What can linear interpolation of neural network loss landscapes tell us?

TL;DR

This paper critically examines the use of linear interpolation in neural network loss landscapes, revealing that such visualizations may not reliably indicate optimization difficulty or model performance.

Contribution

The study systematically tests how linear interpolation results vary with different data, initializations, and architectures, challenging previous assumptions about their interpretability.

Findings

Linear interpolation shape does not correlate with test accuracy.

Certain layers are more sensitive to initialization.

Barriers in loss landscapes may not indicate optimization success.

Abstract

Studying neural network loss landscapes provides insights into the nature of the underlying optimization problems. Unfortunately, loss landscapes are notoriously difficult to visualize in a human-comprehensible fashion. One common way to address this problem is to plot linear slices of the landscape, for example from the initial state of the network to the final state after optimization. On the basis of this analysis, prior work has drawn broader conclusions about the difficulty of the optimization problem. In this paper, we put inferences of this kind to the test, systematically evaluating how linear interpolation and final performance vary when altering the data, choice of initialization, and other optimizer and architecture design choices. Further, we use linear interpolation to study the role played by individual layers and substructures of the network. We find that certain layers are more sensitive to the choice of initialization, but that the shape of the linear path is not indicative of the changes in test accuracy of the model. Our results cast doubt on the broader intuition that the presence or absence of barriers when interpolating necessarily relates to the success of optimization.