In this work, we establish a novel theoretical connection between supervised fine-tuning and offline reinforcement learning under the token-level Markov decision process, revealing that large language models indeed learn an implicit Q-function for inference.Through this theoretical lens, we demonstrate that the widely used beam search method suffers from unacceptable over-optimism, where inference errors are inevitably amplified due to inflated Q-value estimations of suboptimal steps. To address this limitation, we propose **S**upervised **O**ptimism **C**orrection (SOC), which introduces a simple yet effective auxiliary loss for token-level Q-value estimations during supervised fine-tuning. Specifically, the auxiliary loss employs implicit value regularizationto boost model confidence in expert-demonstrated responses, thereby suppressing over-optimism toward insufficiently supervised responses.Extensive experiments on mathematical reasoning benchmarks, including GSM8K, MATH, and GAOKAO, showcase the superiority of the proposed SOC with beam search across a series of open-source models.

Retrieval-augmented generation (RAG) systems have advanced large language models (LLMs) in complex deep search scenarios requiring multi-step reasoning and iterative information retrieval. However, existing approaches face critical limitations that lack high-quality training trajectories or suffer from the distributional mismatches in simulated environments and prohibitive computational costs for real-world deployment. This paper introduces SimpleDeepSearcher, a lightweight yet effective framework that bridges this gap through strategic data engineering rather than complex training paradigms. Our approach synthesizes high-quality training data by simulating realistic user interactions in live web search environments, coupled with a multi-criteria curation strategy that optimizes the diversity and quality of input and output side. Experiments on five benchmarks across diverse domains demonstrate that SFT on only 871 curated samples yields significant improvements over RL-based baselines. Our work establishes SFT as a viable pathway by systematically addressing the data-scarce bottleneck, offering practical insights for efficient deep search systems. Our anonymous code is available at https://github.com/RUCAIBox/SimpleDeepSearcher

With recommender systems broadly deployed in various online platforms, many efforts have been devoted to learning user preferences and building effective sequential recommenders. However, existing work mainly focuses on capturing user implicit preferences from historical interactions and simply matching them with the next behavior, instead of predicting user explicit intentions. This may lead to inappropriate recommendations. In light of this issue, we propose the adversarial user intention learning approach for sequential recommendaiton, named AuriSRec. The major novelty of our approach is to explicitly predict user current intentions when making recommendations, by inferring their decision-making process as explained in target reviews (reviews written after interacting with the ground-truth item). Specifically, AuriSRec conducts adversarial learning between an intention generator and a discriminator. The generator predicts user intentions by taking their historical reviews and behavioral sequences as inputs, while target reviews provide guidance. Beyond typical sequential modeling methods in the field of natural language process (NLP), a decoupling-based review encoder and a hybrid attention fusion mechanism are introduced to filter noise and enhance the generation capacity. On the other hand, the discriminator determines whether the intention is generated or real based on their matching degree to the target item, thereby guiding the generator to produce gradually improved intentions. Extensive experiments on five real-world datasets demonstrate the effectiveness of our approach.