LLM 理论进展

Different optimizers can fit the same training data while selecting classifiers with substantially different geometries, but whether this difference provably affects population performance remains unclear. We show that row-wise normalization can achieve strictly higher population accuracy than full-batch Adam, a proxy for random-reshuffling Adam, and exact-SVD Muon in high-dimensional multiclass classification. Under an isotropic Gaussian-cloud data model, this advantage arises because row normalization's class-wise Euclidean geometry asymptotically preserves the population decision-boundary directions, whereas Adam's coordinate-wise geometry and Muon's spectral geometry introduce nonvanishing distortions. Beyond isotropy, the advantage persists for full-batch training on class means with independently oriented class-mean and test-noise covariances. It holds for power-law spectra with class-mean exponent below one, even under heavily anisotropic test noise. When both covariances are diagonal and sufficiently close, the advantage over Adam can reverse, while applying the same random rotation to both restores it by changing only their alignment with Adam's coordinate axes. Synthetic and last-layer language-model experiments support the predicted advantage.

Large language model agents are being increasingly deployed as autonomous scientists, designing experiments and inferring mechanistic world models with minimal human oversight. Yet identifiability is often overlooked: when a plateau is reached, the agent needs to know whether it is not yet capable enough or the model simply is not identifiable from the data, in which case no amount of further experimentation of the same kind can help. We propose the Identifiability-Driven Experimental Agent (LLM-IDEA) for closed-loop discovery with an identifiability engine that returns a three-way plateau verdict: capability limit, resolvable within the design class, or certified exhausted. On ODEBench, 60 of the 62 systems with free constants are identifiable at round 0; the RC circuit is certified exhausted for every experiment that protocol can run, and a harvesting model is resolvable by one added initial condition. The identifiability engine reproduces known verdicts on Lotka-Volterra, Van der Pol, Lorenz, and a pharmacokinetic model, where it recommends the intravenous arm pharmacologists use, and it ranks the depth scorer of our own benchmark last among four observation designs. On the DiscoverPhysics benchmark, it finds two public worlds whose explanation rubric rewards a distinction no legal experiment can make, and every model there with accurate trajectories failed the explanation grade (15 of 15, against 5 of 9 in identifiable worlds, p = 0.012). On the Alien Universe, a two-body testbed we propose in which a force law switches between a provably non-identifiable and an identifiable protocol, LLM-IDEA on the identifiable protocol reaches discovery depth at least three on 8/8 seeds versus 1/8 without it. An autonomous discovery agent can thus compute, rather than guess, whether a plateau calls for more search, a better experiment of the same kind, or a different kind of experiment.

Tabular in-context learning (ICL) has emerged as a training-free and accurate paradigm for tabular prediction, but current approaches to compressing its in-context examples face an accuracy-throughput tradeoff: fixed subsets can sacrifice accuracy, while query-specific retrieval limits cache reuse and batching across queries, reducing throughput. We propose QCOC (Query-Calibrated Operator Compression), which exploits the exchangeability and repeated use of in-context examples by compiling their full KV cache once into compact memory shared across subsequent queries. Instead of retaining raw examples, QCOC clusters their states into joint-KV prototypes, preserves per-cluster multiplicities and the original example count, and calibrates prototype values against attention query vectors produced by the in-context examples through an anchored closed-form solution. Prototype compression drives the speedup, while value fitting helps preserve accuracy. On 64 held-out OpenML-CC18 datasets, QCOC achieves the highest mean accuracy among the compared compression and retrieval methods at both retained counts. Across 12 configurations on seven long tables, it ranks first among compressed methods in ten and averages 0.23 percentage points below full context. Compressing 8,192 in-context examples to 512 memory slots yields a 10.5x cache compression ratio; excluding one-time compilation, in a single-core CPU online-serving comparison over 1,000 queries, QCOC is up to 508x faster than dynamic retrieval baselines and 1.98x faster than full-context inference. These results show that QCOC enables compact-memory reuse and efficient inference across queries while retaining accuracy close to full context.

The memory-bound nature of the decoding stage of large language model (LLM) inference incurs significant latency. Layer-wise training-free network pruning approaches guided by the Hessian have been a prominent solution to this problem, as pruning reduces the number of nonzero parameters read from memory during decoding. Nevertheless, typical methods in this line compute the Hessian using pre-collected natural sequences, whereas the model is fed self-generated tokens during decoding, creating a distribution shift between the two sequences. The Hessian calculated on the natural sequence is different from that calculated on the generated sequence. We observe that this discrepancy causes the activation distribution during generation to deviate from that used for pruning, further hurting the pruned model performance. Moreover, most existing LLM pruning methods that bring actual speedup primarily target the sparse matrix-matrix (SpMM) multiplication, providing limited support for the sparse matrix-vector (SpMV) operations, which dominate decoding. To solve these problems, we introduce SparseDecoding, a principled decoding-aware pruning framework tailored for accurate and efficient LLM decoding. Specifically, at the algorithmic axis, SparseDecoding constructs calibration matrices from layer-wise activations collected during the dense-model autoregressive generation, excluding prefill, thereby aligning the pruning objective with the decoding activations. At the system axis, we develop an optimized N:M sparse matrix-vector kernel with bitmask indexing and fixed-step traversal. Substantial empirical results on representative LLMs (Llama-3.1-8B, Llama-3.3-70B, Qwen3-14B / 32B) demonstrate that our method consistently outperforms standard fixed-text calibration on the long-form generation benchmarks while achieving up to 1.48x end-to-end wall-clock decoding speedup on A100 GPUs.

LLM agents increasingly improve at inference time by accumulating experience in context rather than by updating parameters. This process is often described as in-context reinforcement learning (ICRL). Whether in-context learning (ICL) can actually play the role of RL, however, has not been tested. We study this question in its simplest form, direct ICRL, where the model conditions directly on raw trajectory-reward pairs, and ask whether the reward acts as a learning signal. Through controlled experiments on four benchmarks across six models, we find that the reward is read, but its effect is small: flipping, randomizing, or removing the reward leaves the improvement curve almost unchanged, and this holds even under meta-prompts that explicitly instruct the model to explore, exploit, or reason over rewards. Trajectories drive improvement, but not through their semantic content: shuffled or corrupted trajectories work as well as real ones. These patterns closely mirror those known in ICL, suggesting that direct ICRL is better understood as a special case of ICL than as inference-time RL. This reframing has implications for agent memory design: ICL factors such as input distribution and demonstrations may matter more than RL elements such as reward shaping and exploration.

Speech-to-LLM systems often connect a frozen speech encoder to a frozen large language model (LLM) through a small trainable bridge. The bridge is usually treated as plumbing, but it in fact defines the geometry of the speech-to-LLM interface, and the pretraining objective decides whether that interface provides a reusable initialization for downstream tasks. We study a transferable bridge through two complementary properties: global alignment with the text side, and local lexical manifold compatibility, where bridge embeddings remain close to the frozen LLM's input-embedding neighbourhoods. We make this property measurable with a fixed, head-free, timestamp-free diagnostic that applies to any objective, and show that next-word prediction (NWP) and sentence-level contrastive pretraining do not fully capture token-level lexical compatibility. We then introduce Local Prototype Reconstruction (LPR), a lightweight training-only regularizer that requires each aligned bridge token to be reconstructable from a small neighbourhood of frozen LLM token embeddings, with a hard single-prototype anchor as its limiting case. On multilingual ASR and speech translation, LPR improves transfer, with the largest gains on translation and low-resource adaptation. Crucially, our independent diagnostic correlates with downstream gains across objectives, suggesting that lexical manifold compatibility is predictive of reusability for speech-to-LLM bridges.

Tokenizer choice affects multilingual language modeling, but vocabulary capacity is finite and vocabulary size is often constrained: improving representation for some languages often comes at the expense of others. We therefore ask whether tokenizer choice matters equally across languages, a question that the current literature leave unanswered. To this end, we train 123 language models spanning 54 tokenizers. In the main comparison, architecture, training corpus, training-token budget, and optimization are held fixed, so the models differ only in their tokenizer. We find that tokenizer choice matters more for languages with less language-model training data: across the 54 tokenizers, the standard deviation of a language's bits-per-byte (BPB) increases as its model training-data share decreases (Spearman rho = -0.52 over the 31 trained languages and -0.69 over the 28 written with word boundaries). Leaving a language out of tokenizer training raises its BPB in every language we study, and the penalty tends to be larger for languages with less language-model training data. Giving lower-resource languages a larger share of tokenizer-training data, however, does not unconditionally help those languages: both equal weighting and an allocation inverting the shares with respect to the language model training data increase their BPB, particularly when language-model training repeats data. Finally, which intrinsic tokenizer properties are associated with better BPB differs across languages, providing further evidence that what makes a good tokenizer depends on the language. We find that the metrics quantifying these properties can be successfully used to predict downstream models' pairwise BPB rankings, suggesting a practical strategy for screening tokenizer candidates before training language models.

Large language model compliance systems are deployed on the assumption that a verdict depends on the regulatory rule it is given. We test this directly across five models and 20 regulatory and platform-policy domains: delete, swap, or negate the governing rule while holding the case fixed, and check whether the verdict changes (OCS) or the model's internal representation of compliance shifts at all (ICS-delta). Neither moves much: models' verdicts are often invariant to substantial perturbations of the supplied rule, and the guard model, evaluated here under a custom-rule adaptation of its native taxonomy, is the least rule-sensitive and least accurate of the five, barely above chance (51%, versus 90-92% for general-purpose models). This reflects easy cases more than blanket neglect: on cases where deleting the rule changes a previously correct model prediction, models do track it closely. Neither better prompting nor direct intervention on the model's internal representations closes this gap. Accuracy alone does not establish that a compliance verdict is grounded in the supplied rule.

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

On-policy distillation (OPD) enables effective capability transfer between language models, yet the mechanisms underlying its failures are not fully understood. Across code generation and mathematical reasoning, OPD with larger-scale teachers exhibits early loss plateaus, with an average final loss reduction of 25.1% after 200 updates, compared with 96.2% for self-RL teachers, obtained by further reinforcement learning (RL) training of the initial student. To understand this difference, we analyze OPD as an idealized continuous-time dynamical system in the small-learning-rate limit. Our training-log diagnostics associate these plateaus with an early decline in a gradient-based learning-signal proxy while substantial loss remains; these measurements do not establish why the underlying gradient weakens. We further prove a local recovery guarantee for teachers sufficiently close to the initial student in a shared parameterization under regularity conditions, offering a conditional explanation for the success of self-RL teachers in our experiments. Across runs with and without loss plateaus, we observe small relative parameter changes (0.025-0.098%) and high similarity between the student's representations before and after OPD (linear CKA $>0.98$ across layers). These observations suggest that limited representation adaptation may contribute to learning-signal collapse, a hypothesis that remains to be tested. Code is available at https://github.com/leizhao7/opd-learning-signals.

In LLM-based agent systems, failures can originate from early steps whose effects propagate through subsequent interactions, making their origins difficult to identify. To trace such failures back to their origin, failure attribution has been formulated as the task of identifying the earliest step responsible for the failure. Recent methods leverage LLM internal signals for failure attribution, typically using hidden states as step representations. We therefore conduct an empirical study to evaluate how effectively these representations distinguish root-cause steps from other steps and find limited separation. Motivated by this observation, we propose ReCast, a step representation learning method that transforms hidden states from a frozen LLM into attribution-oriented step representations. ReCast first selects attribution-relevant layers, then constructs complementary pattern and deviation features, and finally learns contextualized step representations through an encoder trained with contrastive and ranking objectives. We also introduce ReCast-2K, a training dataset for failure attribution. ReCast achieves the best Hit@1 across four benchmarks, surpassing the strongest baseline by 5.65 and 9.19 pp on Who&When Algorithm and Handcrafted, respectively. Code is available at https://anonymous.4open.science/r/ReCast-5FB6 .

Large language models (LLMs) often default to Modern Standard Arabic (MSA) when generating Arabic, even when prompted with dialectal Arabic. A natural explanation is that their internal representations are dominated by MSA. We test this hypothesis by adapting the language-dominance framework of Shani and Basirat (2025) (https://doi.org/10.18653/v1/2025.blackboxnlp-1.7) to 26 Arabic varieties. Across layers and model families, we find no evidence that MSA acts as a dominant internal representation for Arabic dialects. Instead, dialect representations form a dense and highly overlapping space: normalized mutual information drops sharply compared to patterns reported for more distinct languages. Moreover, the strongest separability effects are not confined to intermediate layers, but can shift toward later layers depending on the architecture. These findings challenge a common interpretation of MSA-biased generation: output preference does not necessarily reveal internal representational dominance. Analyses of multilingual and dialectal LLMs should therefore distinguish generation bias from the geometry of internal representations.

Reinforcement learning (RL) methods such as GRPO substantially improve large language model reasoning but often suffer from policy entropy collapse: the loss of sampling diversity weakens exploration and limits further improvement. Existing methods address this issue either through algorithm-level interventions, such as reward modification and entropy/KL regularization, or through token-level reweighting. We investigate a complementary perspective: entropy collapse can also be mitigated by changing which generated rollouts contribute to policy updates. Under the same sampling budget, not all rollouts contribute positively to an update, and selectively excluding some can improve learning. To address this, we propose GRPODropout: before the standard update, we use a simple strategy that selectively removes a small number of high-probability positive-advantage rollouts and recenters the retained advantages. To motivate this design, we develop a rollout-level theoretical analysis that guides method design and threshold selection. The method changes only rollout usage, and adds negligible computational overhead. Experiments show higher accuracy than original GRPO and higher actor entropy while using fewer rollout samples for updates, illustrating "less is more." This work provides insight into RL rollout usage: removing some rollouts can improve performance. Code is available at https://github.com/hexuandeng/GRPODropout/.

Large language models (LLMs) can expose memorized training sequences under prefix-based extraction: given a prefix from a training example, the model may assign high probability to the original continuation. In deployed systems, however, prefixes are rarely evaluated in isolation. They often appear together with instructions, retrieved documents, or other task-specific context, as in retrieval-augmented generation (RAG). This motivates examining whether contextual conditioning mitigates memorization or merely changes the set of memorized samples that become extractable. We investigate this issue through paired item-level measurements of probabilistic suffix extraction. For each prefix-suffix pair, we score the target suffix under an empty prompt and under retrieved contexts of varying relevance, across three open-weight instruction-tuned models. We find that context does not simply erase memorization. Instead, extractable memorization consists of a context-robust core and a context-sensitive boundary. Many samples that are extractable without context remain extractable under the retrieved context, especially as the prefix length increases. At the same time, context mainly affects marginal samples near the extraction threshold: it suppresses some exposures, but also enables new ones that are missed by prefix-only evaluation. These findings qualify the view that RAG reduces memorization risk. Context can lower aggregate extraction by suppressing boundary cases, yet robustly extractable samples persist, and context-enabled extractability remains security-relevant.

Supervised fine-tuning (SFT) adapts pretrained large language models (LLMs) to downstream tasks, but the required concepts can receive substantially different levels of pretrained support. Frequent concepts are more likely to be well learned, whereas rare concepts may remain weakly represented. We introduce a novel notion named prior barrier to quantify how strongly the pretrained model supports competing concepts over the target concept. We observe that prior barriers follow a long-tail distribution, placing head and tail concepts at different starting points for SFT: head concepts face lower prior barriers, whereas tail concepts require additional instructions to overcome their higher prior barriers. Our theoretical analysis further derives a predictive risk bound for SFT under long-tail prior barriers, explicitly characterizing how the prior barrier and accumulated SFT evidence jointly determine predictive performance. Motivated by this prior barrier-dependent demand, we propose PASS, an adaptive SFT instruction selection method that constructs reference-derived concepts and estimates the distinguishing evidence provided by each instruction, and adaptively allocates the selection budget toward concepts that remain insufficiently covered under the current selection. In this way, PASS jointly considers which instructions can provide useful evidence and where additional supervision is needed under a limited budget. Experiments show that our method consistently outperforms seven state-of-the-art instruction selection methods on four backbone-budget settings. An ablation study further shows that PASS's adaptive allocation consistently improves over uniform allocation.

Weight-only post-training quantization (PTQ) relies heavily on reconstruction loss minimization to preserve model quality at low precision. We show that the weights favored by minimizing this loss need not yield better model performance on new tasks. In fact, we find that lower reconstruction loss can even degrade model performance on the same calibration data. Our analysis further shows that weights with lower reconstruction loss on calibration data can have higher loss than other weights when the distribution of input activations changes. Motivated by these observations and our analysis, we propose Distributionally Robust Quantization (DRQ), a post-hoc refinement process that minimizes worst-case reconstruction loss over a constrained set of input activation distributions. DRQ refines the integer codes representing quantized weights within the existing quantization grid, keeping quantization parameters and inference operators unchanged. Extensive experiments show that DRQ improves models quantized by six representative PTQ methods, including AWQ, GPTQ, and ParoQuant, and delivers gains across both dense and mixture-of-experts large language models. These results establish DRQ as a general post-hoc refinement framework for weight-only PTQ, achieving better downstream performance without adding inference overhead.

AI research agents automate the cycle of proposing, implementing, and evaluating experiments, opening a path toward recursive self-improvement. Yet their ability to propose experiments outpaces their capacity to execute them in real environments, making outcome prediction a key capability for sustained self-improvement under limited experimental budgets. We investigate language models as Research World Models (RWMs), which predict the outcomes of candidate interventions across research environments. Our evaluation draws on over 2,600 experimental records from nine research environments spanning pretraining, post-training, and inference, representing more than 171,000 H100 GPU-hours of experimentation. Research knowledge acquired from real experimental experience improves RWM predictions of unseen interventions within the same environment (Spearman +0.27), and can be reused across environments. For example, using only pretraining experience from OLMo3, Marin, and Nanochat, an RWM reduces selection regret in the Qwen3 environment by 78% compared with zero-experience setting. These benefits extend to multi-round Autoresearch under a fixed selection budget: RWMs with in-env and cross-env research knowledge increase the best gain achieved by 15.8% and 11.6%, respectively. Ablations across 13 language models used as RWMs show that adding research knowledge can improve intervention ranking more than changing models or increasing reasoning effort alone. These findings support language models as RWMs and motivate accumulating experimental data for future RWM training.

Effective source recovery is critical to security applications such as malware analysis, vulnerability assessment, and legacy maintenance. Large Language Models (LLMs) are reshaping this field, shifting the paradigm away from rule-based heuristics to probabilistic and high fidelity semantic recovery of source code from assembly or classical decompiler-derived pseudo-C. However, despite rapid progress, the field suffers from fragmentation across numerous approaches as well as their non-unified evaluations, limiting objective comparisons. Further, existing works have limited coverage of embedded, IoT architectures and source languages beyond C/C++. In this work, we present the first Systematization of Knowledge (SoK) focused specifically on LLM-assisted binary-to-source recovery. We provide a granular design-centric taxonomy of LLM-assisted source recovery methods and systematic evaluations using seven key metrics along six evaluation dimensions. We evaluate state-of-the-art methods on 45,000 test samples derived from four standard and five embedded architectures, five optimization levels, and symbol stripping. We ablate the impact of design choices on recovery performance, including input representation, contextual enrichment, model scale, iteration and review roles using controlled in-house recovery pipelines and three off-the-shelf models. Finally, we test same-language and cross-language recovery capability covering four mature and two legacy languages. Our systematization and comprehensive evaluations provide key insights that guide future directions in this field.

Large language model (LLM)-based agents have demonstrated strong capabilities on complex tasks. They typically perform reasoning before each action throughout an interaction trajectory. However, reasoning may not be necessary at every turn, as reasoning produced earlier can continue to support subsequent actions. A key challenge is therefore to determine when existing reasoning remains sufficient and when a new reasoning step is needed, without relying on costly generation-based verification. We find that decreases in the likelihood of subsequent reference actions after removing additional reasoning closely track whether those actions remain recoverable given earlier reasoning, providing an effective and lightweight signal for estimating cross-turn action support. Based on this observation, we propose Reasoning Adaptation through Cross-Turn Estimation (RACE), a training approach for adaptive agent reasoning. RACE introduces a Likelihood-Guided Progressive Reasoning Cover Detection (LoGiC) procedure that progressively identifies reasoning turns whose removal has limited impact on the current and subsequent reference actions. The resulting removal signals are incorporated into both supervised fine-tuning and agentic reinforcement learning, enabling the policy to learn when to reason and when to act directly. Extensive experiments on four representative agent benchmarks show that RACE substantially reduces reasoning cost while maintaining or improving task performance.

Pre-trained vision-language models excel across varied perception tasks, but adapting them to novel downstream settings without sacrificing generalization remains non-trivial. Existing parameter-efficient prompt learning method often yields inconsistent representations and fails to account for semantic distribution shifts. In this work, we present DiscoVL, a disentangled cross-modal representation learning framework that couples orthogonal adversarial regularization with structured cross-modal alignment for vision-language models. To address the insufficient cross-modal interaction, our DiscoVL designs a multi-branch low-rank residual aligner that decomposes representations into subspaces and enables bidirectional cross-modal feedback between visual and textual streams at each layer. Furthermore, while conventional triplet constraints overfit features to class centroids, we design an orthogonal regularization for adversarial triplet loss, which prevents centroid collapse and substantially boosts generalization. Evaluations on 15 benchmarks demonstrate that DiscoVL delivers consistent improvements over state-of-the-art methods for base-to-novel generalization, cross-dataset evaluation, and few-shot learning

Multimodal large language models (MLLMs) often struggle to identify and use geometric relations in diagrams. Recent methods address this challenge by converting geometric entities, relations, and constraints into explicit textual representations for the model to reason over. However, effective formalization is highly non-trivial: on Geometry3K, structure injection fixes 28 errors but introduces 13 new ones among 200 examples. Redundant relations can distract the model, while ambiguous references to diagram elements can lead it to apply constraints incorrectly. This suggests that the key challenge is not merely extracting more geometric facts, but organizing them into representations that support downstream reasoning. To fully exploit the power of formalization, we further propose GeoReform, a reflective formalization evolution framework that treats formalization as an optimizable policy rather than a fixed parser output. GeoReform executes the full reasoning pipeline, collects failed rollouts, diagnoses defects in the current representation, and mutates the policy to better select, ground, group, and present geometric entities, relations, constraints, and targets. On Geometry3K, GeoReform improves Qwen3VL-2B accuracy from 42.0% to 56.0%. Extensive experiments and analyses across geometry reasoning benchmarks demonstrate that effective formalization is crucial for improving multimodal geometry reasoning.

Parameter-efficient fine-tuning (PEFT) enables large language models (LLMs) to adapt to specialized tasks, but often at the cost of degrading general capabilities acquired during pretraining. Existing approaches primarily mitigate this trade-off through data replay or regularization, relying on additional data or explicit optimization constraints. We instead focus on a different question: where should adaptation be applied? We find that fine-tuning different Transformer layers produces different target-task gains and degrees of capability degradation, suggesting that not all layers are equally suitable for adaptation. To characterize this difference, we use layer-wise empirical Fisher information to measure target-task sensitivity. However, computing Fisher scores requires backward computation and becomes increasingly expensive for large models. We therefore introduce input--output cosine similarity as a lightweight, forward-only proxy for ranking layer sensitivity. Across models and tasks, layers with lower input--output similarity consistently exhibit higher empirical Fisher scores. Building on this observation, we propose Layer-Selective LoRA (LS-LoRA), which places trainable LoRA adapters only in layers with low input--output similarity. Experiments on mathematical reasoning and code generation show that LS-LoRA improves average target-task performance while retaining substantially more commonsense reasoning capability than standard all-layer LoRA, demonstrating that carefully choosing where to adapt can provide a simple and effective way to balance target-task adaptation and general capability retention.

LLM developers post-train their models to exhibit prosocial values and behavioral traits, which are enumerated in an alignment target. However, while recent post-training developments have yielded models that score highly on alignment evaluations, training models on sets of narrow behaviors still influences their behavior across unseen contexts and environments in unexpected ways. In this paper, we establish the task of alignment generalization prediction, i.e., predicting how fine-tuning a model to follow a given value changes its behavior across a wide range of held-out values. We conduct a large-scale analysis of alignment generalization effects across 66 values found in modern alignment targets, and benchmark representational techniques on the alignment generalization prediction task. We find that representations based on model activations when applying values in context significantly outperform methods based on textual descriptions of the values. Specifically, the best activations-based methods achieve correlations of 0.45 with our generalization matrix, compared with 0.05 from description-based baselines. We then show the applicability of representations that predict alignment generalization toward downstream tasks by using them to measure how similar the values in a multi-value alignment target are, which we find is significantly correlated with model robustness. Finally, we show initial evidence towards a shared, model-independent value space, which we use to develop the first taxonomy of LLM values grounded in empirical generalization dynamics. Our work demonstrates the importance of studying value generalization in LLMs and its application toward the more empirical design and training of model behavior.

Understanding large language model (LLM) reasoning requires looking beyond behavioral performance to examine how reasoning ability is reflected in internal organization. Inspired by neuroscience findings linking higher intelligence to stronger small-world organization in functional brain networks, we investigate small-world connectivity as a structural signature of LLM reasoning. We construct functional graphs from attention-head activation similarities and find that a higher small-world index (SWI), capturing local clustering and short global paths, consistently correlates with better fluid reasoning performance across models and training checkpoints. Since local clustering is central to small-world organization, we further examine how heads important for model performance connect within and across communities. We find that these heads tend to have a larger share of connection weight within their own communities (high core scores) and a more concentrated weight distribution across communities (low bridge scores). These observations motivate the hypothesis that high core and low bridge scores serve as structural indicators of head importance for reasoning capability. We validate this hypothesis through pruning, introducing Small-World Allocation (SWA), a hierarchical sparsity allocation method guided by these scores. Across six LLMs, SWA better preserves small-world organization and model performance than competing allocation strategies, reducing WikiText perplexity by up to 20%. Together, these findings identify small-world functional connectivity as a measurable signature of LLM reasoning performance, offering a structural perspective that complements behavioral evaluation.

Spatial coding agents significantly improve spatial reasoning in Multimodal Large Language Models (MLLMs) by using external tools to generate verified execution traces. However, this paradigm inherently suffers from prohibitive inference-time overhead and external dependencies. In this paper, we explore whether an MLLM can internalize this agentic capability to operate entirely tool-free. We begin with a simple observation: prompting an MLLM with summarized execution traces of a spatial coding agent naturally unlocks the model's internal spatial Chain-of-Thought (CoT). Motivated by this, we introduce SpatialOPSD, an on-policy self-distillation framework that internalizes spatial reasoning into a standalone MLLM by formulating verified agent traces as privileged information. To mitigate privileged-information leakage during distillation, we introduce Repetition-Aware Distillation, which combines repetition masking with unlikelihood regularization. Experiments across multiple benchmarks demonstrate that self-distilling SpatialOPSD achieves higher average accuracy than SFT and GRPO on both spatial and OOD datasets, exhibiting superior performance and generalization.

Chain-of-thought (CoT) reasoning often improves language-model performance by giving models additional computation before answering. However, explicit CoT expresses this computation as a sequence of autoregressively generated tokens. Latent reasoning replaces these tokens with compact continuous states, but most autoregressive latent-reasoning methods retain a left-to-right dependency among latent vectors. We introduce LLoCoT: a looped latent-reasoning framework that replaces left-to-right latent generation with iterative refinement of a compact latent workspace. A shared transformer is reapplied for a small number of refinement iterations, jointly updating the latent slots based on the prompt and the evolving workspace state. Using the refined state, a probabilistic head predicts a distribution from which latent tokens are sampled in parallel and used to condition an autoregressive decoder for answer generation. Training uses continuous representations derived from explicit CoT together with a final-answer prediction loss and likelihood-based supervision of the latent states. Across HumanEval and MBPP, LLoCoT achieves the highest mean among the evaluated methods, performing on par in accuracy with Reasoning SFT, our explicit-CoT baseline, while outperforming the base model, answer-only SFT and NF-CoT. Relative to Reasoning SFT, LLoCoT reduces time to the first answer token by approximately $36\times$ and reasoning-phase latency by approximately $42\times$, while increasing end-to-end throughput by $9.2%$. This design replaces serial thought generation with parallel latent-slot refinement while retaining probabilistic latent modeling and autoregressive answer decoding.

Vision-language models (VLMs) show great potential for damage assessment after a disaster, but a recurring deficiency is that they are reluctant to declare a hazard; that is, recall is low even when overall accuracy appears adequate. This study examines that deficiency by using signal detection theory to decompose the decision behavior into perceptual capability and decision-criterion placement. We then propose a novel method for correcting the over-conservative decision policy, inspired by the finding that fear makes humans risk-averse, and ask whether an affective representation associated with fear can be causally manipulated to similarly alter a VLM's decision tendency. Using mechanistic interpretability, we localize a causally implicated affective circuit in the model and use activation steering to manipulate it while observing the effect on downstream prediction. The method is tested on a two-stage SeisMLLM pipeline built on Qwen2.5-VL-7B-Instruct, which flags only 27.0% of genuinely unsafe buildings on the SeisMLLM-1K test split and never issues a false Red, an SDT criterion of c = +1.354, despite adequate evidence quality (d' = 1.521). An affective direction is localized on emotion-rich natural scenes, causally validated by sparse-neuron knockout and distributed steering on held-out emotion data, and then injected into the building task. Fear-direction injection raises Red recall to 75.7% (p<0.001), and subtracting the same direction suppresses Red predictions entirely, whereas norm-matched random and matched happiness directions show no significant effect. The mechanism is a shift in criterion (c=-1.515) while discrimination is not improved (d'=-0.493). These results show that VLM decisions can be adjusted at inference time without retraining and demonstrate how mechanistic interpretability can be used to diagnose and control VLM decision behaviors in engineering applications.

Scaling laws describe power-law improvements in model performance with dataset size and parameter count, yet their underlying mechanisms are not fully understood. To explain the parameter count scaling, existing theory posits power-law scaling with model depth. In linear-attention models, this scaling is tied to a power-law data spectrum: unable to selectively attend to relevant tokens, these models learn according to global spectral strength, with stronger directions learned before weaker ones. Large language models, however, can be strongly nonlinear. Here, we show that nonlinear attention yields inverse-depth decay of loss across all tested data spectra. Nonlinearity enables attention to focus selectively on relevant tokens, allowing strong and weak spectral directions to be learned in parallel. Similar focusing across layers motivates a connection to the central limit theorem: shared error across layers sets the loss plateau, while aggregation turns layer-specific differences into continued gains with depth. Our findings suggest that depth scaling may arise from nonlinearity in attention, which allows large language models to focus locally and may make the global covariance structure less relevant.

Current frontier LLMs can theoretically process long contexts with 1M tokens or more. But to what extent can they go beyond simple retrieval and perform deeper reasoning over such long contexts? We empirically investigate long-horizon reasoning capabilities of LLMs, focusing on deductive logic expressed in Prolog. We construct ProloNg, a synthetic testbed to probe Prolog Long Reasoning, which systematically varies the complexity (reasoning depth) of problems, where the hardest case has a reasoning depth of 22 and 62k context length. We study 8 reasoning models across 5 families of frontier LLMs, and find that performance degrades substantially as reasoning depth grows, with the majority of models approaching chance beyond depth 10.

Supervised fine-tuning (SFT) equips large language models (LLMs) with specialized capabilities, but often comes at the cost of forgetting the general capabilities of their parent models (i.e., the pretrained models before fine-tuning). This trade-off is especially limiting for queries that require both specialized and general capabilities. We introduce SFT-as-context, a training-free method in which the parent model uses the SFT model's response as context to answer the query. This allows the parent model to acquire fine-tuned capabilities from the SFT response through in-context learning while preserving its own general capabilities. Across 19 parent-SFT model pairs and 11 benchmarks, SFT-as-context remains close to the SFT models on fine-tuned capabilities, with gaps of only 2.2 and 2.1 percentage points on AIME 2024 and LiveCodeBench and 2.0 macro MAE on NutriBench-English, while staying within 2.2 percentage points of the parent models on general capabilities on average. Remarkably, it can solve queries requiring both fine-tuned and general capabilities, even when neither the parent nor SFT model succeeds alone. This approach also extends beyond parent-SFT pairs: responses from a small open-source SFT model can improve a strong closed-source LLM, outperforming either model alone. Furthermore, we use a Bayesian framework to derive theoretical guarantees that bound the error of SFT-as-context relative to the SFT model on fine-tuned capabilities and to the parent model on general capabilities. In addition, we visualize the attention weights and find that the parent model attends more to useful SFT responses and less to irrelevant ones, suggesting that selective attention helps the parent model use the SFT response through in-context learning.