Sparse Logit Sampling: Accelerating Knowledge Distillation in LLMs

Knowledge distillation can be a cost-effective technique to distill knowledge in Large Language Models, if the teacher output logits can be pre-computed and cached. However, successfully applying this to pre-training remains largely unexplored. In this work, we prove that naive approaches for sparse knowledge distillation such as caching Top-K probabilities, while intuitive, provide biased estimates of teacher probability distribution to the student, resulting in suboptimal performance and calibration. We propose an importance-sampling-based method `Random Sampling Knowledge Distillation', which provides unbiased estimates, preserves the gradient in expectation, and requires storing significantly sparser logits. Our method enables faster training of student models with marginal overhead (<10%) compared to cross-entropy based training, while maintaining competitive performance compared to full distillation, across a range of model sizes from 300M to 3B.

@article{anshumann2025_2503.16870,
  title={ Sparse Logit Sampling: Accelerating Knowledge Distillation in LLMs },
  author={ Anshumann and Mohd Abbas Zaidi and Akhil Kedia and Jinwoo Ahn and Taehwak Kwon and Kangwook Lee and Haejun Lee and Joohyung Lee },
  journal={arXiv preprint arXiv:2503.16870},
  year={ 2025 }
}