hard query, escalating it to a cloud model, gives up the privacy and cost advantages of running locally. A deployment that stays local faces two decisions for hard queries instead. First, it can spend more computation on a query, e.g., reasoning before answering, which raises accuracy at a cost in latency, so it must decide which queries are worth the extra computation (efficiency). Second, some queries are beyond the local model, and delivering a wrong answer is worse than deferring the query to a human in the loop, so it must decide which answers are safe to deliver (safety). We show that both decisions can be made from the model's own hidden states. The prefill state, computed before any token is generated, predicts whether the model will answer correctly, and the answer state, at the end of the generated answer, predicts whether that answer is correct. HARISSA fine-tunes the model so that both states predict correctness, then makes both decisions with one policy that cascades through the ways of answering from cheapest to most expensive, skipping a way the prefill state predicts will fail and deferring the query when the answer it stops with is predicted wrong. On a device running a single model, HARISSA is within one accuracy point of chain-of-thought at 2.7 times lower latency. On a server holding four sizes of one model, HARISSA is more accurate than the FrugalGPT and Self-REF cascades at the same latency, and at the same deferral rate the answer state leaves fewer wrong answers than the standard confidence signals in five of six task and setting pairs.

Indirect prompt injection makes an LLM agent treat untrusted retrieved text as instructions. We present CounterSteer, an inference-time defense that suppresses this behavior inside the model. Per model, a five-step recipe fits a residual-stream direction from paired episodes differing only in whether an embedded instruction is followed, and retains it only if it passes pre-specified causal and capability gates. At deployment, the direction is subtracted from every tool-result token during prefill. The edit is always on--there is no detection decision to evade--and requires no fine-tuning, auxiliary model, or added tokens, only white-box serving and tool-result span boundaries. Across five open-weights models (8B-106B, five vendor lineages), held-out attack success falls from 0.21-1.00 undefended to 0.00-0.17 defended, and AgentDojo compromise rate from 0.10-0.49 to 0.006-0.079, at 93-100% typography-normalized benign utility, with larger task-dependent costs when reasoning over steered content. A benchmark-level adaptive attacker reaching 0.67-0.73 undefended is held to roughly a quarter of that on the two most deeply evaluated models. Among the defenses we measured on capable models, those achieving lower compromise rates either lost 22-89% of benign utility or fine-tuned the served weights. White-box gradient attacks through the deployed vector compromise at most 2 of 52 episodes, and none of 2,052 replayed human red-team attacks succeeds. CounterSteer largely neutralizes instructional takeover: a black-box framing search cracks 3 of 18 development samples. Parameter manipulation--attacker-chosen arguments in otherwise legitimate calls--is only partially resisted (13 of 18); the decision becomes linearly readable at argument emission but not at the examined pre-generation sites, and is not removed by the tested prefill- or decode-time steering, motivating argument-provenance controls.

LLM-based multi-agent systems (MAS) increasingly use latent collaboration to avoid the information loss and repeated encoding-decoding overhead of natural-language communication. However, directly forwarding all sender latents makes the receiver-side context scale with both the number of agents and the reasoning length, increasing computation, memory usage, and collaboration latency. A natural solution is latent compression. But we find that cross-agent redundancy remains unresolved in existing latent compression approaches, which typically compress each sender independently and then concatenate the results. We propose LatCom, a cross-agent latent compression framework for efficient multi-agent latent collaboration. LatCom maps multiple sender latents into a fixed number of receiver-readable and task-relevant slots. Rather than reconstructing all sender hidden states, it optimizes the compressed latents for receiver-side task utility. LatCom trains the compressor in two stages: single-sender readability learning first establishes a latent interface interpretable by the frozen receiver, and multi-sender fusion learning then trains the compressor to fuse complementary evidence and remove redundancy across agents. Experiments on multiple benchmarks with Qwen3-4B show that LatCom achieves an average 2.46x inference speed-up over LatentMAS and reduces output token usage by 70.3% while maintaining comparable average accuracy.

Self-speculative decoding accelerates large language model (LLM) inference by drafting tokens from the target model itself, but faces a sharp tradeoff between the quality and cost of the draft. Early-exit methods produce drafts cheaply by terminating computation at intermediate layers, but forgo the deeper representations that later layers provide and thus suffer in draft quality. Multi-token prediction preserves draft quality by emitting from the model's final hidden states, but pays for a full forward pass to produce those states at every drafting step. We propose self-speculative encoder-decoder (SEED), a self-speculative method that obtains high-quality drafts cheaply by reusing the deep contextual representations already computed during verification. We reinterpret the standard decoder-only transformer as an implicit encoder-decoder: the first layers (encoder) build deep contextual representations, and the last few layers (decoder) emit tokens from them. Encoding and verification are merged into a single step: verification is performed by the full encoder-decoder, and the contextual representations of the verified prefix are cached for reuse during drafting. Drafting is therefore very fast: between verifications, the lightweight decoder drafts multiple tokens autoregressively, each conditioned on the cached representations and on preceding drafts. Experiments across multiple benchmarks show that SEED achieves up to 2.7$\times$ average speedup on 4B-scale models, outperforming both early-exit and MTP-style self-speculative baselines and running 28% faster than the state-of-the-art EAGLE-3, while preserving or even improving the generation quality of standard autoregressive fine-tuning. Code is available at https://github.com/lhk2004/SEED.

Multimodal large language models (MLLMs) incur high inference latency from long visual token sequences. Existing pruning methods commonly use attention maps or output features to estimate token importance or redundancy. Several recent approaches also exploit representation changes, but when and how these changes reflect foreground saliency and semantic consistency remain insufficiently understood. We analyze visual token representation dynamics across encoder depth and uncover two findings. First, the relationship between token update magnitudes and foreground saliency is layer-dependent: large token updates concentrate on foreground regions in two depth intervals, separated by several sink-dominated layers at intermediate depths. Second, similarities between token update directions better distinguish same-class from different-class tokens than those between encoder output features. Building on these findings, we propose MSDG-Prune, a training-free method that uses update magnitudes and directions to preserve salient and diverse visual information. Specifically, we group tokens by update-direction similarity and use query-weighted saliency derived from update magnitudes across a chosen depth window for group-wise token pruning. Extensive experiments across four MLLMs demonstrate the effectiveness and generalizability of MSDG-Prune. On LLaVA-NeXT, it retains 91.9% of uncompressed performance on average with only 5.6% of visual tokens, while achieving a 7.8x prefilling speedup. Code is available at https://github.com/liweixuan-hitsz/MSDG-Prune.

Reading behaviour varies not only with linguistic input, but also with reader proficiency. In this study, we investigate whether the layer-wise relationship between surprisal from large language models (LLMs) and human gaze behaviour differs across readers with different levels of proficiency and across gaze measures. Using eye-tracking data from the MECO L2 corpus, we compare readers with high and low vocabulary proficiency on first-pass gaze duration (FPGD) and total gaze duration (TGD). We quantify the distribution of the predictive power of surprisal across model layers using Predictive Depth. Across 12 tested LLMs, we find that readers with lower vocabulary proficiency tend to show deeper Predictive Depth for FPGD, while this difference is smaller for TGD. Also, TGD itself shows deeper Predictive Depth than FPGD in both proficiency groups. These patterns suggest that where predictive power is concentrated across LLM layers may be related to the timing and breadth of the reading processes captured by different gaze measures, and that this relationship can vary with reader proficiency. Our leave-one-out analysis further shows that the advantage of informative internal layers extends to unseen texts, although the practical improvements in prediction are limited. Overall, our results show that layer-wise LLM surprisal provides a useful perspective on variation in reading behaviour across both reader groups and gaze measures.

Brain-AI alignment is often interpreted as a sign that model and brain perform similar computations. Whether the aligned units are causally involved in model computation is rarely checked. On an abstract pattern-completion task (AAABAAA $\rightarrow$ B), we compare LLM attention-head representations with human EEG and test how ablating those heads affects task performance. Alignment and causation dissociate: brain-aligned heads contribute to performance, but their removal is substantially less disruptive than removal of heads selected via attribution patching. We compare two head sets that prior interpretability work defines without reference to the brain: concept vectors (CVs), which represent abstract patterns across formats, and function vectors (FVs), selected for their contribution to correct-answer prediction. Brain alignment shows little association with FV scores, while its association with CV scores varies across models. Among brain-aligned heads, we find recurring attention profiles: one emphasizes distinctive elements (novelty heads), the other repeating elements (repetition heads). The novelty family tracks salience and attends to the same elements that humans look at, yet its removal is less damaging than random ablation on average. Repetition heads contribute modestly to performance and are associated with abstract-pattern representation (CVs). Across 17 models spanning 3B-72B parameters, FV-ranked removal is substantially more disruptive than brain-ranked removal. Brain alignment thus captures how the model reads the stimulus, and only faintly captures how it represents the pattern and solves the task.

Audio large language models (ALLMs) can reason about the content of audio recordings to perform complex tasks. However, these capabilities usually collapse in real-world environments when background noise and competing sources mix the target sound. Inspired by long-term memory in human listening, we propose Long-Term Memory-Guided Audio Enhancement (LTM-AE) to improve selective target perception by refining the audio representations of ALLMs without training. LTM-AE extracts representations in hidden states from separate clean reference recordings as long-term memory for each category, guiding enhancement toward a user-specified listening target. We reconstruct incoming audio tokens in the selected category long-term memory and interpolate the reconstructions with the original tokens before language backbone decoding. This interpolation controls the influence of stored auditory experience while keeping all ALLM parameters fixed. Diagnostic readouts across twenty sound categories and three ALLMs show that LTM-AE strengthens responses to a specified target amid three interfering sources. Averaged over constrained and free-form classification, accuracy gains over raw mixtures range from 29.53 to 46.15 percentage points across multiple open source models. For speech content recovery, LTM-AE with an additional learned token-level gate reduces Qwen2-Audio's word error rate from 23.07% to 14.77%. This work takes an initial step toward using principles of human long-term memory to enhance ALLMs for real-world listening. Our code is available at https://github.com/aynlp/ltm-audio-code

Tabular foundation models (TFMs) are increasingly popular because they deliver strong predictions on new datasets through in-context learning, without task-specific training or extensive tuning. Yet released TFMs differ simultaneously in their pretraining priors, architectures, and objectives, obscuring their respective inductive biases. We therefore examine one concrete capability: irrelevant-feature suppression. Across synthetic tasks and real-world datasets, adding null features causes substantially greater predictive degradation in the row-token model TabDPT, whereas the cell-token alternating-axis model TabPFN v2 and other TFMs remain comparatively stable. This gap motivates us to ask whether architecture contributes to irrelevant-feature suppression. Because released TFMs remain confounded by other design choices, we train streamlined row-token and alternating-axis transformers under identical sparse-to-dense linear priors. Exact Bayes analysis shows that sparse prediction requires context-dependent feature gating, whereas the dense endpoint requires only uniform feature weighting. Consistent with this distinction, the alternating-axis model is substantially closer to the Bayesian optimal predictor on sparse tasks, while the architecture gap becomes negligible on dense tasks; almost all of the sparse gap arises from linear coefficient-estimation error. Finally, in both the controlled model and frozen TabPFN v2, we examine the effect of interventions on the feature-attention outputs on the linear coefficients, finding evidence of task-dependent selective routing of computation through feature-indexed pathways. Together, these results support architecture-prior alignment: preserving an addressable feature axis provides an inductive bias for task-adaptive relevance inference. Code is available at https://github.com/Tianqi-Zhao/ArchitecturePriorTFMs.

Large language models often preserve meaning despite substantial changes in wording, style, and syntax, while small semantic edits can systematically alter their hidden representations. This suggests that semantic variation may be organized along recurring local directions. We propose the Invariant Atom Hypothesis: local semantic motion admits preferred sparse coordinates along directions that remain stable under meaning-preserving transformations. We learn a shared semantic frame and sparse coordinates that reconstruct semantic displacements while suppressing nuisance variation, with anchor-dependent diagonal modulation adjusting atom strengths without sample-specific rotations. Empirically, the atoms exhibit strong semantic--nuisance separation, sparse reconstruction, reproducible directions, and causal effects on model predictions. The learned geometry generalizes to unseen semantic neighborhoods and nuisance families, while local reweighting improves semantic selectivity and preserves a consistent global-to-local structure. Atom signatures also remain stable under model modification. These findings support reusable invariant directions as a sparse coordinate system for local semantic geometry in language models.

Users of language-based assistive agents often make ambiguous requests. In response, an assistant can either directly act on its interpretation of the request --- risking misalignment with the user --- or ask a clarifying question. Which option is the most safe and helpful? A common approach is to ask questions that minimize uncertainty about the user's intent until a threshold is reached. However, this neglects the impact of uncertainty reduction on downstream performance, the costs of asking versus acting immediately, and the possibility that users may provide corrections without being asked. To navigate these trade-offs, we introduce Rational Enquiry via Value-of-Information Reasoning (REVOIR). REVOIR makes clarification decisions via inference-time reasoning about the value-of-information of a question, which captures the expected improvement in task reward due to the answer received. In two assistive tasks --- ambiguous question answering (CondAmbigQA) and preference-aligned household task planning (ADAPT) --- we show that REVOIR achieves greater success with fewer questions than approaches based on prompting, chain-of-thought, fine-tuning, or information gain, improving preference satisfaction on ADAPT by 13-15% over a fine-tuned clarification policy while requiring no training and asking five times fewer questions. Furthermore, when the assistant can receive cheap user corrections after acting, REVOIR naturally infers that asking questions is not always efficient, demonstrating the adaptivity of our approach. In contrast, we find that vanilla reasoning agents fail to adaptively clarify user requests, and request fewer clarifications as reasoning effort increases.

LLMs trained with Chain-of-thought excel in reasoning capability, but often come with excessive token cost. We find that the core of reasoning capacity lies in the Thinking model's weight component within the null space of a projection defined by the corresponding Non-thinking model's dominant singular directions, and removing the subspace component can largely improve reasoning efficiency without hurting the accuracy gained during thinking-mode post-training. Unlike existing efforts that mostly operate within the dominant subspace, we are the first to unveil the critical role of the null space and harness it for model optimization. Motivated by this finding, we propose Spectral Null-Space Swap ($S^3$), a training-free composition of paired Non-thinking and Thinking checkpoints. Our method keeps the Non-thinking model inside its own dominant subspace and takes the Thinking checkpoint outside it, improving reasoning efficiency while maintaining accuracy. We extensively evaluate $S^3$ on 2B-30B dense and mixture-of-experts (MoE) architectures spanning 28 evaluation environments across mathematical, multimodal, and audio reasoning domains. $S^3$ establishes new empirical Pareto Frontiers among training-free model composition strategies: across all settings, it reduces inference token overhead by an average of 27.4% compared to full Thinking models while simultaneously improving overall task accuracy by 1.0 percentage point (e.g., yielding +8.3% accuracy on HMMT25 alongside a 33.0% token speedup). We further use attention entropy for explanation and find that the retained component produces more concentrated attention, and we use a simplified analytical model about optimization to demonstrate why null-space can effectively reduce attention entropy, thereby improving the efficiency of reasoning.

Transformer language models build predictions through successive residual updates, but how their representations become specific to an eventual outcome remains unclear. We study this process by comparing intermediate residual states with their own final states and an empirical bank of final states from other contexts. Across six pretrained language models, the own endpoint becomes preferable to the average alternative early, while many individual endpoints remain closer. These competing sets generally shrink with depth, but their membership changes and their surviving endpoints need not become more similar to one another. Directional alignment and endpoint rank can therefore improve while Euclidean distance to the final state changes little. We develop a simple high-dimensional model that separates the roles of norm, alignment, and endpoint geometry, showing how gradual directional changes can produce sharp reductions in competition. We also prove that a straight path toward the own endpoint cannot introduce new competitors under either Euclidean or cosine distance; observed entries thus establish departures from straight-line convergence. Finally, endpoints associated with lower-ranked output tokens tend to lie farther away in cosine distance across all studied models, connecting residual geometry to output organization. Together, these findings characterize increasing geometric specificity during transformer inference and explain why distance, competitor count, and concentration of the surviving endpoints provide distinct views of that process.

Protein Language Models (PLMs) have made remarkable progress following scaling laws established in natural language processing across sequence- and structure-based tasks, yet the potential of tokenization remains underexploited. Unlike human language, proteins preserve structure despite extensive sequence variation a property standard tokenization strategies fundamentally fail to capture. We introduce ZEST (Zoned Encoding of Sequence Traits), an evolution-informed vocabulary derived from conserved regions of multiple sequence alignments. ZEST allows embedding domain-level biological priors directly at the tokenization stage rather than learning them implicitly through scale. ZEST natively compresses sequences to an average token length of 4 residues, enabling our model to process 4,000 residues within a standard 1024-token context window. Building on this, we present LEMON (Layered Extraction of Molecular Ordering from Nature), a compact 200M-parameter sequence-based model for detection of remote homology between protein sequences trained on a single H100 GPU for one week. Despite its modest size, LEMON outperforms state-of-the-art models ranging from 600M to 3B parameters. Our results demonstrate that evolution-informed tokenization can substitute for massive parameter scaling, opening a new direction for efficient, biologically-grounded protein representation learning. All code, model weights, and results are publicly available under the MIT license.

Relational in-context learning (ICL) uses labeled support examples and their linked relational context to predict labels for new queries. This creates a failure mode when target-derived features are present in the support context but unavailable for the query. We study this setting as support-set target leakage. We construct 20 controlled target-derived features that vary in signal fidelity, representation, semantic transparency, coverage, and zero-, one-, and two-hop relational placement, and evaluate them across 13 RelBench tasks and five relational ICL configurations that vary the ICL head, message-passing depth, pretraining cohort, or relational encoder architecture. We evaluate matched 0-hop, 1-hop, and 2-hop leakage settings, together with a Full leakage condition containing all 20 leaker columns. Within the tested configurations, target-table (0-hop) and Full leakage produce the largest aggregate deviations from clean evaluation, while higher-hop effects are often weaker, consistent with differences in effective exposure associated with temporal reachability, sampling, and aggregation fidelity. Leakage effects are strongly task- and model-dependent and can reverse relative conclusions between model variants even when aggregate changes are small. For leaker detection, we compare an Integrated Gradients (IG)-based screening method with mutual information (MI) and leave-one-column-out (LOCO) on a common Baseline subset. Ranking quality is strongest in the high-impact 0-hop and Full leakage conditions, but detector-based removal does not consistently restore the clean evaluation. A four-task rel-salt case study further shows the same evaluation concern with native-schema leakage candidates from the original relational schema. These results identify the support/query information boundary as an important component of reliable relational ICL evaluation.

Large language models are thought to represent features by vectors in a hidden space of dimension given by the model's width. Superposition, in which more features are represented than the width by letting representation vectors overlap, is a leading account of how representation vectors are organized. However, how model width and data statistics determine the configuration of representation vectors and the resulting loss when the number of features and the width are large remains less understood. Here we show, in Anthropic's toy model of superposition, that increasing the width drives a continuous phase transition from a partial-representation phase, where only a subset of features receives appreciable representation vectors while the rest vanish, to a full-representation phase, where every feature is represented. Our theory via a partial random projection approximation predicts, and experiments confirm, that the critical width grows linearly with the number of active features up to a logarithmic factor. The loss scaling changes across the transition: below the critical width, the loss grows linearly with the number of active features and depends weakly on the width in a form set by data statistics; above it, the loss grows approximately quadratically with the number of active features and decays inversely with the width. Non-uniform firing probabilities delay the transition and lower the loss, as more frequent features occupy more space. Our results provide an account of how model width and data statistics jointly shape representations and loss, a step toward understanding representation scaling in large models.

Unlearning in large language models (LLMs) is typically evaluated at the output level, where a model appears to suppress sensitive or undesirable content. In this work, we show that such evaluations can create an illusion of forgetting: even when output-level leakage is eliminated, sensitive information can remain encoded in the model's hidden representations. We first provide a theoretical analysis establishing a fundamental separation between output suppression and representational erasure. Specifically, we show that the decoder can be made arbitrarily insensitive to sensitive directions, driving output-level leakage to zero, while the hidden representations retain the underlying information. To empirically validate this phenomenon, we train generative probe decoders on hidden states across transformer layers, enabling layer-wise measurement of information leakage. Across three widely used benchmarks, TOFU, MUSE, and WMDP, and state-of-the-art unlearning methods, we find that substantial sensitive information remains recoverable from hidden representations, even when standard output-level metrics indicate successful unlearning. To address this gap, we propose Probe-Adversarial Representation Suppression (PARS), an unlearning objective that adversarially minimizes the extractable information from hidden representations. PARS directly targets representational leakage and provides significantly stronger guarantees of erasure under adversarial probing and relearning attacks, outperforming all evaluated baselines. Our results highlight a fundamental limitation of existing unlearning paradigms and suggest that true forgetting in LLMs requires controlling not only model outputs, but also the information encoded in hidden representations. Codes are available at https://github.com/OptimAI-Lab/HiddenStateUnlearning.

Evolutionary program search driven by large language models (LLMs) has produced record-breaking constructions for open problems in combinatorics and beyond. We apply this approach to the longstanding problem of improving the best-known bounds for binary linear codes. Building on the EvoTune evolutionary framework and the ShinkaEvolve codebase, we introduce LinCodeEvolve, which evolves code-construction programs against an exact minimum-distance evaluator. A strategy loop combines diversity-driven search and expert supervision: when progress plateaus, new strategies are used to redirect the search. LinCodeEvolve discovers seven record-breaking codes, $[172,21,66]$, $[173,20,68]$, $[176,21,68]$, $[181,21,70]$, $[184,21,72]$, $[189,22,72]$ and $[200,21,77]$, six of which have concise quasi-cyclic descriptions. With standard code modification techniques, they improve $22$ entries of the tables. Every code is verified by exhaustive enumeration. These results suggest that LLM-guided search can help find improved codes and complement existing methods in coding theory.

Can reasoning models trick chain of thought (CoT) monitors and perform hidden computation without revealing it in their thinking traces? We show that the answer depends on the underlying task difficulty and the model size. Simple computations can be performed covertly; however, beyond a threshold depending on model size, successfully solving the task necessarily leaks a near-linear amount of information about the covert task input into the CoT. Therefore, sufficiently complex hidden computation always leaves an information-theoretic footprint. However, concerningly, this leakage need not be readable: Under plausible cryptographic assumptions, even a one-layer Transformer can encrypt its reasoning online so that no polynomial-time monitor can extract information about the hidden computation. Overall, our theoretical and empirical results provide a holistic view of both the opportunities and the limitations of CoT monitoring.

Large language models often improve problem-solving performance by generating multi-step reasoning paths, yet how to analyze the hidden states along these paths remains unclear. Existing approaches typically assign each intermediate state the final-answer correctness label and train probes across heterogeneous questions. We argue that this protocol obscures reasoning dynamics in two ways: (1) correctness prediction can exploit question-level variation rather than path quality, and (2) states aligned by absolute step indices may correspond to different functional phases of reasoning. In this work, we propose to view reasoning paths as phase-structured trajectories within fixed questions. We instantiate this view as PAIR, short for Phase-Aligned Intra-question Reasoning. PAIR samples multiple trajectories for each question, maps variable-length paths into shared relative phases based on normalized trajectory progress, and compares successful and unsuccessful trajectories only within the same question and phase. This yields phase-specific path-quality directions that better isolate path-quality signals from question-level variation. Empirically, we find that standard across-question correctness probes lose much of their predictive power under within-question evaluation, suggesting that these probes partly rely on question-level information. PAIR improves within-question trajectory ranking and Best-of-N trajectory selection across models and benchmarks. Phase-wise steering further shows that the learned directions can change generation outcomes, providing causal evidence that they capture trajectory-relevant information.

Language models expose internal signals that predict whether an answer is correct, readable from a single forward pass of a frozen model without additional generations. Yet existing probes often commit to one signal family or layer and can be brittle under distribution shift; in retrieval-augmented settings, many specialized detectors instead target passage faithfulness, which can diverge from correctness when retrieved evidence is unhelpful or conflicting. We therefore ask where answer correctness is readable, which internal signal families carry it, and how they should be combined. We search over hidden states, token probabilities, residual-stream features, attention, and their fusion, treating the selected readouts as a predictive measurement rather than a mechanistic localization. We run this analysis separately in closed-book and with-context settings, since context can change which readouts are informative. A consistent anatomy emerges: correctness concentrates in the answer span, recovered from the answer tokens even under retrieval, and the families carry it complementarily, so fusing them helps most out of distribution, where a single signal is weakest. The protocol is effective across two backbones and gates a retrieval controller as one downstream use.

Transformers have demonstrated remarkable in-context learning (ICL) capabilities, enabling them to perform new tasks without additional fine-tuning. However, their performance often deteriorates when encountering out-of-distribution (OOD) inputs that deviate from the training distribution, and the underlying theory remains poorly understood. To fill this gap, we characterize the OOD error under the input distribution shift through the interplay between the dynamics of the so-called $α$-type and $β$-type attention weights, which represent the transformer's confidence in identifying the correct and incorrect features, respectively. Our results indicate that the OOD error for each feature depends on all pairwise interactions between the training features and OOD features, and under certain cases the transformer performs no better than random guessing. To improve the OOD generalization performance, we next investigate the impact of model finetuning with the OOD data, and particularly, characterize the model forgetting performance on the source domain. Interestingly, the performance on the source domain may not always degrade after finetuning, which highly depends on the nature of the feature shift: finetuning on OOD domain keeps enhancing the confidence of identifying correct features from the original distribution, while the interference from other incorrect features may either increase or decrease. Extensive experiments on both synthetic and real data are conducted to corroborate the theoretical insights.

Incorporating rich task-relevant context, such as domain knowledge and external observations, is a key capability yet remains challenging for Bayesian optimisation (BO). Recently, practitioners have started to use large language models (LLMs) to generate and execute BO programs through coding harnesses. In such emerging practices, the posterior belief is shaped not only by Bayesian inference but also by LLM-generated model and data artefacts, offering a flexible route for task context to enter BO as executable code. To study whether and how LLMs can be harnessed to compile diverse contextual signals for BO, we formulate LLM-compiled BO as generalised-context decision making. We propose HarBO, a BO-specialised harness that compiles generalised context into the core artefacts of standard BO through a validated multi-stage workflow. Our theory analyses the regret under imperfect compilation and the effect of adding new context. Across synthetic functions and real-world benchmarks, we find that LLM harnesses can effectively compile context into standard BO, achieving competitive performance with specialised LLM-embedding-based and direct LLM-in-the-loop BO methods. General coding harnesses can be effective in familiar domains such as hyperparameter optimisation, but fall short in unfamiliar, context-rich domains. Together, these results establish LLM harnesses as a promising, but not automatically reliable, route for making rich task context usable in BO.

Localizing latent structures in the activation space of language models (LMs) is central to understanding and controlling their behavior. Yet, localized structures can differ substantially in their causal influence, raising the question of what makes a structure actionable. We tackle this question by casting causal influence as a product of three factors and showing empirically that they act as interpretable, distinct constraints: capacity, measuring the sensitivity of the model's output to movement along the structure, responsiveness, capturing how promotable the concept is given the current context, and alignment, reflecting how well the structure aligns with the context-specific representation of the concept. Across 4 LM families and 50 concepts, we observe that causal effectiveness requires all factors to be high; low capacity and responsiveness reduce it by 84% and 95%, respectively, while low alignment can reverse it, suppressing concept expression. Moreover, we find that causality is context-dependent rather than an intrinsic property of the structure, with causally effective directions forming a low-dimensional subspace that varies across contexts. By restricting the training of linear probes to this subspace, we introduce causal probes that achieve 17%-118% improvement in steering across models, with only 3% reduction in concept detection.

Explicit textual Chain-of-Thought (CoT) has improved the reasoning ability of large audio language models (LALMs). However, textual CoTs are often constructed from text captions of audio and provide limited access to the acoustic evidence, which can introduce problems like hallucination. To address this modality-gap issue, we introduce JELAR, a Joint-Embedding Predictive Architecture (JEPA)-based latent reasoning framework that conditions latent reasoning supervision on acoustic representations learned from raw waveforms. During training, a frozen WavJEPA model provides representations learned directly from raw waveforms. A non-causal expert first constructs answer-aware queries, which cross-attend to WavJEPA embeddings to produce latent reasoning targets. The LALM is trained to predict these targets before generating its response. Experimental results show that JELAR improves the Audio-Reasoner baseline by 2.70 and 9.10 absolute percentage points on MMAU-mini and MMAR, respectively, demonstrating the effectiveness of JEPA-conditioned latent reasoning as an alternative to explicit textual CoT supervision.

AI systems often feel brittle and fragmented. A large language model (LLM) may correctly explain a concept but fail to apply it, or follow safety instructions in one context but not another. This behavior suggests a general failure to lift local information to a global understanding. To gain fundamental insight, we frame "understanding" as learning constraints and propagating their consequences. We construct learning tasks on monoid worlds, sets of states connected by action transitions, where observed training transitions and an unseen constraint jointly determine held-out transitions. Measuring generalization tests whether models can learn global constraints from local transitions and propagate their consequences. We consider inverse, commutativity, composition, and periodicity constraints relevant to spatial and semantic structure. Across attention, recurrent, and state-space architectures, next-state training fits the data but fails to propagate non-trivial constraints. Compositional training, which uses identical paths but hides intermediate states from the input, achieves 96% accuracy on inverse, commutativity, and composition constraints across architectures, yields corresponding improvements in geometric generalization of world models trained on embodied environments and relational generalization in Wikidata-finetuned LLMs. How far do models propagate constraints when inferring an unseen fact may depend on first inferring others? We define proof depth d of a held-out transition, measuring the minimum number of inference rounds to infer the transition, and find that model generalization decreases sharply with proof depth. Increasing compositional path length T improves generalization. These results provide a formal way to investigate global understanding in language and world models and demonstrate that compositional training promotes information propagation and integration.

Names are personal identifiers, but they also carry social meaning and are widely used to evaluate how language models treat different people. Such evaluations typically assume that matched names are comparable model inputs. We show that this assumption often fails at the lexical interface: matched names are not necessarily matched inputs. Some names receive direct single-token access, while others are assembled from multiple subwords, creating unequal name-surface support. Across nearly half a million first names and 12 LLM-associated tokenizers, direct lexical access is highly selective, model dependent, and uneven across race- and gender-associated name metadata. We introduce NameTrace, a model-native, fine-grained, pre-behavioral framework for measuring whether unequal name-surface support remains a vocabulary property or becomes visible in task-relevant internal representations. NameTrace measures concept accessibility from the model's own probabilities over task-specific adjective axes with continuous task-aligned weights. On matched atomic and short-fragmented names within the same race/ethnicity--gender-associated strata, support predicts systematic differences in concept accessibility across fellowship, hiring, clinical assessment, and lending. These differences persist across all eight matched strata, extend across model families, and transfer to unseen names. Hidden-state interventions further show that the measured task directions have downstream leverage, shifting later constrained choices. Unequal lexical support is therefore demographically structured at the input and remains visible in task-relevant model computation. NameTrace makes lexical comparability measurable, supporting a broader principle: behavioral comparability begins with lexical comparability.

Large language models (LLMs) have demonstrated strong capabilities in biological reasoning; however, genomic disease inference remains largely dependent on memorized gene-disease associations rather than understanding biological pathways. This shortcut learning undermines robustness and generalization, and breaks down when molecular identifiers are unavailable. We present GenoMorph, a multimodal genomic reasoning framework that shifts disease prediction from associative gene-disease mapping toward pathway-grounded reasoning. GenoMorph couples a frozen DNA foundation model with question-conditioned cross-attention fusion, self-adaptive latent reasoning (LatentSp), a residual reasoning gate for iterative genomic evidence reinjection, and rejection sampling fine-tuning regularized by hierarchical optimal transport (OT). Rather than learning direct gene-disease mappings, GenoMorph aligns genomic sequence representations with latent pathway dynamics, enabling reasoning trajectories that follow molecular interactions before producing disease predictions. LatentSp dynamically allocates computation according to reasoning confidence, reducing unnecessary reasoning steps and improving inference efficiency. We further construct an anonymized benchmark from the Kyoto Encyclopedia of Genes and Genomes (KEGG), replacing every gene and molecular identifier with anonymous symbols while preserving sequences and pathway topology, thereby removing memorization shortcuts. GenoMorph raises the weighted F1 from 0.7863 (BioReason) to 0.9412, and rejection sampling fine-tuning with self-adaptive latent reasoning pushes it to 0.9725 while cutting latency nearly 60%. On the anonymized benchmark it reaches 0.9465 F1, substantially outperforming prior systems and confirming that accurate disease prediction can arise from pathway reasoning rather than memorized gene-disease associations.