Large Language Models (LLMs) represent substantial intellectual and economic investments, yet their effectiveness can inadvertently facilitate model imitation via knowledge distillation (KD). In practical scenarios, competitors can distill proprietary LLM capabilities by simply observing publicly accessible outputs, akin to reverse-engineering a complex performance by observation alone. Existing protective methods like watermarking only identify imitation post-hoc, while other defenses assume the student model mimics the teacher's internal logits, rendering them ineffective against distillation purely from observed output text. This paper confronts the challenge of actively protecting LLMs within the realistic constraints of API-based access. We introduce an effective and efficient Defensive Output Generation (DOGe) strategy that subtly modifies the output behavior of an LLM. Its outputs are accurate and useful for legitimate users, yet are designed to be misleading for distillation, significantly undermining imitation attempts. We achieve this by fine-tuning only the final linear layer of the teacher LLM with an adversarial loss. This targeted training approach anticipates and disrupts distillation attempts during inference time. Our experiments show that, while preserving the performance of the teacher model, student models distilled from the defensively generated outputs demonstrate catastrophically reduced performance, demonstrating DOGe as a practical safeguard against KD-based model imitation.

The unusual properties of in-context learning (ICL) have prompted investigations into the internal mechanisms of large language models. Prior work typically focuses on either special attention heads or task vectors at specific layers, but lacks a unified framework linking these components to the evolution of hidden states across layers that ultimately produce the model's output. In this paper, we propose such a framework for ICL in classification tasks by analyzing two geometric factors that govern performance: the separability and alignment of query hidden states. A fine-grained analysis of layer-wise dynamics reveals a striking two-stage mechanism: separability emerges in early layers, while alignment develops in later layers. Ablation studies further show that Previous Token Heads drive separability, while Induction Heads and task vectors enhance alignment. Our findings thus bridge the gap between attention heads and task vectors, offering a unified account of ICL's underlying mechanisms.

Mathematical reasoning is central to artificial intelligence, with applications in education, code generation, and research-level mathematical discovery. Mathematical competitions highlight two problem types: theorem proving, requiring rigorous proofs, and answer construction, requiring creative generation and formal verification of mathematical objects. Existing research reveals that LLMs can tackle difficult answer-construction tasks but are prone to errors from hallucinations and unverifiable steps, while symbolic methods guarantee rigor but falter in creative answer construction. This raises a key understudied question: how to solve answer-construction problems while preserving both LLM creativity and mathematical rigor? To address this problem, we introduce the Enumerate-Conjecture-Prove (ECP) framework, a modular neuro-symbolic method integrating LLM-based enumeration and pattern-driven conjecturing with formal theorem proving in Lean, and ConstructiveBench, a dataset of 3,640 formal answer-construction problems from math competitions. ECP is model agnostic and shows consistent improvements over pure LLM baselines: on the subset of PutnamBench for answer construction, ECP formally solves 6 out of 337 answer-construction problems end to end (up from 4 without ECP) using GPT-5 mini and DeepSeek-Prover-V2-7B. On ConstructiveBench, ECP achieves 33.1% end-to-end state-of-the-art accuracy (up from 32.5%), demonstrating its potential to advance formal mathematical reasoning by combining LLM conjecturing with formal verification. Our code and dataset are publicly available at GitHub (https://github.com/sunjia72/ECP) and Hugging Face (https://huggingface.co/datasets/sunjia72/ConstructiveBench).

While Large Language Models (LLMs) can generate fluent and convincing responses, they are not necessarily correct. This is especially apparent in the popular decompose-then-verify factuality evaluation pipeline, where LLMs evaluate generations by decomposing the generations into individual, valid claims. Factuality evaluation is especially important for medical answers, since incorrect medical information could seriously harm the patient. However, existing factuality systems are a poor match for the medical domain, as they are typically only evaluated on objective, entity-centric, formulaic texts such as biographies and historical topics. This differs from condition-dependent, conversational, hypothetical, sentence-structure diverse, and subjective medical answers, which makes decomposition into valid facts challenging. We propose MedScore, a new pipeline to decompose medical answers into condition-aware valid facts and verify against in-domain corpora. Our method extracts up to three times more valid facts than existing methods, reducing hallucination and vague references, and retaining condition-dependency in facts. The resulting factuality score substantially varies by decomposition method, verification corpus, and used backbone LLM, highlighting the importance of customizing each step for reliable factuality evaluation by using our generalizable and modularized pipeline for domain adaptation.

Post-training has demonstrated its importance in enhancing the reasoning capabilities of large language models (LLMs). The primary post-training methods can be categorized into supervised fine-tuning (SFT) and reinforcement fine-tuning (RFT). SFT is efficient and well-suited for small language models, but it may lead to overfitting and limit the reasoning abilities of larger models. In contrast, RFT generally yields better generalization but depends heavily on the strength of the base model. To address the limitations of SFT and RFT, we propose Unified Fine-Tuning (UFT), a novel post-training paradigm that unifies SFT and RFT into a single, integrated process. UFT enables the model to effectively explore solutions while incorporating informative supervision signals, bridging the gap between memorizing and thinking underlying existing methods. Notably, UFT outperforms both SFT and RFT in general, regardless of model sizes. Furthermore, we theoretically prove that UFT breaks RFT's inherent exponential sample complexity bottleneck, showing for the first time that unified training can exponentially accelerate convergence on long-horizon reasoning tasks.

Despite bilingual speakers frequently using mixed-language queries in web searches, Information Retrieval (IR) research on them remains scarce. To address this, we introduce MiLQ, Mixed-Language Query test set, the first public benchmark of mixed-language queries, qualified as realistic and relatively preferred. Experiments show that multilingual IR models perform moderately on MiLQ and inconsistently across native, English, and mixed-language queries, also suggesting code-switched training data's potential for robust IR models handling such queries. Meanwhile, intentional English mixing in queries proves an effective strategy for bilinguals searching English documents, which our analysis attributes to enhanced token matching compared to native queries.

Large Language Models (LLMs) have demonstrated strong generative capabilities but remain prone to inconsistencies and hallucinations. We introduce Peer Elicitation Games (PEG), a training-free, game-theoretic framework for aligning LLMs through a peer elicitation mechanism involving a generator and multiple discriminators instantiated from distinct base models. Discriminators interact in a peer evaluation setting, where utilities are computed using a determinant-based mutual information score that provably incentivizes truthful reporting without requiring ground-truth labels. We establish theoretical guarantees showing that each agent, via online learning, achieves sublinear regret in the sense their cumulative performance approaches that of the best fixed truthful strategy in hindsight. Moreover, we prove last-iterate convergence to a truthful Nash equilibrium, ensuring that the actual policies used by agents converge to stable and truthful behavior over time. Empirical evaluations across multiple benchmarks demonstrate significant improvements in factual accuracy. These results position PEG as a practical approach for eliciting truthful behavior from LLMs without supervision or fine-tuning.

Model merging provides a scalable alternative to multi-task training by combining specialized finetuned models through parameter arithmetic, enabling efficient deployment without the need for joint training or access to all task data. While recent methods have shown promise, existing evaluations are limited in both model scale and task diversity, leaving open questions about their applicability to large, domain-specialized LLMs. To tackle the challenges, we introduce MergeBench, a comprehensive evaluation suite designed to assess model merging at scale. MergeBench builds on state-of-the-art open-source language models, including Llama and Gemma families at 2B to 9B scales, and covers five key domains: instruction following, mathematics, multilingual understanding, coding and safety. We standardize finetuning and evaluation protocols, and assess eight representative merging methods across multi-task performance, forgetting and runtime efficiency. Based on extensive experiments, we provide practical guidelines for algorithm selection and share insights showing that model merging tends to perform better on stronger base models, with techniques such as merging coefficient tuning and sparsification improving knowledge retention. However, several challenges remain, including the computational cost on large models, the gap for in-domain performance compared to multi-task models, and the underexplored role of model merging in standard LLM training pipelines. We hope MergeBench provides a foundation for future research to advance the understanding and practical application of model merging. Our project page is at \href{https://yifei-he.github.io/mergebench/}{https://yifei-he.github.io/mergebench/}.

Plug-and-play (PnP) methods with deep denoisers have shown impressive results in imaging problems. They typically require strong convexity or smoothness of the fidelity term and a (residual) non-expansive denoiser for convergence. These assumptions, however, are violated in Poisson inverse problems, and non-expansiveness can hinder denoising performance. To address these challenges, we propose a cocoercive conservative (CoCo) denoiser, which may be (residual) expansive, leading to improved denoising. By leveraging the generalized Helmholtz decomposition, we introduce a novel training strategy that combines Hamiltonian regularization to promote conservativeness and spectral regularization to ensure cocoerciveness. We prove that CoCo denoiser is a proximal operator of a weakly convex function, enabling a restoration model with an implicit weakly convex prior. The global convergence of PnP methods to a stationary point of this restoration model is established. Extensive experimental results demonstrate that our approach outperforms closely related methods in both visual quality and quantitative metrics.

Genuine human-like causal reasoning is fundamental for strong artificial intelligence. Humans typically identify whether an event is part of the causal chain first, and then influenced by modulatory factors such as morality, normality, and intention to make the final judgment. These two stages naturally map to the fields of 1) actual causality that provides formalisms for causal chain membership and 2) causal judgment from cognitive science that studies psychological modulators that influence causal selection. However, these two domains have largely been studied in isolation, leaving a gap for a systematic method based on LLMs. Therefore, we introduce HCR-Reasoner, a framework that systematically integrates the theory of actual causality and causal judgment into LLMs for human-like causal reasoning. It simulates humans by using actual causality formalisms to filter for structurally necessary candidate causes and causal judgment factors to determine the psychologically selected cause. For fine-grained evaluation, we introduce HCR-Bench, a challenging benchmark with 1,093 annotated instances with detailed reasoning steps. Results show HCR-Reasoner consistently and significantly improves LLMs' causal alignment with humans, and that explicitly integrating theory-guided reasoning into LLMs is highly effective for achieving faithful human-like causal reasoning.