ViViT: Curvature access through the generalized Gauss-Newton's low-rank structure
arXiv:2106.02624
Abstract
Curvature in form of the Hessian or its generalized Gauss-Newton (GGN) approximation is valuable for algorithms that rely on a local model for the loss to train, compress, or explain deep networks. Existing methods based on implicit multiplication via automatic differentiation or Kronecker-factored block diagonal approximations do not consider noise in the mini-batch. We present ViViT, a curvature model that leverages the GGN's low-rank structure without further approximations. It allows for efficient computation of eigenvalues, eigenvectors, as well as per-sample first- and second-order directional derivatives. The representation is computed in parallel with gradients in one backward pass and offers a fine-grained cost-accuracy trade-off, which allows it to scale. We demonstrate this by conducting performance benchmarks and substantiate ViViT's usefulness by studying the impact of noise on the GGN's structural properties during neural network training.
Main text: 10 pages, 6 figures; Supplements: 26 pages, 27 figures, 5 tables
References in corpus (8)
- PyTorch: An Imperative Style, High-Performance Deep Learning Library
- Gradient Descent Happens in a Tiny Subspace
- An Investigation into Neural Net Optimization via Hessian Eigenvalue Density
- The Early Phase of Neural Network Training
- Practical Gauss-Newton Optimisation for Deep Learning
- Measurements of Three-Level Hierarchical Structure in the Outliers in the Spectrum of Deepnet Hessians
- On the Promise of the Stochastic Generalized Gauss-Newton Method for Training DNNs
- Cockpit: A Practical Debugging Tool for the Training of Deep Neural Networks