LLM 理论进展

Illusory pattern perception is a well-documented human cognitive tendency to infer meaningful relationships in data that is actually random. Such a tendency, often described as "connecting the dots" where none exist, can result in systematic reasoning errors. This paper investigates whether Large Language Models (LLMs) exhibit such perceptual tendencies, which can lead to systematic errors in downstream applications. To our knowledge, this work presents the first systematic study of illusory pattern perception in LLMs, adapting classic psychological paradigms to three tasks with direct empirical comparison to human behaviors. We find that LLMs frequently exhibit stronger illusory pattern perception than humans. In particular, models tend to over-associate frequent positive attributes with majority groups or large organizations, and show increased tendencies to construct causal narratives from ambiguous events. To uncover the mechanism behind these behaviors, we develop a feature interpretability framework based on Sparse Autoencoders (SAEs) to analyze internal representations. Our results reveal that holistic frequency perception and analytic cognitive orientation are linked to the emergence of illusory perceptions. These findings highlight a previously underexplored cognitive-like illusion that may affect the reliability of LLM reasoning. Code available at https://github.com/NusIoraPrivacy/illusory.

Scientific search systems can find papers that are relevant to a question, but they generally do not assess the quality of the evidence that those papers provide. We present Kurate, a system that uses large language models (LLMs) to assess the quality of published studies. Kurate uses both the paper and its related documents (e.g., the study's trial registration and protocol), and links each of its judgments to the passage of text on which that judgment is based. We applied Kurate to a corpus of 4,347 papers (3,913 of which report randomized trials) and scored each paper on 8 dimensions of study design and reporting: specifically, statistical power, causal identification, preregistration, selective reporting, measurement validity, analysis prespecification, reporting transparency, and conflict of interest and funding. Across the corpus, we found that papers most often exhibited issues with statistical power, selective reporting, and analysis prespecification, although average quality differed between clinical areas. When compared against expert annotations of 60 held-out clinical-trial documents, the information Kurate extracted matched the expert label in 221/242 protocol scorepoints and 294/370 results-publication scorepoints, with AC1 0.94 and 0.81, respectively. Using a well-reputed, high quality clinical trial as a worked example, we show how a single paper's overall grade breaks down into separate judgments, with each linked to specific evidence from the trial's registration, protocol, and published report. Together, these results show that large-scale quality assessment of this kind is feasible, and that it can be used to address meta-scientific research questions.

Large language models (LLMs) have become increasingly capable of generating code. However, achieving stronger code-generation performance still often relies on costly model adaptation, i.e., fine-tuning pretrained model parameters. Prior studies have shown correspondence between human code processing and neural models' attention or internal computation. Human-aligned learning approaches use cognitive signals to guide training, but typically adapt a large portion of the model, leaving training costs largely unchanged. Human cognitive signals may indicate not only what the model must learn from, but also where adaptation is most useful. We investigate whether human responses during code reading correspond to code-model behavior and can guide selective adaptation without sacrificing performance. We present CogAdapt, a cognition-informed framework for task-dependent sparse adaptation of code models. CogAdapt first learns transferable program-level and token-level priors from human Electroencephalography (EEG) and attention data, then combines these priors with the frozen model's response to each coding task to determine how much adaptation to allocate and which transformer blocks should receive updates. During fine-tuning, only the selected blocks are updated, while no new human recordings are required for inference. Across Qwen and GLM, we find consistent correspondence between human reading behavior and Mixture-of-Experts (MoE) computation. CogAdapt achieves the best pass@1 across both LiveCodeBench and BigCodeBench, including gains of 10.86 and 6.29 percentage points over matched regular fine-tuning on LiveCodeBench, while reducing gradient-eligible adaptation parameters by 86.21-87.21%. These results suggest that human comprehension signals can provide useful guidance for making code-model adaptation both more selective and more effective.

Interpretability methods for neural networks are predominantly reactive: they analyse activations produced during specific forward passes, requiring known inputs to find hidden capabilities such as backdoors. We propose Weight Oracles, fine-tuned language models that diagnose properties of a target network by reading its raw weights directly, without behavioural testing. We investigate this paradigm in two phases. Phase I establishes feasibility: through a staged curriculum and an external chain-of-computation that delegates parameter-free operations to deterministic code, an explainer LLM learns to simulate the forward pass of small transformers from their weights, achieving 99% holdout accuracy on unseen targets. Phase II repurposes this infrastructure for safety auditing. We train an oracle on natural language diagnostic questions about weight anomalies using only benign pathologies as training signal, and evaluate it zero-shot on backdoors absent from training. The oracle achieves AUROC 0.93 on attention-routed backdoors and 0.81 across a diversified threat distribution including stealth and adversarially regularized variants. Hand-crafted statistical detectors are sharp on the threat models they implicitly target but collapse on threat-model shift, while the oracle remains uniformly competent across attack types. Scaling to realistic model sizes remains the principal open challenge.

Safety auditing of post-trained large language models typically relies on model behavior, requiring model execution and depending on the coverage of available evaluations. This work asks a different question: Do the target behaviors optimized during supervised fine-tuning (SFT) leave readable evidence directly in checkpoint updates? We find that harmful-compliance SFT induces a continuous, objective-dependent ordering in checkpoint-update space. Using a reference geometry defined by pure harmful-compliance, safety-targeted, and benign-utility SFT, we find that a checkpoint-level coordinate s_H tracks controlled harmful-objective composition with Spearman correlations of 0.986-0.992 across four 7-8B backbones, with the same ordering persisting at larger model scales. Matched compliance-versus-refusal controls show that this checkpoint trace reflects the SFT objective rather than harmful-input exposure, while additional controls rule out simple explanations based on harmful-example count or generic training intensity. Building on this structure, we introduce TRACE, a weights-only auditing method that localizes an unknown checkpoint update relative to frozen harmful and non-harmful reference prototypes and converts this geometry into a continuous harmful-objective score. TRACE requires neither model queries nor access to the unknown SFT data, and can be evaluated directly from checkpoint updates. Across distribution shifts, unseen data, different SFT configurations, partial checkpoint access, and LoRA/full-parameter fine-tuning, the trace remains stable and is positively associated with independently measured attack success rates. TRACE remains informative even at low harmful-objective proportions, providing a complementary auditing signal when behavioral evaluation is unavailable or incomplete. Code is available at https://anonymous.4open.science/r/Code4TRACE-54D3.

LLMs have advanced rapidly, raising growing concerns about their safety. Recent work has proposed approaches to detect and defend against attacks including defenses at decoding stage that leverage models' hidden states. However, existing decoding-stage defenses suffer from two limitations. First, they introduce a trade-off between safety and over-refusal, where strengthening safety degrades the model's helpfulness on benign queries. Second, many of these methods rely on internal hidden states and are thus restricted to specific architectures, incurring substantial overhead and limited generalization across models. To address these limitations, we introduce LADE (Latent Safety Signals for Defense), which leverages latent safety signals extracted by contrasting harmful and benign queries from dark knowledge (i.e., information carried by the output probability distribution beyond its argmax) in the first-token output probability distribution. Our key insight is that, beyond surface-level refusal tokens, the dark knowledge in the first-token distribution contains latent safety signals, defined as tokens whose probabilities differ sharply between harmful and benign queries. We show that these signals consistently align across LLMs, forming a model-agnostic direction that emerges from safety alignment. LADE consists of three components: (1) Extracting Latent Safety Signals from Dark Knowledge, which selects top-k safety-discriminative tokens from the first-token probability distribution; (2) Tokenizer Mapping, which maps these tokens across different tokenizers to enable model-agnostic application; and (3) kNN-based Discrimination, which classifies queries via a k-Nearest Neighbors search over the mapped tokens. Across diverse LLMs and benchmarks, LADE is robust against a wide range of jailbreak attacks and lowers attack success rates while maintaining a competitive safety-utility trade-off.

Visual latent reasoning compresses rendered derivations into compact intermediate states, reducing textual reasoning overhead. Existing approaches differ in how they represent these states: continuous methods avoid vocabulary constraints, whereas discrete methods improve accuracy through quantization into a finite codebook. Our analysis of representative continuous and discrete systems identifies two functional requirements: answers must rely on latent states, and those states must carry valid, problem-specific reasoning. Continuous latents influence answers despite collapsed reasoning content, whereas discrete latents retain recoverable intermediate reasoning that answer prediction largely bypasses. To address these challenges, we propose Continuous Anchored Latent Reasoning (CALR), which connects latent formation with answer use through functional anchoring. With reference latents from information-balanced compression, CALR couples latent-mediated answer supervision with derivation-level semantic anchoring: the former routes answer supervision through intermediate states, while the latter grounds their decoded content in problem-specific derivations. A parallel-to-autoregressive curriculum develops sequential reasoning by conditioning subsequent latent blocks on generated prefixes. Evaluations on five mathematical reasoning benchmarks across model families show substantial accuracy gains. Under matched budgets, CALR gains 26.0 percentage points over a comparable continuous latent reasoning method. Further analyses show that its latents support answer prediction and carry problem-specific intermediate reasoning.

Post-training quantization is a powerful tool for compressing large language models. The most scalable methods quantize every layer in parallel, but quantization errors then compound through the residual stream, as no layer corrects for the errors of the layers before it. Sequential quantization accounts for this error compounding by re-calibrating each layer on the already-quantized outputs of its predecessors, yielding stronger results but at the cost of a serial schedule that becomes a bottleneck at scale. As a solution, we propose parallel quantization with activation denoising, which recovers much of the sequential benefit while keeping quantization fully parallel. Rather than re-calibrating layer-by-layer, we take a robustness perspective and model the upstream error as noise, regularizing to be robust to it through a preprocessing step followed by metric-weighted rounding. Applied at every layer, this regularization forms a depth-compounding smoothness penalty that dampens how strongly quantization errors amplify through the model. Unlike orthogonal rotations commonly used in quantization, which must preserve the model's function, we multiply the weights by a more general linear transformation. We find that the two are complementary and their effects compound. Empirically, our robustness regularization recovers a significant part of sequential quantization's benefit in a single parallel pass, at a fraction of its time. Overall, by treating compounding quantization errors as a robustness problem, we offer a principled foundation for more efficient and accurate LLM quantization at scale.

Representations of translated sentences are similar in the inner layers of multilingual language models — an observation connected to the platonic representation hypothesis, yet unexplained theoretically. We provide an explanation based on the assumption that data have a hidden hierarchical structure whose abstract levels are shared across languages while surface levels are modality- or language-specific. Concretely, we generate synthetic languages from probabilistic context-free grammars sharing upper-level but not lower-level production rules. In this setting the Bayes-optimal next-token predictor is belief propagation (BP); encoding its messages in successive layers yields analytical predictions that agree well with transformers trained on the same data. The framework explains why cross-lingual similarity peaks in middle layers, coexists with language-specific structure, and strengthens with language proximity, model quality and data exposure. It distinguishes similarity (shared neighborhood geometry) from alignment (shared coordinates), showing that the latter occurs when code-switched data, i.e. mixed-language sentences, are abundant enough. It further predicts that subtracting from each layer the component linearly predictable from the preceding one increases cross-lingual similarity, which we confirm in pretrained LLMs.

Large language models make claims about themselves that are both consequential and increasingly difficult to verify from behavior alone. How can we distinguish plausible confabulations from genuine introspection? In this paper, we identify mechanistic signatures of faithful self-report in a controlled setting. Using low-rank adapters, we train models to make decisions on behalf of fictitious characters, according to latent linear preference functions. We find sustained fine-tuning on an implicit decision task can lead to the emergence of accurate self-reporting of models' learned preferences, even without explicit self-report supervision. We ask two research questions about this emergent phenomenon. First: is the emergence of accurate self-reporting accompanied by a measurable structural change in the model? Weight ablations and frozen-layer experiments together indicate that preference representations shift to earlier layers over training, consistent with the hypothesis that faithful self-report requires preferences to be located where pre-existing verbalization mechanisms can access them. Second: can these structural differences distinguish faithful models from unfaithful ones? Using attribution patching, we find that faithful models exhibit significantly higher attribution similarity between the decision-making and self-report tasks — a mechanistic signature of faithful self-report that does not require us to understand the content of the report itself. Previous work on self-report has observed behaviorally that models can be faithful or unfaithful; our work proposes that, at least in our restricted setting, it is possible to distinguish between the two patterns of computation by examining the structure of the networks themselves.

Explicitly eliciting reasoning substantially improves LLM performance. Existing approaches require a predefined characterization of reasoning, whether through CoT prompt design, contrastive CoT directions, or via SAE derived reasoning features. For mathematical reasoning with verifiable answers, we show that a much simpler signal suffices, which is the correctness of the model's own direct answer attempts. This signal yields a latent direction that elicits reasoning. This direction is decodable within the activations of most attention heads, but only a small subset of them can be effectively intervened. We introduce COMPASS, an inference-time steering method that identifies these heads using a logit-space attribution score and steers their activations along the correctness direction, requiring only per-head activation statistics. Across three model families and multiple math benchmarks, COMPASS outperforms the activation-steering baselines we compare against, improves GSM8K accuracy by 16 percentage points on average, and approaches CoT accuracy with 20-70% fewer generated tokens. Interventions transfer without re-fitting to unseen benchmarks, and ablations show that both the correctness direction and the small set of heads carrying it are necessary, with the effect concentrated in remarkably few heads.

Evaluating text generation requires measuring how well the generated distribution matches the data distribution. For autoregressive models, this is done by the perplexity. Diffusion and flow-based language models can only provide a likelihood bound, whose tightness differs between model families. Sample-based substitutes such as generative perplexity with entropy do not consider the distribution fit. We propose SOL, a distance between text distributions. Each sequence is represented by the empirical measure of its hidden states under a fixed transformer and the distributions of these measures are compared by the double sliced Wasserstein distance. We prove that SOL is a metric if the transformer is injective. Experiments show that SOL detects distributional failures, recovers expected model trends, and provides stable sample-based estimates. We put forward SOL to fill the gap in the current evaluation protocol used for non auto-regressive models. As a first step we use SOL to re-evaluate a variety of models trained on OpenWebText.

Tokenizer-free language models remove the inductive bias of fixed tokenizers by modeling text directly as bytes, but the resulting longer sequences substantially increase computation and eliminate explicit text abstractions. We ask whether this additional computation can be useful, and whether standard Transformers can learn the abstractions that tokenization provides. We study these questions on Transformers without specialized tokenization-related architectures. With token-superposition training and hash embeddings, byte Transformers consistently outperform subword Transformers as model size scales. We further find that byte Transformers build local text abstractions as external tokenizers: a set of segmentation-like positions are used to collect local context representations, and restricting up to $25%$ of intermediate layers to these local representations preserves downstream performance. Finally, these learned structures induce highly non-uniform generation difficulty, with uncertainty concentrated near local structure boundaries; exploiting them for speculative decoding yields $3.4\times$ more accepted tokens than in subword Transformers.

The robustness of Personally Identifiable Information (PII) protection in Large Language Models (LLMs) is a critical concern, yet the risks associated with cross-lingual data extraction remain under-explored. This study evaluates the vulnerability of English-centric and multilingual models to Training Data Extraction (TDE) attacks when prompted in non-English languages. We construct a multi-domain PII dataset comprising social media handles, email addresses, and phone numbers and translate the attack contexts into Italian, Spanish, French, and German. Our results show that TDE attacks against both English-centric and multilingual models transfer to different languages: the attacks are successful on translated prompts, even though only the original English prompt might have been included in the pre-training data. A web-presence check on a sample of the translations confirms that they are not available online. The share of English leaks recovered in other languages grows with the multilingual capability of the model, and it drops sharply when the original wording is lost, even without a change of language. This suggests that native multilingual pre-training facilitates the emergence of latent cross-linguistic bridges that simplify the retrieval of personally identifiable information (PII). We analyze the activations of multilingual large language models (LLMs) and find that different translations of the same prompt are bridged in similar representations, with the strongest alignment in the middle layers. Our results highlight a fundamental security gap in modern LLMs, necessitating more robust, language-agnostic sanitization strategies for future model alignment.

In this paper, we study how training data creates associations between the tokens at the start of a base model's response and the reasoning behavior that follows. First, we demonstrate that fixing particular starting token cues makes a base model's performance competitive with that of its reinforcement learning (RL)-trained counterparts on math and coding. For instance, the cue ".\n\nOkay" raises Olmo-3-7B's MATH-500 pass@1 accuracy from 42% to 78%, while "Alright," raises Qwen3-14B's from 72% to 87%. Second, RL makes these cues more likely, while fixing them recovers much of its performance gain over the base model. Third, we trace the reasoning effects of token cues to the training data. We perform causal data interventions to turn an arbitrary word, such as "chicken", into an effective reasoning cue, or remove an existing cue's effect. A similar edit makes the prompt instruction "Think duck duck goose" as effective as "Think step by step" at eliciting reasoning. We also find that the hidden state representations induced by different cues correlate with different document types from the training set. Finally, we extend our study of token cues with a case study in language model safety, finding that different cues elicit distinct refusal and compliance behaviors that correspond to different types of training data.

Large language model (LLM)-based agents can exhibit deceptive behavior during task execution, including hiding failures, fabricating results, or falsely signaling task completion. Existing monitoring approaches mainly detect deception after it appears in observable actions or outputs. In this paper, we investigate whether deceptive behavior can be predicted from an agent's internal representations before it becomes externally visible. We frame deception monitoring as a trajectory-level representation analysis problem and align agent trajectories around key decision points. Using hidden states extracted before these points, we show that future honest and deceptive outcomes can be reliably distinguished, with predictive signals remaining detectable several model calls before the final decision. We further characterize the temporal evolution of these signals: deception-related representations are weak early in execution but become increasingly identifiable as trajectories progress, while transferable structure can emerge before the strongest decision-adjacent signals appear. Finally, we intervene on the identified honest-deceptive representation directions during inference and find that activation steering reduces downstream deceptive behavior, suggesting that these representations influence agent decisions. Our findings indicate that agent deception is an evolving internal process that can be detected and potentially mitigated before it is expressed externally.

Large Vision-Language Models (LVLMs) frequently suffer from object hallucination. Existing training-free interventions primarily manipulate attention weights, which indirectly affect the deep semantics reaching the final predictive layers. In this work, we shift our focus to the hidden state vectors extracted after self-attention and residual addition. Empirical analysis reveals that hallucinated tokens do not simply over-rely on linguistic priors; instead, they exhibit an anomalous contextual deviation, showing significantly lower similarities to both textual and visual contexts in intermediate layers. Motivated by this, we propose ROT, a layer-specific, training-free framework. ROT dynamically detects semantic deviation in the middle layers and applies a norm-preserving rotation to steer the hidden states back toward the local multimodal context plane spanned by the contexts. For subsequent layers, a representational smoothing mechanism is introduced to stabilize the calibrated trajectory. Extensive experiments on multiple benchmarks demonstrate that ROT consistently reduces hallucinations across various model architectures and scales, offering an efficient, geometry-driven solution for grounded generation.

A representation family is a distinct way of extracting features from time series. Ensemble algorithms that combine several representation families remain the most accurate approach to time series classification. Current state-of-the-art ensembles, most notably HIVE-COTE~2.0, pair a bespoke classification algorithm with each representation family and combine their predictions using a fixed, non-adaptive rule. We present TIGER (Time-series classification with In-context-learning Gated Ensemble of Representations), which instead applies the same small portfolio of three general-purpose classifiers (Ridge, Extra Trees, and Naive Bayes) to four representations from four distinct families, stacking the resulting twelve base learners' predictions into a meta-feature matrix. The final prediction is produced by an adaptive meta-classification rule that chooses, independently for each data set, between a weighted hard majority vote and TabICLv2, a pretrained tabular foundation model used in-context as a meta-classifier, based on the mean number of training samples available per class. On a 142-data-set benchmark drawn from the UCR time series classification archive, TIGER obtains the best mean accuracy, balanced accuracy, and F1-score among six compared algorithms, including HIVE-COTE~2.0, and significantly outperforms each of the other five individually. TIGER's adaptive rule also meaningfully outperforms either of its two constituent meta-classification methods used alone, and its single hyperparameter, tuned using only a twenty-data-set development subset, is shown to generalize to the full evaluation benchmark. We further characterize TIGER's design through an extensive set of ablation experiments and report the design alternatives that we investigated and ultimately discarded.

Tabular foundation models perform in-context learning (ICL) by conditioning predictions on labeled training examples provided as context. Unlike traditional models that separate training from inference, these models must process all training examples in every forward pass, making each prediction expensive. Restricting the number of training examples reduces this cost but substantially degrades performance. Instead of discarding context, we propose activation alignment, a method that leverages the full context to teach a model how to behave when seeing only a subset. This is achieved by training a lightweight linear transformation on synthetic unlabeled data to map the intermediate activations of a data-constrained "student" (using partial context) toward those of a full-context "teacher" (using all data). Training the aligner requires no GPU and converges in seconds to minutes on commodity hardware. We evaluate on 38 classification datasets from the TabArena benchmark using the leading two tabular foundation models, TabPFN-3 and TabFM. Across all context budgets, the aligned student yields broad, statistically significant improvements over the unaligned baseline for both models. In low-data regimes, alignment recovers nearly half of the teacher's predictive advantage. The method provides a practical, low-overhead approach to achieving the inference speed of compact contexts while closing a significant fraction of the performance gap to the full-context teacher.

Multimodal Large Language Models (MLLMs) have demonstrated remarkable potential in video understanding, yet their reliance on retrospective summarization and text-centric priors often limits their ability to bridge unobserved causal transitions when applied to Video Event Prediction (VEP). To address this, we propose VepAgent, an agentic framework that integrates causal-transition reasoning with tool-augmented reinforcement learning (RL) for robust VEP. Unlike prior methods that passively project future trajectories from historical dependencies, our approach explicitly models the logical progression from terminal observed states to future events. Specifically, we first construct futurebench-4K, a high-quality chain-of-thought dataset for supervised fine-tuning (SFT) that effectively bridges the causal-logic gap by structuring the deduction of unobserved intermediate states. Subsequently, we develop a diagnostic tool library integrating state tracking, frame retrieval, and region magnification, enabling the agent to dynamically augment reasoning with external tools to recover missing spatio-temporal evidence and resolve visual ambiguities during inference. Moreover, we propose a composite reward mechanism that jointly optimizes prediction accuracy, causal coherence, and reliable prior, compelling the agent to rely on genuine visual grounding rather than superficial textual similarities. Extensive evaluations on FutureBench and NEPBench datasets demonstrate that our method achieves state-of-the-art performance, significantly outperforming larger MLLMs and validating the empirical effectiveness of our agentic, future-oriented reasoning paradigm.

Recent work on multi-agent LLM systems reaches sharply different conclusions: some results show that a single agent with the same information and compute should dominate a delegated system, others that multi-agent gains grow with task depth. We argue that much of the disagreement comes from modelling different bottlenecks, and introduce a stylised reliability model built around two trade-offs. Decomposition reduces the burden of long contexts but incurs a handoff tax when information is compressed or transferred between agents. Redundancy gains from multiple samples, but its benefit depends on how much their failures are shared. With reasoning budget, verification, and task structure added, the model yields two crossover conditions: decomposition becomes preferable once the attention cost avoided by resetting context exceeds the handoff cost, and parallel sampling at equal budget is eventually preferable when its shared-failure floor lies below the error floor of one agent thinking longer. We connect these regimes to recent theoretical and empirical results. On a ledger-reconciliation task we measure the context-degradation curve and the handoff tax from single-agent and handoff runs alone. From these the model places the crossover at depth 10 and predicts decomposition to win at depths 20, 50, and 100. It does, on step-level and final-balance accuracy, and the decomposed system's success, which the prediction never sees, lands within 9 percentage points of the predicted rate at every depth.

Transformers asked to multiply multi-digit numbers in a single forward pass often fail, and interpretability studies of pretrained language models find arithmetic solved by input-range heuristics rather than by an explicit carry. We train small Llama-style transformers from scratch on 4x4 multiplication without chain of thought and find that the input format is decisive: inserting a space token between digits raises exact-match accuracy from 1% to 89%. Output positions are learned in carry-chain order, with the middle digits, which have the longest-range dependencies, learned last. Inside the model, the separator token that predicts each digit (its prediction slot) encodes the carry-in as an angle on a ring in the residual stream; examples with more distinct carry values fill more of the ring. Activation patching between examples matched on the column sum shows that this state is causally used before the last layer: patching the prediction slot alone transfers the source carry in up to 84% of cases after block 4 for one middle column of our best model, while for other columns the carry is first assembled at the neighboring answer slot before reaching its own. Remaining errors are almost always off by one, consistent with a small error on the carry or on the circular digit code.

LLM agents are starting to own the full customer experience. Soon, LLMs may be selling and buying on behalf of companies and customers respectively. Small models are more cost-efficient at scale, but can reinforcement learning train them into competent sellers? We train four Gemma 4 checkpoints (2.3B to 31B effective parameters) with GRPO on a programmatic utility reward for bilateral multi-issue bargaining, and evaluate every arm on the same 1,152 negotiations against two frontier buyers it never saw in training. With the same learning rate ($10^{-6}$) for every size, the gain of the RL model over its base rises from $+0.001$ at 2.3B to $+0.078$ at 31B. Each size was trained once and the two smallest checkpoints use a different architecture, so we fit no scaling law. Tripling the learning rate, with the same or fewer training steps, improves on the shared rate at every size by $+0.032$ (2.3B) to $+0.081$ (4.5B). In exploratory comparisons with two frontier models run as sellers, the 12B seller trained at the tripled rate scores above both, though its untrained base already scores as high as they do. The 4.5B seller at that rate shows no detectable difference from either and fits on one 48 GB GPU. A further 2.3B arm at ten times the shared rate raises pooled score, but its gain concentrates on the evaluation buyer that shares a model family with the training pool. These results suggest tuning the learning rate before concluding that a small model cannot learn to negotiate, and testing against buyers from more than one model family.

We investigate the use of formal methods to provide tight and sound generalization bounds for learning algorithms. By casting the traditional notion of algorithmic stability as a specification to be verified, we demonstrate that recent advances in reachability analysis can yield provable bounds on the generalization of a given model and algorithm on a sample dataset. As sample-specific algorithmic stability is insufficient to bound the usual distributional notion of generalization, we develop a novel concentration inequality to connect the sample-specific results of formal certification algorithms to the required distributional analysis for bounding the expected generalization gap. The resulting framework enables the analysis of prior generalization bounds to extend far beyond their original restrictive assumptions. Our approach computes sound bounds on the expected generalization gap in a constant number of algorithm runs without making any analytical assumptions on the algorithm; to achieve non-vacuous bounds we only require that the certified reachable parameter set is bounded --- a condition that we do not assume but formally verify. In practice, we demonstrate that our framework provides formal generalization guarantees that are orders of magnitude tighter than alternative sound computational approaches at scales ranging from toy datasets to fine-tuning classification heads on top of modern large language models. While we implement certification-enhanced versions of several well-known stability results, future extensions of our approach will enable tighter bounds and enhanced practical adoption across the spectrum of modern generalization bounds.

We consider the stability of multi-step reasoning processes, which have extensive applications in language models, including chain-of-thought and algorithmic reasoning. While longer sequences of reasoning can improve a model's generation capability at test time, the errors due to intermediate reasoning steps can accumulate in autoregressive generation, and thus grow substantially at the end. In this paper, we ask: What are the key factors determining the stability of multi-step reasoning? First, we show an inference error bound governed by the product of spectral norms of the Jacobians taken through the input space across generation steps. This product can be viewed as an error amplification factor, which could scale exponentially with the number of reasoning steps, serving as a quantitative measure of reasoning stability. Second, we analyze this measure in transformer models trained to predict simple tasks like linear and quadratic functions. We theoretically prove that the transformer model converges to a solution where the stability measure decays, thus yielding nearly zero inference loss over (arbitrarily) long steps. Finally, the stability analysis leads to several algorithmic implications for controlling the stability, through (i) chain-of-thought length compression that reduces the sensitivity of each step, and (ii) quantization-aware training that regularizes the input Jacobian norms. We validate the proposed algorithms by fine-tuning language models on graph-algorithmic reasoning tasks and symbolic state-tracking tasks. Across seven evaluations, our algorithms improve over baseline comparisons by 3.5% on average, and by 8.2% for longer-length inputs. Ablation analysis validates that the stability measure is drastically reduced by 3-8$\times$, confirming the regularization effect on the spectral norms of the (input space) Jacobians.

Verifier-guided decoding can prevent harmful reasoning steps from contaminating subsequent generation, but typically relies on an external learned verifier. We ask whether a language model can instead reject its own bad reasoning steps. We define a prefix's recoverability as the probability that the frozen generator can complete it correctly. Diagnostics show that adjacent recoverability changes are often difficult to resolve with practical Monte Carlo budgets, while same-prefix candidates exhibit a sparse low-recoverability tail. We introduce Self-Step Rejection (SSR), which trains a lightweight LoRA acceptance gate on the generator backbone while keeping the base model frozen. SSR uses confidence-qualified first-passage supervision: steps before the first resolved crossing of a root-relative recoverability barrier are accepted, the crossing step is rejected, and unresolved steps and suffixes are excluded. Training combines pointwise classification, same-prefix pairwise learning, and group-relative policy refinement using final-answer correctness. At inference, SSR accepts candidates or resamples from the unchanged prefix under rejection budgets, without an external learned verifier. Across three reasoning models and five mathematical reasoning benchmarks, SSR improves macro-average accuracy over single-pass decoding by 5.4--10.1 points using 1.21--1.40x as many generated tokens, and achieves the highest macro-average accuracy among evaluated step-level methods. Full-solution scaling methods require 4.47--8.27x the single-pass token cost for comparable performance.

Latent reasoning lets a large language model (LLM) think in a continuous space and verbalize only the answer. We argue that an effective latent thought must meet five requirements: it should be useful, helping produce the correct answer rather than merely changing it, diverse, so that resampling yields different reasoning trajectories, explainable, so that a decoded chain of thought (CoT) reflects reasoning the answer actually follows, refinable with more inference compute, and efficient, costing less than an explicit CoT at comparable accuracy. Current methods rarely meet these requirements: they learn shortcuts from the question, distill the explicit CoT into their weights, or imitate it one token at a time. We focus on flow matching in a learned latent space, the family we argue is best placed to meet them, and identify the training choices that make it work. The result is Flow-based Latent Reasoning (FLaRe), a simple recipe covering what the latent space encodes and how to shape it, where to train the flow, how to read out the answer, and a final stage of training on the model's own verified thoughts. A probe for each requirement shows that FLaRe improves on prior latent methods in all five. It also compares favorably with them on arithmetic benchmarks, while reaching 97% of the accuracy of explicit CoT at a quarter of its latency.

Next-token prediction (NTP) is the standard pretraining objective for large language models, yet it provides an explicit training signal only for the immediate next token, which can lead models to exploit local patterns instead of capturing longer-range structure and ideas. Multi-token prediction (MTP) addresses this by training models to predict several future tokens. However, existing MTP methods often introduce a large number of new parameters with limited improvements in downstream performance. Latent MTP approaches address this efficiency issue by encoding future tokens into a vector representation. However, these approaches usually rely on external helper models for future token encoding. We propose LightMTP, a lightweight, i.e., parameter-efficient, latent MTP approach that bootstraps the future token representations from the model's own hidden states. Our two LightMTP variants extend supervision to more future tokens without requiring the additional computational overhead of conventional MTP nor the external supervision latent MTP normally relies on. LightMTP adds at most 1% extra parameters, retains better performance on general language modeling benchmarks, and achieves similar gains in planning, coding, and reasoning.

Large language models (LLMs) have achieved substantial performance gains through increases in model size, training data, and computational resources. However, traditional scaling approaches produce diminishing returns, rising financial and environmental costs, and barriers to participation for researchers operating outside large industrial laboratories. This review examines the evolution of LLM scaling theory from empirical scaling laws to compute-optimal training, with particular emphasis on parameter efficiency, token utilization, data efficiency, and resource-constrained environments. Foundational work on scaling laws is synthesized alongside later research on compute-optimal training, data pruning, efficient architectures, quantization, low-rank adaptation, and edge-oriented optimization. The literature indicates a shift from scale maximization toward more deliberate allocation of parameters, tokens, compute, and hardware resources. At the same time, important empirical, theoretical, and methodological gaps remain regarding whether scaling principles established on enterprise-grade infrastructure generalize to smaller models and constrained computing environments. This review organizes these developments into a unified framework for resource-efficient LLM training and argues that future progress should evaluate efficiency not solely through model performance, but through the relationship among performance, parameter count, computational cost, token allocation, and hardware constraints.

Reasoning models write most of their KV cache while decoding long chains of thought (CoT), so the cache has to be compressed online under a fixed memory budget. Decode-time methods mostly decide which tokens to evict. We ask how a fixed byte budget should be split between the number of cached tokens and their precision. BreadthKV spends the bytes on more tokens at low precision, combining quantization with eviction, and picks the bit-width for each model and budget with a 60-problem end-to-end calibration, since offline attention error does not predict it reliably. On three reasoning models and four math and science benchmarks, it scores above eviction alone in 17 of 18 settings and produces shorter outputs. Much of what eviction loses comes from derailed runs, which keep reasoning until the length cap without reaching an answer. On Qwen3-8B at our tightest budget, eviction sends 91% of AIME samples to the cap and BreadthKV 40%. Under the same protocol, BreadthKV is statistically indistinguishable from a joint rate-distortion allocator (RDKV) that uses 27% more KV memory-time, and it outperforms our re-implementation of ThinKV.