  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.
