Visualizing the Loss Landscape of Neural Nets

TL;DR

This paper investigates the structure of neural network loss landscapes and how architecture and training parameters influence their shape and generalization, using novel visualization techniques for better understanding.

Contribution

Introduces a filter normalization method for visualizing loss landscapes and analyzes how architecture and training choices affect the loss surface and generalization.

Findings

Loss landscape shape varies with architecture and training parameters.

Filter normalization aids in meaningful visualization of curvature.

Certain architectures produce smoother loss landscapes that generalize better.

Abstract

Neural network training relies on our ability to find "good" minimizers of highly non-convex loss functions. It is well-known that certain network architecture designs (e.g., skip connections) produce loss functions that train easier, and well-chosen training parameters (batch size, learning rate, optimizer) produce minimizers that generalize better. However, the reasons for these differences, and their effects on the underlying loss landscape, are not well understood. In this paper, we explore the structure of neural loss functions, and the effect of loss landscapes on generalization, using a range of visualization methods. First, we introduce a simple "filter normalization" method that helps us visualize loss function curvature and make meaningful side-by-side comparisons between loss functions. Then, using a variety of visualizations, we explore how network architecture affects the loss landscape, and how training parameters affect the shape of minimizers.