[Paper Review] How Does Batch Normalization Help Optimization?

Shibani Santurkar, Dimitris Tsipras+2 more|arXiv (Cornell University)|May 29, 2018

Domain Adaptation and Few-Shot LearningComputer Science30 references229 citations

TL;DR

The paper argues that BatchNorm’s effectiveness comes from making the optimization landscape smoother and gradients more predictive, rather than primarily reducing internal covariate shift; similar smoothing effects are observed with other normalization schemes.

ABSTRACT

Batch Normalization (BatchNorm) is a widely adopted technique that enables faster and more stable training of deep neural networks (DNNs). Despite its pervasiveness, the exact reasons for BatchNorm's effectiveness are still poorly understood. The popular belief is that this effectiveness stems from controlling the change of the layers' input distributions during training to reduce the so-called "internal covariate shift". In this work, we demonstrate that such distributional stability of layer inputs has little to do with the success of BatchNorm. Instead, we uncover a more fundamental impact of BatchNorm on the training process: it makes the optimization landscape significantly smoother. This smoothness induces a more predictive and stable behavior of the gradients, allowing for faster training.

Motivation & Objective

• Motivate a deeper understanding of why BatchNorm improves training performance beyond the internal covariate shift narrative.
• Empirically investigate the relationship between ICS and BatchNorm performance.
• Characterize the smoothing effect BatchNorm has on the loss landscape and gradient predictability.
• Provide theoretical analysis showing how BatchNorm affects Lipschitzness and gradient smoothness.

Proposed method

• Compare networks with and without BatchNorm using CNNs and linear networks on standard benchmarks.
• Inject deliberate distributional instability to test the role of ICS.
• Define and measure internal covariate shift in terms of gradient changes across layers (G and G′).
• Analyze the loss landscape and gradient predictiveness along gradient directions.
• Theoretically analyze a single BN layer to derive Lipschitz and smoothness bounds.
• Explore alternative normalization schemes (ℓp-normalizations) to compare smoothing effects.

Experimental results

Research questions

• RQ1 Is BatchNorm’s performance strictly tied to reducing internal covariate shift as traditionally claimed?
• RQ2 Does BatchNorm primarily smooth the optimization landscape and improve gradient predictiveness?
• RQ3 Do other normalization schemes yield similar smoothing and training benefits?
• RQ4 What theoretical guarantees can explain the observed empirical improvements when BatchNorm is used?

Key findings

• BatchNorm networks often show more stable training and faster convergence, even when internal covariate shift is not reduced.
• ICS, defined via gradient changes, can be similar or higher in BatchNorm networks, yet they still perform better.
• BatchNorm reparametrizes the optimization problem to make the loss and gradients more Lipschitz, and the gradient directions more predictive.
• The smoothing effect also appears with other normalization schemes, not just BatchNorm, suggesting the effect is not unique to BN.
• Theoretical analysis shows BN can reduce the loss gradient's Lipschitz constant and increase gradient predictiveness, under mild conditions.
• BN may help converge to flatter minima, potentially aiding generalization.