LLM Self-Refinement

Test-time training (TTT) adapts large language models (LLMs) during inference using only unlabeled test inputs. Existing methods, however, face two major bottlenecks on hard reasoning tasks: (1) \emph{lack of learnable samples}, as self-generated pseudo-labels on difficult questions are often noisy and yield unstable rewards; and (2) \emph{inefficient exploration}, as performance gains depend on repeatedly sampling many rollouts without explicit diagnosis of why previous attempts fail. We propose \textbf{TTSR} (\textbf{T}est-\textbf{T}ime \textbf{S}elf-\textbf{R}eflection), a self-evolving framework based on a \emph{reflect-then-synthesize} paradigm. A single pretrained model alternates between a \textit{Student} role and a \textit{Teacher} role: the Student solves test questions and updates, while the Teacher analyzes failed trajectories and synthesizes targeted variant questions closer to the Student's capability frontier. TTSR further maintains a cross-iteration \textit{weakness memory} and compiles persistent weaknesses into a lightweight \textit{strategy note} prepended to subsequent Student inputs, so diagnostic knowledge can guide exploration and gradually fade as weaknesses are resolved. Experiments on challenging mathematical reasoning benchmarks show consistent test-time improvements, strong cross-backbone generalization, and transfer to general-domain reasoning tasks.

Supervised fine-tuning (SFT) datasets are critical to the downstream performance of large language models, yet they often contain low-quality or harmful question-response pairs. To improve SFT data quality, we develop a unified bilevel framework that combines offline data selection with the online self-refining generation. In the offline setting, bilevel data selection (BDS) selects question-response pairs from the offline SFT dataset to maximize the validation performance. We theoretically show that the optimal model given by BDS outperforms direct data mixing approach in useful data coverage. Moreover, we provide a global convergence analysis for gradient-based BDS approach for one-layer Transformer, showing that the epsilon-global optimum of offline BDS is achievable in finite time. Although efficient, offline BDS discards potentially harmful questions together with responses, thereby reducing question diversity. We address this limitation by refining the responses to selected questions using online self-refining generation framework. However, BDS is inefficient to update the response weights when responses are regenerated online. To address this issue, we introduce bilevel multi-objective optimization (BMO) for response-level weighting. We show that BMO recovers the same validation-aligned solution as BDS, but admits a closed-form importance-ratio weight that adapts to regenerated responses. Experiments on LLM quality enhancement and safety-aware fine-tuning demonstrate that the proposed framework consistently improves both data quality and downstream fine-tuning performance.