Not All Negative Samples Are Equal: LLMs Learn Better from Plausible Reasoning

Learning from negative samples holds great promise for improving Large Language Model (LLM) reasoning capability, yet existing methods treat all incorrect responses as equally informative, overlooking the crucial role of sample quality. To address this, we propose Plausible Negative Samples (PNS), a method that synthesizes high-quality negative samples exhibiting expected format and structural coherence while ultimately yielding incorrect answers. PNS trains a dedicated model via reverse reinforcement learning (RL) guided by a composite reward combining format compliance, accuracy inversion, reward model assessment, and chain-of-thought evaluation, generating responses nearly indistinguishable from correct solutions. We further validate PNS as a plug-and-play data source for preference optimization across three backbone models on seven mathematical reasoning benchmarks. Results demonstrate that PNS consistently outperforms other negative sample synthesis methods, achieving an average improvement of 2.03% over RL-trained models.

From Atoms to Chains: Divergence-Guided Reasoning Curriculum for Unlabeled LLM Domain Adaptation

Adapting Large Language Models (LLMs) to specialized domains without human-annotated data is a crucial yet formidable challenge. Widely adopted knowledge distillation methods often devolve into coarse-grained mimicry, where the student model inefficiently targets its own weaknesses and risks inheriting the teacher's reasoning flaws. This exposes a critical pedagogical dilemma: how to devise a reliable curriculum when the teacher itself is not an infallible expert. Our work resolves this by capitalizing on a key insight: while LLMs may exhibit fallibility in complex, holistic reasoning, they often exhibit high fidelity on focused, atomic sub-problems. Based on this, we propose Divergence-Guided Reasoning Curriculum (DGRC), which constructs a learning path from atomic knowledge to reasoning chains by dynamically deriving two complementary curricula from disagreements in reasoning pathways. When a student and teacher produce conflicting results, DGRC directs the teacher to perform a diagnostic analysis: it analyzes both reasoning paths to formulate atomic queries that target the specific points of divergence, and then self-answers these queries to create high-confidence atomic question-answer pairs. These pairs then serve a dual purpose: (1) providing an atomic curriculum to rectify the student's knowledge gaps, and (2) serving as factual criteria to filter the teacher's original reasoning chains, yielding a verified CoT curriculum that teaches the student how to integrate atomic knowledge into complete reasoning paths. Experiments across the medical and legal domains on student models of various sizes demonstrate the effectiveness of our DGRC framework. Notably, our method achieves a 7.76% relative improvement for the 1.5B student model in the medical domain over strong unlabeled baseline.

Bootstrap Generalization Ability from Loss Landscape Perspective

Domain generalization aims to learn a model that can generalize well on the unseen test dataset, i.e., out-of-distribution data, which has different distribution from the training dataset. To address domain generalization in computer vision, we introduce the loss landscape theory into this field. Specifically, we bootstrap the generalization ability of the deep learning model from the loss landscape perspective in four aspects, including backbone, regularization, training paradigm, and learning rate. We verify the proposed theory on the NICO++, PACS, and VLCS datasets by doing extensive ablation studies as well as visualizations. In addition, we apply this theory in the ECCV 2022 NICO Challenge1 and achieve the 3rd place without using any domain invariant methods.