Two mathematical models of knowledge distillation

Practical Tips

Practical tips and how-to guidance will be added by our editorial team.

中文解读

中文解读待补充：本站将优先为睡眠改善、失眠治疗、助眠方法等高价值文章补充中文说明。

Article Summary

Many hypotheses compete to explain the successes of knowledge distillation. To help address this, we propose and analyze a mathematical model of distillation, which suggests that distillation's performance comes not from obtaining better models but from easier to optimize landscapes. For generalized linear models trained with stochastic gradient descent, we prove that distillation fits performant student models asymptotically more quickly than non-distilled models. In rank-1 matrix approximation, we characterize conditions on the target matrix under which gradient descent with distillation converges strictly faster than training on the supervised objective. The theory helps delineate the ways distillation provides benefits (i.e., in optimization speed, not in generalization), and experiments on real datasets corroborate the theoretical predictions.

Sources & References

• Original source
• Full article (PDF)

Comments