Batch Normalization Is Blind to the First and Second Derivatives of the Loss

TL;DR

This paper demonstrates that Batch Normalization (BN) impairs the back-propagation of the first and second derivatives of the loss, affecting training dynamics and feature representations, especially in tasks with similar sample losses.

Contribution

It provides a theoretical analysis showing BN blocks the influence of derivatives of the loss and verifies this with experimental evidence.

Findings

BN affects the influence of first and second derivatives of the loss

Standardization phase causes the derivative blocking effect

BN significantly impacts feature representations in certain tasks

Abstract

In this paper, we prove the effects of the BN operation on the back-propagation of the first and second derivatives of the loss. When we do the Taylor series expansion of the loss function, we prove that the BN operation will block the influence of the first-order term and most influence of the second-order term of the loss. We also find that such a problem is caused by the standardization phase of the BN operation. Experimental results have verified our theoretical conclusions, and we have found that the BN operation significantly affects feature representations in specific tasks, where losses of different samples share similar analytic formulas.