Recent advances in synergizing large reasoning models (LRMs) with retrieval-augmented generation (RAG) have shown promising results, yet two critical challenges remain: (1) reasoning models typically operate from a single, unchallenged perspective, limiting their ability to conduct deep, self-correcting reasoning over external documents, and (2) existing training paradigms rely excessively on outcome-oriented rewards, which provide insufficient signal for shaping the complex, multi-step reasoning process. To address these issues, we propose an Reasoner-Verifier framework named Adversarial Reasoning RAG (ARR). The Reasoner and Verifier engage in reasoning on retrieved evidence and critiquing each other’s logic while being guided by process-aware advantage that requires no external scoring model. This reward combines explicit observational signals with internal model uncertainty to jointly optimize reasoning fidelity and verification rigor. Experiments on multiple benchmarks demonstrate the effectiveness of our method. Our code is available at [link](https://github.com/lakhfskn/anonymous-code-of-arr).

Large Language Models (LLMs) often suffer from "Reasoning Collapse" on challenging mathematical reasoning tasks, where stochastic sampling produces lexical variations of the same erroneous logic rather than genuine semantic exploration. We observe that failed reasoning traces are often associated with a low-rank bias manifold in the model’s hidden-state geometry, which reduces exploration toward corrective solution directions. To address this, we propose Spectral Orthogonal Exploration (SOE), a geometric inference framework under a "Student Guides Teacher" paradigm. Instead of using a weak auxiliary agent for imitation, SOE uses it as an orthogonal probe to introduce semantically heterogeneous reasoning signals into the teacher’s orthogonal complement of its dominant subspace. This intervention steers the teacher toward more diverse reasoning trajectories and improves exploration beyond standard sampling. Experiments on mathematical benchmarks show that SOE improves average accuracy by 62.4% and average sampling efficiency by 113.7% over baseline methods, suggesting that geometric interventions can be effective for mitigating reasoning collapse in mathematical reasoning. We further provide preliminary evidence that SOE is also effective on logic and code generation benchmarks. Code is available at https://github.com/dayuwang401/spectral-orthogonal-exploration.

Large Visual Language Models (LVLMs) have demonstrated impressive capabilities across multiple tasks. However, their trustworthiness is often challenged by hallucinations, which can be attributed to the modality misalignment and the inherent hallucinations of their underlying Large Language Models (LLMs) backbone. Existing preference alignment methods focus on aligning model responses with human preferences while neglecting image-text modality alignment, resulting in over-reliance on LLMs and hallucinations. In this paper, we propose Entity-centric Multimodal Preference Optimization (EMPO), which achieves enhanced modality alignment than existing human preference alignment methods. Besides, to overcome the scarcity of high-quality multimodal preference data, we utilize open-source instruction datasets to automatically construct high-quality preference data across three aspects: image, instruction, and response. Experiments on two human preference datasets and five multimodal hallucination benchmarks demonstrate the effectiveness of EMPO, e.g., reducing hallucination rates by 80.4% on Object HalBench and 52.6% on MM HalBench, thereby enhancing the trustworthiness of LVLMs. The code and dataset will be made publicly available.