GradVis: Visualization and Second Order Analysis of Optimization Surfaces during the Training of Deep Neural Networks

TL;DR

GradVis is an open source toolbox that enables scalable visualization and second order analysis of deep neural network loss landscapes, helping researchers understand optimization surfaces more efficiently.

Contribution

The paper introduces GradVis, a novel, efficient, and scalable library for visualizing and analyzing deep neural network loss landscapes, including second order information.

Findings

Enables high-resolution visualization of large networks' loss surfaces

Provides efficient computation of second order gradient information

Facilitates better understanding of optimization dynamics

Abstract

Current training methods for deep neural networks boil down to very high dimensional and non-convex optimization problems which are usually solved by a wide range of stochastic gradient descent methods. While these approaches tend to work in practice, there are still many gaps in the theoretical understanding of key aspects like convergence and generalization guarantees, which are induced by the properties of the optimization surface (loss landscape). In order to gain deeper insights, a number of recent publications proposed methods to visualize and analyze the optimization surfaces. However, the computational cost of these methods are very high, making it hardly possible to use them on larger networks. In this paper, we present the GradVis Toolbox, an open source library for efficient and scalable visualization and analysis of deep neural network loss landscapes in Tensorflow and PyTorch. Introducing more efficient mathematical formulations and a novel parallelization scheme, GradVis allows to plot 2d and 3d projections of optimization surfaces and trajectories, as well as high resolution second order gradient information for large networks.