LLM 理论进展

Large Language Models (LLMs) have recently shown promise in molecular discovery, yet a gap remains between their probabilistic nature over discrete sequential tokens and the rigid topological constraints of chemical space. This raises the question of whether molecular LLMs can generalize beyond the local neighborhoods induced by their sequence-based representations. To systematically investigate this question, we introduce a Molecular Perturbation framework that generates syntax-valid structural variants of training molecules under controlled Graph Edit Distance (GED) to probe the manifold regularity of molecular LLMs. Our analysis shows that even a single edit can cause substantial performance drops on common molecular tasks, revealing a narrow local trust region and fragile sensitivity to structural changes. Since similar molecules tend to exhibit similar properties, In-Context Tuning (ICT), which anchors predictions on structurally similar molecules, offers a natural way to mitigate such fragility. Our experiments also examine whether ICT confers robustness under controlled structural perturbations, and the results suggest that it can partially expand the local trust region and offer a promising direction for stabilizing molecular LLMs against structural variation.

As Large Language Models (LLMs) and agentic systems become integrated into real-world applications, ensuring their safety and security is critical. Guardrail systems that detect and block malicious instructions sent to and from an LLM are an essential component of AI security. However, researchers conducting black-box adversarial emulation against production AI systems often struggle to determine whether a guardrail block or an LLM rejection has occurred. This distinction is important because the techniques used to bypass guardrails can differ substantially from those used to bypass LLM safety alignment, and has a material impact on attack technique selection and optimization. We propose the first black-box guardrail reconnaissance methodology, which detects the presence of a guardrail within a target AI system through behavioral monitoring of HTTP, lexical, and timing signals, assuming only black-box access and zero prior knowledge of the guardrail or AI system. Experiments demonstrate that our approach detects guardrail presence with 100% accuracy, with statistically significant behavioral separation between benign and malicious interactions (q < 0.001). Our approach further identifies the content categories a guardrail is designed to block, and distinguishes guardrail blocks from LLM rejection on unseen prompts with an average F1 score of 98%.

Large language models (LLMs) are increasingly consulted on contested scientific questions, raising the concern that they will sycophantically retreat from established consensus when a user signals doubt — drifting toward a false balance that treats settled science as one view among several. We test this across three open instruction-tuned models (Llama-3.1-8B, Qwen2.5-7B, Mistral-7B), three consensus-science domains (climate, vaccines, evolution), and single- and multi-turn settings, combining behavioral measurement with linear probing and activation patching. We do not observe sycophantic retreat. Instead, models show three distinct policies under the same skeptical pressure: reactive assertion, where consensus assertion increases rather than decreases (Llama); surface hedging, where tone softens while the position holds (Qwen); and non-response (Mistral). Pairwise judgments confirm the reactive shift is stance, not style (63.6%, p=.007), and a decomposition identifies increased consensus assertion, not false balance, as its driver (beta=+0.042 per dose, p<1e-77). Linear probes localize the divergence to middle layers — perfect separation in Llama and Qwen versus 72% in Mistral, with non-overlapping confidence intervals — indicating the non-responsive model does not linearly represent the skepticism signal at all. Crucially, this robustness does not transfer: it attenuates across domains and, in the safety-critical vaccine domain, can reverse, with myth-rebuttal weakening under skeptical pressure. We synthesize these into a four-way taxonomy separating active from accidental robustness, and argue that behavioral evaluation alone cannot distinguish a model that resists skepticism because it understands the signal from one that only appears to resist because it fails to perceive it.

Vibe coding democratizes software development by allowing users to generate code via natural-language (NL) interaction with large language models (LLMs). However, the code is reliable only when it faithfully implements the user's intent, which is difficult and labor-intensive for users to validate. Existing validation methods either rely on LLM-assisted automated testing, which suffers from prompt ambiguity and model fallibility, or involve users only in partial software artifacts such as prompts and test cases, which may overlook corner cases and program details. Motivated by a bug study of LLM-generated code, we find that detailed human feedback is essential, as failures often stem from underspecified requirements or subtle semantic deviations. This paper presents verifiable literate programming (VLP), a human-in-the-loop framework designed to make the review/validation process of LLM-generated code accessible to users at all programming levels. At its core, VLP proposes unambiguous NL-based documentation as a readable intermediate layer between prompts and code. The documentation demonstrates concrete program semantics and enables users to provide feedback on potential intent-code mismatches. It supports human-involved, end-to-end repair and validation via three techniques: (i) an NL-style literate language with unambiguous syntax and mostly deterministic code-to-documentation translation, (ii) LLM-based fine-grained mismatch detection that uses trace links between prompts and documentation to focus users' review effort on suspicious documentation lines, and (iii) a verification module that leverages user-validated documentation to derive API-usage checks and formal properties, which are then verified against the generated code using model checking. Our evaluation shows that VLP improves code pass@1 from 28.7%-73.2% to 65.4%-93.5% with reasonable user effort.

Mechanistic interpretability often relies on component-level interventions to discover how a model produces a behavior. This guides attribution, capability knockout, and model pruning downstream to operate by scoring each unit by the effect of ablation in isolation. Such first-order scoring is natural when component importance is additive, but becomes misleading when a transformer self-repairs: after a primary component is removed, a dormant backup can take over, muting the primary's measured effect while the backup itself appears irrelevant on the intact model. We recast this failure as a recovery task, conditional circuit completion, and introduce Conditional Co-Ablation (CoAx), a label-free, output-grounded score that asks how much each remaining unit's ablation effect grows once a primary set has been removed. This conditional growth exposes the second-order interaction that single-unit scores discard. On the GPT-2-small IOI circuit, CoAx raises backup-head recovery from 0.33 to 0.91 ROC-AUC, outperforming all baselines, including self-repair-aware gradient scores (best 0.82); counterfactual patching verifies that the recovered heads causally carry the repair. The same label-free procedure transfers to induction across eight models. Beyond discovery, the recovered backups correct self-repair-masked attribution, identify the components required for capability knockout, and yield repair-aware structured pruning scaling from 124M to 7B. Component importance is therefore not merely an isolated-unit property: in robust circuits, the components that matter can become visible only under the interventions that make them necessary.

Instruction tuning for speech language models (SLMs) is substantially more challenging than for text-based large language models (LLMs), as it requires learning a new modality and a wide range of speech-specific instructions in addition to those supported by text LLMs. Existing SLM training approaches largely replicate the text LLM training paradigm by synthesizing large-scale speech pre-training and instruction-tuning datasets. However, this strategy is difficult to scale, since speech sequences are significantly longer than text sequences. In this paper, we propose SpeechCombine, an instruction-following speech language model trained without any instruction tuning, using only a single round of speech pre-training on 30k hours of data. Starting from a text LLM base model, we perform continuous pre-training on speech utterances to obtain a speech-adapted model, and then directly combine its weights with the weight difference between the instruction-tuned and base versions of the text LLM. Our results show that this simple combination strategy not only preserves the knowledge and capabilities of the original text LLM, but also effectively transfers them to the speech domain. These findings suggest a new direction for SLM training that avoids reliance on massive speech data.

Scalable and reliable grading of command-line examinations remains a challenge in computing education, where rising enrolments make manual marking difficult and rule-based autograders cannot handle partial credit, equivalent solutions, or syntactic variation. This paper evaluates whether four frontier Large Language Models (GPT, Claude Opus, Gemini, and GLM) can approximate expert judgment when grading short Linux/bash command responses. The study adopts a four-level cognitive taxonomy that combines cognitive complexity and operational impact, ranging from information retrieval (L1) and basic file manipulation (L2) to structural operations (L3) and advanced system management (L4). The models were tested with two prompt variants, a minimal baseline and a rubric-enhanced version, on 1200 real responses from second-year Computer Engineering students independently graded by three expert instructors. Gemini~3.0 Pro with rubric-guided prompting achieved the highest human-AI agreement (ICC(3,1) = 0.888, MAE = 0.10, Bland-Altman bias = -0.014). Agreement declined consistently as taxonomy level increased, with the largest discrepancies at higher levels. Across all models, rubric quality had a larger effect than provider choice, with structured prompts consistently improving agreement. These results show that question complexity is a reliable predictor of the difficulty LLMs face in grading accurately, and they establish a principled, taxonomy-based framework for determining which questions are suitable for AI-assisted grading and which require human review, while also providing a transferable evaluation protocol and prompt templates.

Large language models (LLMs) are often asked to produce JSON conforming to a fixed schema, powering information extraction, tool calling, agentic planning, and knowledge-graph construction. Measuring how closely an output matches a gold reference is essential yet surprisingly hard: exact match is brittle, text similarity ignores structure, and an LLM judge is expensive, opaque, and non-deterministic. We address this with Object Aligner (OA), an open-source Python library that scores two JSON objects deterministically by recursively aligning their trees (the Hungarian algorithm for unordered collections, sequence alignment for ordered ones) and awarding partial credit at the granularity the schema declares. The Object Aligner is configured entirely through a set of JSON Schema extensions, so adapting it to a new task involves annotating a schema rather than writing code. Complex structured data, however, are rarely flat trees: records may form graphs or hypergraphs keyed by arbitrary identifiers, breaking the assumptions of prior similarity metrics. Our central contribution, referential alignment, closes this gap by inferring a bijection between gold and candidate identifiers and scoring every reference through it, so the score is invariant to relabeling. Since recovering this bijection exactly is graph isomorphism, the Object Aligner approximates it with Weisfeiler-Leman color refinement. An order-sensitive sequence regime targets ranking and planning. Since the same alignment localizes every mismatch, the Object Aligner emits ranked repair suggestions at no extra cost. Used as a reward inside the GEPA prompt optimizer, Object Aligner helps or stays neutral across all datasets.

Large language models (LLMs) are increasingly deployed in domains requiring guardrails to detect unsafe, off-topic, or adversarial prompts. Existing guardrails predominantly rely on fine-tuning to build classifiers, which often suffer from low generalization and high inference latency. We present kNNGuard, a training-free guardrail that utilizes the activation space of an off-the-shelf LLM. Given a small bank of 50 safe and unsafe prompts, kNNGuard extracts hidden activations and performs multi-layer kNN fusing activation-space and embedding-space scores for classification. Across six domains spanning topical and security prompts, kNNGuard achieves competitive or superior F1 compared to fine-tuned state-of-the-art guardrails while running 2.7x faster than the best comparable guardrail, and 10x faster than a fine-tuned safety classifier without gradient updates or fine-tuning. Domain adaptation requires only updating the labeled bank, which can be constructed in under 10 seconds and several orders of magnitude faster than established guardrails. We also analyze the impact of system prompts, layer selection, and integration into production LLM pipelines as a configurable, low-latency guardrail.

Ontology learning (OL) aims to automatically construct structured knowledge models from text, yet progress remains fragmented across methods, domains, and evaluation practices. Despite decades of research, OL lacks a shared infrastructure for systematic evaluation and ontology access. This absence has hindered progress and fragmented research, leaving the central challenges of OL largely unaddressed. We introduce OntoLearner, a modular, cross-domain, and first-of-its-kind framework that unifies ontology access, large language model (LLM)-driven learning pipelines, and standardized benchmarking. OntoLearner releases 180 machine-readable ontologies spanning 22 domains and provides pipeline-ready datasets with train/dev/test splits for three core OL tasks: term typing, taxonomy discovery, and non-taxonomic relation extraction. Using this infrastructure, we conduct a large-scale empirical study of OL, evaluating 22 retrieval models and 12 LLMs across domains and tasks. The results converge on a finding that reframes the central challenge of OL: failure modes scale with ontological complexity rather than model size or architectural sophistication. The primary bottleneck is not model capability, but a structural mismatch between how models encode knowledge and how ontologies organize it. These findings establish that effective OL is reachable through the cross-domain, multi-task benchmarking enabled by OntoLearner. OntoLearner is open-source (MIT license) at https://github.com/sciknoworg/OntoLearner/.

Steering and monitoring activations in Large Language Models (LLMs) are increasingly used for both safety and interpretability. Early work assumed behaviours are encoded along single linear directions, but recent findings suggest complex behaviours, such as the refusal to answer harmful queries, live in multi-dimensional subspaces. However, existing methods for extracting these subspaces are computationally expensive, which becomes prohibitive on reasoning models who produce long reasoning traces. By adapting the Recursive Feature Machine (RFM) algorithm — which can be computed efficiently — with a probe-informed initialization, we are able to identify the multi-dimensional refusal subspace in seconds, on reasoning (Qwen 3) and non-reasoning (Qwen 2.5) models. While RFM allows for faster subspace identification, it also showed better performances on the ablation task than its alternatives. More work is planned to better understand the relations between subspaces found by different methods. If confirmed, RFM could be a cheap and scalable complement to existing subspace-extraction methods in LLMs.

Effective brain disease diagnosis requires the synergy of brain connectivity patterns and high-level semantic knowledge. Existing methods, however, largely treat semantics from large language models (LLMs) as auxiliary features or supervision, limiting their direct role in decision-making and constraining classification stability and robustness. To overcome this, we propose a semantic-aligned brain network framework that actively integrates LLM-derived semantics into the prediction process. Specifically, ROI-level semantics are first incorporated via global self-attention to enrich node representations and provide whole-brain context. Multi-scale hypergraphs are then constructed to explicitly model functional subnetworks and multi-ROI interactions, addressing the locality limitations of traditional GNNs and capturing high-order dependencies. Finally, a decision-level semantic alignment mechanism selectively injects patient-specific textual embeddings into graph representations, enabling semantics to directly guide predictions without perturbing the underlying network structure. Experiments on public brain network datasets ABIDE and ADHD-200 demonstrate state-of-the-art performance, enhanced stability, and improved interpretability, particularly in small-sample settings.

Personalization changes what a model says to a user; we show that it can also change the reasoning trajectory used to justify the response. Modern LLMs personalize interactions by storing user attributes, preferences, and prior context, then injecting this information into future prompts. We study whether such memory reshapes reasoning on open-ended questions where no single ground-truth answer exists. To quantify this effect, we introduce DRIFTLENS, a ground-truth-free framework that maps each expressed reasoning step to a value category and measures divergence between a question's no-memory trajectory and its trajectory under injected user-attribute memory. We first validate that DRIFTLENS distinguishes content-free pragmatic noise from substantive reasoning changes. Across four LLMs and 10 user-attribute categories, including age, occupation, and disability, user-attribute memory induces medium-to-large reasoning drift above each model's pragmatic-noise floor, even when final answers remain fluent, on-topic, and plausible. We then evaluate GRPO- and DPO-based post-training methods for reducing drift. Both reduce drift, but neither uniformly dominates; effects on downstream capability, helpfulness, and instruction following are model-and reward-dependent. These results suggest that memory-induced reasoning drift is a measurable and only partly mitigated failure mode of personalized language models.

Understanding and reasoning over long contexts has become a key requirement for deploying large language models (LLMs) in realistic applications. Although recent LLMs support increasingly long context windows, they often fail to use relevant evidence that is already present in the input, revealing a gap between context access and effective context utilization. In this work, we propose Recursive Evidence Replay as LLM Harness for Long-Context Reasoning (RECONTEXT), a training-free inference method for improving long-context reasoning. RECONTEXT uses model-internal relevance signals to construct a query-conditioned evidence pool and replays it before final generation while preserving the full original context. This recursive selection process separates evidence organization from answer generation without training, external memory, or context pruning. We also provide a theoretical analysis based on associative memory, which characterizes the context as a memory store, the question as a retrieval cue, attention as cue-trace association, and replay as trace reactivation. Experiments on eight long-context datasets with 128K context length show that RECONTEXT consistently improves evidence utilization across Qwen3-4B, Qwen3-8B, and Llama3-8B, achieving the best average rank on all three backbones. Code is available at https://github.com/Yanjun-Zhao/ReContext.

Video reasoning requires Large Multimodal Models (LMMs) to remain grounded in dense evidence, yet existing systems largely adopt "read-once, generate-many" paradigm, in which visual grounding weakens during generation. This phenomenon has been widely observed and is known as Visual Anchoring Decay. To fill this gap, we introduce Latent Video Cache (Latent-VC), a recurrent latent visual cache inserted into the decoder to preserve compact visual memories throughout reasoning. The cache is trained with supervised contrastive cache alignment and vision-grounded GRPO with a latent grounding reward, while maintaining strict train-inference alignment through native decoder hidden states. Built on Qwen3.5-9B, Latent-VC consistently outperforms strong CoT and SFT+GRPO baselines across six video benchmarks, with especially clear gains on grounding-intensive and long-video tasks. In addition, it also achieves higher accuracy with substantially shorter responses, suggesting that latent visual caching improves video reasoning by preserving visual evidence rather than relying on longer textual chains.

We present Wiola, a fully original Small Language Model (SLM) architecture built from first principles, sharing no structural lineage with any existing model family including GPT, LLaMA, Mistral, or Falcon. Wiola introduces five independently novel components: (i) Spiral Rotary Positional Encoding (SRPE), which embeds token positions on a three-dimensional helical manifold combining absolute, relative, and hierarchical positional signals; (ii) Gated Cross-Layer Attention (GCLA), providing each decoder layer with soft cross-attention access to compressed summaries of two preceding layers for inter-layer coherence; (iii) Adaptive Token Merging (ATM), which dynamically merges se mantically redundant adjacent tokens in middle network layers to reduce attention complexity without information loss; (iv) Dual Stream Feed-Forward (DSFF), replacing the conventional MLP with two parallel streams fused by a learned per-dimension gate; and (v) WiolaRMSNorm, a modified normalisation introducing a per-dimension learned offset vector that prevents representation collapse. We provide complete mathematical derivations, architectural block diagrams, complexity analyses, and systematic comparisons against GPT-2, LLaMA-2, and Mistral. Wiola is released in four sizes (120M, 360M, 700M, and 1.5B parameters) and is fully compatible with the HuggingFace Transformers ecosystem, with all 22 architectural unit tests passing.

Aligning large language models with diverse and heterogeneous human values requires multi-objective alignment methods to effectively trade off conflicting preference dimensions. Current methods achieve this trade-off by training policies conditioned on preference vectors and leveraging online direct preference optimization. However, exploration uncertainty can cause the reward distributions of responses generated under different preference vectors to overlap, and the generated responses may fail to effectively align with the corresponding preference vectors. In this paper, we propose Multi-Objective Exploration and Preference Optimization via Mutual Information (MI-EPO), an information-theoretic framework. It unifies multi-objective exploration and alignment by maximizing the joint conditional mutual information among generated responses, preference feedback, and preference vectors. By incorporating a probabilistic routing mechanism, MI-EPO naturally decomposes objective alignment and preference-aware exploration, encouraging the model to generate responses that are distinguishable and aligned with different preference conditions. Experiments on safe alignment and helpful assistant tasks show that MI-EPO significantly improves the alignment between generated responses and preference vectors, makes the outputs more controllable, and achieves stable trade-offs across multiple objectives.

At the heart of human visual perception lies the ability to maintain a continuous and coherent understanding of the external world. By integrating observations with accumulated experience, the human visual system can continuously adapt to variations in both the target and its surrounding environment, while preserving robust visual continuity as scene dynamics evolve. Human vision can therefore integrate prior knowledge, spatial geometry, and semantic context to understand complex scenes and their changes. As a core problem in computer vision, visual object tracking aims to bring machine perception closer to human visual perception. These capabilities are central to the task of Generic Object Tracking (GOT). In this task, a visual tracker is initialized only with the bounding box of an arbitrarily specified target in the first frame, and must continuously localize the target in subsequent dynamic visual streams. However, future events, observations, and real-world variations are inherently unpredictable; therefore, the model's generalization and online adaptation capabilities remain bottlenecks. Tracking reliability can deteriorate when the target undergoes severe deformation, is affected by complex distractors, encounters significant environmental changes, or belongs to a category unseen during training. This dissertation aims to narrow the gap between machine visual tracking systems and human visual perception by proposing a series of methods that systematically enhance the target discrimination, robust adaptation, and geometric reasoning capabilities of tracking models.

Concept Bottleneck Models (CBMs) provide an intrinsically interpretable alternative to post-hoc explanations. However, existing CBMs often rely on predefined concept vocabularies or supervised annotations, lack explicit concept grounding, and summarize each concept with a single image-level score — discarding spatial recurrence and inter-concept dependencies. We propose a Graph-based Concept Bottleneck Model (G-CBM), an intrinsically interpretable framework that performs unsupervised concept discovery via Non-negative Matrix Factorization (NMF) and represents the discovered concepts as nodes in a per-image concept-graph representation. G-CBM matches region-level features to these concept nodes — providing concept grounding and capturing concept recurrence across the image — and applies a tunable concept filtering threshold $τ$ to suppress weak region-level features. A Graph Attention Network (GAT) then performs concept-level reasoning by modeling nonlinear dependencies across nodes. Across ImageNet, HAM10000, PH2, and Derm7pt, G-CBM achieves an average relative AUC improvement of 3.7% over a ResNet-50 baseline. Concept filtering frequently improves predictive performance while inducing selective concept use, achieving peak AUC of $0.96$ on PH2 with only 2 of 10 concepts and 0.92 on HAM10000 with 3.8 of 9 concepts. On dermoscopy benchmarks, G-CBM is competitive with supervised approaches requiring external annotations. Deletion/insertion analyses with random ablation controls show that the learned concept ranking faithfully reflects model predictions.

We present RuleChef, a framework that uses large language models (LLMs) to generate executable rules for NLP tasks such as text classification, Named Entity Recognition (NER), or relation extraction. Rules are generated based on a task description and a set of labeled examples, then they are iteratively improved based both on additional examples and on human feedback overexisting rules. RuleChef can also be used to bootstrap rules using the observed input-output pairs from any existing model for a given task. LLMs are used only at learning time, synthesizing rules and iteratively patching them based on failures measured on a held-out split. The result of this process is a fast, deterministic, and inspectable rule system. Preliminary evaluation is performed on both classification and NER tasks. We release RuleChef as open-source software under an Apache 2.0

Divergent thinking is a crucial aspect of creativity, yet large language models (LLMs) tend to consistently generate similar responses to open-ended questions, in what has been termed the artificial hivemind effect. Here, we introduce CreativityNeuro, a data-free method for enhancing divergent thinking in LLMs via contrastive weight steering. We evaluate our method across multiple creativity assessments and report several main findings. On the Divergent Association Task (DAT), a vocabulary-space creativity test, CreativityNeuro improves performance by up to 14 human percentile points. Next, in a large-scale human evaluation (N=720) on the Alternative Uses Test (AUT) and the Task Task, CreativityNeuro achieves significant improvements in originality, surprise, and creativity, transferring to longer-form and more open-ended tasks. Importantly, we find that across all three tasks, CreativityNeuro demonstrably reduces measures of mode collapse. Moreover, activation steering achieves comparable performance to CreativityNeuro on the DAT, but it does not transfer to the AUT and Task Task, demonstrating the effectiveness of weight-space steering in generalizing to unseen tasks. In conclusion, CreativityNeuro improves divergent thinking and reduces mode collapse without requiring behavioral data, re-training, or gradient-based fine-tuning, providing a straightforward way to enhance LLM performance in creative domains.

Language models (LMs) raise an intriguing alternative to vector-based retrieval: conditioning on an in-context corpus and directly generating a relevant answer. However, prior work has largely focused on proprietary systems or the smaller-scale reranking task, leaving corpus-scale in-context retrieval largely unexplored. In this work, we present the first systematic study of in-context retrieval on two scales practical retrievers demand: million-token corpora and length-generalization far beyond training-time sizes. We first introduce BlockSearch, a 0.6B LM retriever whose architectural and training modifications improve over prior LM baselines and length-generalize up to 10 times beyond its training regime. Nevertheless, retrieval still collapses under more extreme extrapolation. We trace this failure to an attention dilution effect: as the corpus grows, irrelevant documents dominate the softmax denominator, reducing the normalized mass on the gold document even when its pre-softmax score stays high. Motivated by this analysis, we introduce length-aware adjustments to the attention softmax and document-level sparse attention. With these modifications, at the million-token scale, our model matches dense retrieval on widely studied benchmarks (e.g, MS MARCO and NQ), while outperforming the concurrent model MSA despite being 7 times smaller. Furthermore, it significantly outperforms dense retrieval on tasks requiring entirely different notions of similarity, such as LIMIT, achieving a 3 times higher score. Together, our results position in-context retrieval a promising alternative to classical retrieval while emphasizing attention control under extreme context growth as a new challenge.

Chain-of-thought (CoT) reasoning has emerged as an effective approach for activating latent reasoning capabilities in large language models. However, most existing CoT methods use reasoning chains mainly as inference-time prompts, while the generated reasoning traces are rarely reused as semi-supervised learning signals. In this report, we define Semi-supervised Chain-of-Thought Learning and propose Semi-CoT, a simple framework that uses unlabeled questions to construct pseudo reasoning supervision. Semi-CoT samples multiple pseudo-CoTs for each unlabeled question, estimates answer-level semantic entropy, and selects low-entropy reasoning chains as reliable pseudo-CoT demonstrations. This extends the self-training view of CoT from inference-time refinement to semi-supervised pseudo-supervision. Pilot experiments on AQuA, SVAMP, GSM8K, and MultiArith show that the entropy gate selects high-precision pseudo-CoTs, with pseudo-answer precision ranging from $91.36%$ to $100%$. Semi-CoT also gives small gains on SVAMP and GSM8K, while AQuA shows negative transfer and MultiArith reaches a ceiling. These results suggest that unlabeled questions can provide reliable pseudo reasoning signals, but their effective use still requires stronger demonstration selection or student training.

Deep learning has outgrown any single mathematical explanation. From Approximation to Emergence develops a unified, proof-oriented account of modern deep learning theory, tracing a path from the classical foundations of approximation, optimization, and generalization to the contemporary mechanisms of overparameterization, robustness, generative modeling, transformers, in-context learning, scaling laws, interpretability, alignment, and emergence. Rather than presenting isolated results, the book organizes a broad literature into a coherent research narrative: each theory is examined through the object it controls, the assumptions that make it valid, and the phenomena it leaves unexplained. Written for researchers, graduate students, and mathematically trained practitioners, this monograph offers a rigorous map of deep learning theory as it stands today: powerful, incomplete, and increasingly centered on the question of how learned mechanisms arise from scale, data, architecture, and training.

In Large Language Model (LLM) training, data mixing plays a pivotal role in determining model performance. Recent methods optimize mixture weights via proxy models, but they rely on the assumption of static data distributions. As a result, when the underlying data pool shifts, these methods require costly retraining from scratch. This limitation restricts their ability to scale seamlessly from small settings to larger data pools and model sizes. In this paper, we propose CausalMix to address this limitation by casting data mixture optimization as a causal inference problem. We formulate the statistical features of the data pool as covariates and the domain mixture as the treatment. After fitting a causal model on 512 runs of Qwen2.5-0.5B to estimate the Conditional Average Treatment Effect (CATE), we extrapolate the optimal mixture for an 800K data pool and apply it to train a 7B model. Furthermore, we successfully generalize the framework to long chain-of-thought data on Qwen3-4B-Base. By leveraging causal modeling to isolate confounding biases, CausalMix dynamically infers state-dependent optimal data mixtures. Extensive experiments show that the mixture guided by CausalMix consistently improves performance across multiple downstream tasks, outperforming RegMix and other baselines. In addition, we use the CATE Interpreter to provide visual analysis of the learned mixing strategy. Overall, CausalMix offers a causal and interpretable framework for optimizing LLM data mixtures.

Zeroth-order (ZO) optimization enables fine-tuning large language models when backpropagation is unavailable or memory-prohibitive, but existing methods often perturb full model weights or randomly constructed low-dimensional subspaces, yielding high-variance estimates and limited performance. We propose ZO-Act, an activation-informed ZO fine-tuning method that restricts perturbations to a fixed low-rank subspace derived from input activations. For each linear layer, ZO-Act computes a small activation basis once at initialization and optimizes only lightweight coefficient matrices using forward-only loss evaluations. This reduces the effective perturbation dimension, exposes explicit trainable variables compatible with momentum-based optimizers such as Adam, and naturally supports quantized LLM fine-tuning by keeping low-bit weights frozen. We analyze ZO-Act as zeroth-order optimization over a restricted coefficient space and show that perturbing the low-dimensional coefficients reduces both the variance-dependent convergence term and the finite-difference error of the ZO estimator, at the cost of a controlled subspace approximation bias that is mitigated by the low-rank structure of LLM activations and gradients. Experiments on Llama-3-8B, OPT-13B, and INT4 Llama-3-8B show consistent gains over strong ZO fine-tuning baselines across language understanding, question answering, and commonsense reasoning.

In recent years, large language models have achieved remarkable success and have seen growing adoption in financial applications. At the same time, explainability remains critical in finance, a domain characterized by high stakes and strict regulatory requirements. Although numerous methods have been proposed to explain black box machine learning models, the majority of these approaches are designed for general purpose tasks and do not incorporate domain specific knowledge. In this work, we study the explainability of financial textual data modeled by large language models through the lens of the Shapley value. Specifically, we investigate whether Shapley based attributions align with established financial domain knowledge. Through rigorous theoretical analysis and extensive empirical evaluations, we demonstrate that Shapley values can yield explanations that are consistent with financial reasoning and can offer meaningful insights into the model's behavior in text based financial applications.

Mixed-precision quantization (MPQ) has become a key technique for deploying large language models under stringent memory and compute constraints. We first identify a phenomenon that we term the Perplexity Illusion: layers ranked as important by perplexity-based sensitivity show little rank correlation with those that are most influential for complex reasoning performance, with Kendall $τ\approx 0$ in our analysis. We further reveal an Alignment-Diversity Tradeoff: using only target-task calibration data can degrade post-quantization performance, whereas incorporating general-domain data stabilizes sensitivity estimation and improves robustness across tasks. Based on these observations, we propose TASA (Task-Aware Sensitivity Analysis), a two-level framework that jointly optimizes calibration-data composition and mixed-precision bit allocation. Specifically, TASA searches for a calibration-data mixture using a training-free gradient-trace alignment criterion, and then aggregates perplexity and reasoning-oriented sensitivity signals to guide both inter-layer and intra-layer bit allocation. Experiments on LLaMA-3-8B and Qwen2.5-7B reveal a precision inversion: appropriately allocated 3.5-bit models can match or surpass less task-aware 4-bit baselines. At an average precision of 3.5 bits, TASA matches or outperforms several competitive 4-bit uniform baselines in aggregate accuracy, and improves over the strongest W3 baseline on GSM8K by more than 20 absolute points on LLaMA-3-8B. These results show that calibration-data composition substantially affects task-sensitive quantization, a factor underexplored in prior work.

While inference-time scaling has improved the reasoning abilities of large language models (LLMs), the need to generate long chains-of-thought (CoTs) is a computational bottleneck. Thus, in contrast to sequential scaling methods like CoT, recent parallel scaling techniques instead use fork and join (FJ) primitives to divide work across multiple LLM threads. However, in the fork-join paradigm, threads are typically transient and do not communicate pointwise with one another which limits scalability. To tackle this, we introduce Message Passing Language Models (MPLMs), a framework for LLM reasoning in which threads communicate directly via lightweight send and receive primitives. MPLMs enable efficient scaling through two key mechanisms: (1) reduced communication costs, achieved by avoiding redundant context sharing, and (2) preemption, which allows threads to terminate early based on partial information from their peers. We demonstrate the promise of MPLMs on 3 classes of tasks. First, on Sudoku puzzles, we show that MPLMs require an asymptotically smaller context than both serial CoT and parallel FJ. We then fine-tune a single model to solve 25 x 25 puzzles that remain challenging for standard CoT and FJ approaches, as well as frontier reasoning models without tools. Second, on 3-SAT puzzles, the capability of preemption allows termination of unpromising branches, which results in improved efficiency. Finally, we show that appropriately prompted large pre-trained models follow the MPLM protocol, achieving competitive results on long-context question answering relative to popular fork-join approaches.

Large Language Models (LLMs) represent one of the most significant advances in AI and natural language processing in recent years. Still, many pressing questions about their mechanisms, capabilities, and relationship to human cognition remain highly debated. This chapter aims to outline our current understanding of LLMs by discussing recent evidence on emerging capabilities and their mechanistic implementation within processing layers. We begin with a concise overview of the Transformer architecture, emphasizing how the attention mechanism enables training on massive datasets, allowing LLMs to function as generalist rather than specialized models. Next, we examine emergent LLM capabilities that appear to resemble aspects of human cognition, including symbolic reasoning, theory of mind, and deception strategies. Several studies provide evidence that LLMs can solve tasks previously thought to require human-like cognition. Other studies reveal insightful failure cases that shed light on the differences between human and LLM cognition. Alongside these findings, we review explainable AI approaches ranging from neuron activation analysis to circuit tracing. In the final section, we address current debates concerning what LLMs genuinely understand versus what they merely appear to understand. Prominent arguments against AI anthropomorphism point to the simplicity of LLM training objectives, claiming that LLM behavior is better explained by pattern memorization of training data than by genuine cognition. We argue that this standpoint is guided by misconceptions about optimization processes and cognitive capacity, and advocate for a more nuanced discussion of LLM cognition that neither dismisses the differences between humans and LLMs nor precludes the possibility of AI cognition through overly simplistic reductionist arguments.