arXiv:2604.03557v1 Announce Type: new Abstract: Reasoning hallucinations in large language models (LLMs) often appear as fluent yet unsupported conclusions that violate either the given context or underlying factual knowledge. Although such failures are widely observed, the mechanisms by which decoder-only Transformers produce them remain poorly understood. We model next-token prediction as a graph search process over an underlying graph, where entities correspond to nodes and learned transitions form edges. From this perspective, contextual reasoning is a constrained search over a sampled subgraph (intrinsic reasoning), while context-free queries rely on memorized structures in the underlying graph (extrinsic reasoning). We show that reasoning hallucinations arise from two fundamental mechanisms: \textbf{Path Reuse}, where memorized knowledge overrides contextual constraints during early training, and \textbf{Path Compression}, where frequently traversed multi-step paths collapse into shortcut edges in later training. Together, these mechanisms provide a unified explanation for reasoning hallucinations in LLMs and connected to well-known behaviors observed in downstream applications.

arXiv:2508.07995v5 Announce Type: replace-cross Abstract: Retrieval-augmented generation has achieved strong performance on knowledge-intensive tasks where query-document relevance can be identified through direct lexical or semantic matches. However, many real-world queries involve abstract reasoning, analogical thinking, or multi-step inference, which existing retrievers often struggle to capture. To address this challenge, we present DIVER, a retrieval pipeline designed for reasoning-intensive information retrieval. It consists of four components. The document preprocessing stage enhances readability and preserves content by cleaning noisy texts and segmenting long documents. The query expansion stage leverages large language models to iteratively refine user queries with explicit reasoning and evidence from retrieved documents. The retrieval stage employs a model fine-tuned on synthetic data spanning medical and mathematical domains, along with hard negatives, enabling effective handling of reasoning-intensive queries. Finally, the reranking stage combines pointwise and listwise strategies to produce both fine-grained and globally consistent rankings. On the BRIGHT benchmark, DIVER achieves state-of-the-art nDCG@10 scores of 46.8 overall and 31.9 on original queries, consistently outperforming competitive reasoning-aware models. These results demonstrate the effectiveness of reasoning-aware retrieval strategies in complex real-world tasks.

arXiv:2509.18001v5 Announce Type: replace-cross Abstract: Sharpness-aware minimization (SAM) has emerged as a highly effective technique to improve model generalization, but its underlying principles are not fully understood. We investigate m-sharpness, where SAM performance improves monotonically as the micro-batch size for computing perturbations decreases, a phenomenon critical for distributed training yet lacking rigorous explanation. We leverage an extended Stochastic Differential Equation (SDE) framework and analyze stochastic gradient noise (SGN) to characterize the dynamics of SAM variants, including n-SAM and m-SAM. Our analysis reveals that stochastic perturbations induce an implicit variance-based sharpness regularization whose strength increases as m decreases. Motivated by this insight, we propose Reweighted SAM (RW-SAM), which employs sharpness-weighted sampling to mimic the generalization benefits of m-SAM while remaining parallelizable. Comprehensive experiments validate our theory and method.Code is available at https://github.com/RitianLuo/RW-SAM.