BLUR: A Bi-Level Optimization Approach for LLM Unlearning

Enabling large language models (LLMs) to unlearn knowledge and capabilities acquired during training has proven vital for ensuring compliance with data regulations and promoting ethical practices in generative AI. Although there are growing interests in developing various unlearning algorithms, it remains unclear how to best formulate the unlearning problem. The most popular formulation uses a weighted sum of forget and retain loss, but it often leads to performance degradation due to the inherent trade-off between forget and retain losses. In this work, we argue that it is important to model the hierarchical structure of the unlearning problem, where the forget problem (which \textit{unlearns} certain knowledge and/or capabilities) takes priority over the retain problem (which preserves model utility). This hierarchical structure naturally leads to a bi-level optimization formulation where the lower-level objective focuses on minimizing the forget loss, while the upper-level objective aims to maintain the model's utility. Based on this new formulation, we propose a novel algorithm, termed Bi-Level UnleaRning (\texttt{BLUR}), which not only possesses strong theoretical guarantees but more importantly, delivers superior performance. In particular, our extensive experiments demonstrate that \texttt{BLUR} consistently outperforms all the state-of-the-art algorithms across various unlearning tasks, models, and metrics. Codes are available at https://github.com/OptimAI-Lab/BLURLLMUnlearning.

EPiC: Towards Lossless Speedup for Reasoning Training through Edge-Preserving CoT Condensation

Large language models (LLMs) have shown remarkable reasoning capabilities when trained with chain-of-thought (CoT) supervision. However, the long and verbose CoT traces, especially those distilled from large reasoning models (LRMs) such as DeepSeek-R1, significantly increase training costs during the distillation process, where a non-reasoning base model is taught to replicate the reasoning behavior of an LRM. In this work, we study the problem of CoT condensation for resource-efficient reasoning training, aimed at pruning intermediate reasoning steps (i.e., thoughts) in CoT traces, enabling supervised model training on length-reduced CoT data while preserving both answer accuracy and the model's ability to generate coherent reasoning. Our rationale is that CoT traces typically follow a three-stage structure: problem understanding, exploration, and solution convergence. Through empirical analysis, we find that retaining the structure of the reasoning trace, especially the early stage of problem understanding (rich in reflective cues) and the final stage of solution convergence, is sufficient to achieve lossless reasoning supervision. To this end, we propose an Edge-Preserving Condensation method, EPiC, which selectively retains only the initial and final segments of each CoT trace while discarding the middle portion. This design draws an analogy to preserving the "edge" of a reasoning trajectory, capturing both the initial problem framing and the final answer synthesis, to maintain logical continuity. Experiments across multiple model families (Qwen and LLaMA) and benchmarks show that EPiC reduces training time by over 34% while achieving lossless reasoning accuracy on MATH500, comparable to full CoT supervision. To the best of our knowledge, this is the first study to explore thought-level CoT condensation for efficient reasoning model distillation.