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

arXiv: https://arxiv.org/abs/1909.12108 · HTML: https://mlsanity.com/paper/1909.12108/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2019.

## Built on by (most cited first, 5 of 5)

- [Neural Architecture Design and Robustness: A Dataset](https://mlsanity.com/paper/2306.06712/) (2023)
- [A Defense of the Quadratic Model](https://mlsanity.com/paper/2607.21716/) (2026)
- [Explore the Effect of Data Selection on Poison Efficiency in Backdoor Attacks](https://mlsanity.com/paper/2310.09744/) (2023)
- [Neuro-Visualizer: An Auto-encoder-based Loss Landscape Visualization Method](https://mlsanity.com/paper/2309.14601/) (2023)
- [Exploring End-to-end Differentiable Neural Charged Particle Tracking -- A Loss Landscape Perspective](https://mlsanity.com/paper/2407.13420/) (2024)

## Abstract (arXiv)

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.