Entropy-Based Adaptive Weighting for Self-Training
This work addresses the problem of improving mathematical reasoning in large language models for researchers and practitioners, but it is incremental as it builds on existing self-training methods with a specific weighting enhancement.
The paper tackles the challenge of optimizing self-generated data for training large language models on mathematical reasoning tasks by proposing an entropy-based adaptive weighting strategy (EAST) that prioritizes uncertain examples, resulting in a 1% gain on MATH and a 1-2% boost on GSM8K compared to baseline methods.
The mathematical problem-solving capabilities of large language models have become a focal point of research, with growing interests in leveraging self-generated reasoning paths as a promising way to refine and enhance these models. These paths capture step-by-step logical processes while requiring only the correct answer for supervision. The self-training method has been shown to be effective in reasoning tasks while eliminating the need for external models and manual annotations. However, optimizing the use of self-generated data for model training remains an open challenge. In this work, we propose Entropy-Based Adaptive Weighting for Self-Training (EAST), an adaptive weighting strategy designed to prioritize uncertain data during self-training. Specifically, EAST employs a mapping function with a tunable parameter that controls the sharpness of the weighting, assigning higher weights to data where the model exhibits greater uncertainty. This approach guides the model to focus on more informative and challenging examples, thereby enhancing its reasoning ability. We evaluate our approach on GSM8K and MATH benchmarks. Empirical results show that, while the vanilla method yields virtually no improvement (0%) on MATH, EAST achieves around a 1% gain over backbone model. On GSM8K, EAST attains a further 1-2% performance boost compared to the vanilla method.