ViViT: Curvature access through the generalized Gauss-Newton's low-rank structure
This work addresses the need for accurate and scalable curvature estimation in deep learning, particularly for researchers and practitioners dealing with optimization and model analysis, though it appears incremental as it builds on existing GGN approximations by focusing on noise and low-rank structure.
The paper tackles the problem of efficiently computing curvature information (via the generalized Gauss-Newton approximation) for deep networks, which is crucial for training, compression, and explanation tasks, by introducing ViViT, a model that leverages low-rank structure without additional approximations, enabling scalable computation of eigenvalues, eigenvectors, and derivatives with demonstrated performance benchmarks.
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.