Learning from Your Own Mistakes: Constructing Learnable Micro-Reflective Trajectories for Self-Distillation

Self-distillation improves reasoning in large language models by using the model's own rollouts as training signal, typically through implicit logit-level alignment that minimizes KL divergence toward a privileged target distribution. However, because this supervision is generated via uncontrolled sampling, it provides no diagnostic insight into the model's specific errors or corrective guidance for its individual failure patterns. Consequently, the model learns to imitate a privileged distribution rather than receiving fine-grained corrections that pinpoint where and why its reasoning fails. In this paper, we propose Trajectory-Augmented Policy Optimization (TAPO), which advances self-distillation from implicit distributional alignment to explicit trajectory construction. During RL training, the model produces both correct and incorrect rollouts to the same query, and TAPO leverages this contrastive structure to construct micro-reflective corrections, new training trajectories that retain the model's erroneous reasoning up to the point of failure, then insert a natural-language diagnosis and corrected reasoning guided by a correct reference from the same sampling group. Since each trajectory is anchored in the learner's own prefix and solutions, the corrective signal preserves the model's on-policy distribution to a greater extent than the position-wise alignment imposed by KL-based methods. To integrate these trajectories, TAPO introduces difficulty-aware candidate selection at the model's capability boundary and decoupled advantage estimation to prevent gradient contamination. Experiments on AIME 2024, AIME 2025, and HMMT 2025 show that TAPO achieves consistent improvements over GRPO under the same number of training steps. Further analysis demonstrates that TAPO strengthens both first-pass reasoning and error-correction effectiveness.

Controlling Output Rankings in Generative Engines for LLM-based Search

The way customers search for and choose products is changing with the rise of large language models (LLMs). LLM-based search, or generative engines, provides direct product recommendations to users, rather than traditional online search results that require users to explore options themselves. However, these recommendations are strongly influenced by the initial retrieval order of LLMs, which disadvantages small businesses and independent creators by limiting their visibility. In this work, we propose CORE, an optimization method that \textbf{C}ontrols \textbf{O}utput \textbf{R}ankings in g\textbf{E}nerative Engines for LLM-based search. Since the LLM's interactions with the search engine are black-box, CORE targets the content returned by search engines as the primary means of influencing output rankings. Specifically, CORE optimizes retrieved content by appending strategically designed optimization content to steer the ranking of outputs. We introduce three types of optimization content: string-based, reasoning-based, and review-based, demonstrating their effectiveness in shaping output rankings. To evaluate CORE in realistic settings, we introduce ProductBench, a large-scale benchmark with 15 product categories and 200 products per category, where each product is associated with its top-10 recommendations collected from Amazon's search interface. Extensive experiments on four LLMs with search capabilities (GPT-4o, Gemini-2.5, Claude-4, and Grok-3) demonstrate that CORE achieves an average Promotion Success Rate of \textbf{91.4\% @Top-5}, \textbf{86.6\% @Top-3}, and \textbf{80.3\% @Top-1}, across 15 product categories, outperforming existing ranking manipulation methods while preserving the fluency of optimized content.