🤖 AI Summary
This work addresses the issue of systematic bias propagation in student-teacher learning, where directly matching the teacher’s outputs can inadvertently transfer its biases to the student. To mitigate this, the authors propose “Residuals as Teachers” (RaT), a novel approach that introduces residual learning into the student-teacher framework: the teacher estimates the residual between the student’s current prediction and the target, effectively guiding the student to mimic a proximal gradient optimization process. Theoretical analysis demonstrates that RaT achieves minimax optimal convergence rates under non-asymptotic excess risk, whereas conventional soft-target matching suffers from a persistent approximation error. Empirical evaluations on both synthetic data and the ImageNette covariate shift classification benchmark confirm that RaT substantially outperforms baseline methods and effectively suppresses bias propagation.
📝 Abstract
We study statistical estimation in a student--teacher setting, where predictions from a pre-trained teacher are used to guide a student model. A standard approach is to train the student to directly match the teacher's outputs, which we refer to as student soft matching (SM). This approach directly propagates any systematic bias or mis-specification present in the teacher, thereby degrading the student's predictions. We propose and analyze an alternative scheme, known as residual-as-teacher (RaT), in which the teacher is used to estimate residuals in the student's predictions. Our analysis shows how the student can thereby emulate a proximal gradient scheme for solving an oracle optimization problem, and this provably reduces the effect of teacher bias. For general student--teacher pairs, we establish non-asymptotic excess risk bounds for any RaT fixed point, along with convergence guarantees for the student-teacher iterative scheme. For kernel-based student--teacher pairs, we prove a sharp separation: the RaT method achieves the minimax-optimal rate, while the SM method incurs constant prediction error for any sample size. Experiments on both synthetic data and ImageNette classification under covariate shift corroborate our theoretical findings.