We leverage recent insights from second-order optimisation for neural networks to construct a Kronecker factored Laplace approximation to the posterior over the weights of a trained network. Our approximation requires no modification of the training procedure, enabling practitioners to estimate the uncertainty of their models currently used in production without having to retrain them. We exten...

It is showed that Kronecker product can be applied to construct not only new Lax representations but also new zero curvature representations of integrable models. Meantime a different characteristic between continuous and discrete zero curvature equations is pointed out. Lax representation and zero curvature representation play an important role in studying nonlinear integrable models in theore...

We propose an efficient method for approximating natural gradient descent in neural networks which we call Kronecker-factored Approximate Curvature (K-FAC). K-FAC is based on an efficiently invertible approximation of a neural network’s Fisher information matrix which is neither diagonal nor low-rank, and in some cases is completely non-sparse. It is derived by approximating various large block...

Let f(x) be a given positive function in Rn+1. In this paper we consider the existence of convex, closed hypersurfaces X so that its GaussKronecker curvature at x ∈ X is equal to f(x). This problem has variational structure and the existence of stable solutions has been discussed by Tso (J. Diff. Geom. 34 (1991), 389–410). Using the Mountain Pass Lemma and the Gauss curvature flow we prove the ...

For convex hypersurfaces in the affine space $\mathbb{A}^{n+1}$ ($n\geq2$), A.-M.\ Li introduced notion of $\alpha$-normal field as a generalization normal field. By studying Monge-Amp\`ere equation with gradient blowup boundary condition, we show that regular domains $\mathbb{A}^{n+1}$, defined respect to proper cone and satisfying some regularity assumption if $n\geq3$, are foliated by comple...

Kronecker-factor Approximate Curvature (Martens & Grosse, 2015) (K-FAC) is a 2nd-order optimization method which has been shown to give state-of-the-art performance on large-scale neural network optimization tasks (Ba et al., 2017). It is based on an approximation to the Fisher information matrix (FIM) that makes assumptions about the particular structure of the network and the way it is parame...

We saw in Lecture 3 how to efficiently multiply integers, and, using Kronecker substitution, how to efficiently multiply polynomials with integer coefficients. This gives us what we need to multiply elements in finite fields, provided that we have a way to reduce the result to our standard representations of Fp ' Z/pZ and Fq ' Fp[x]/(f), using integers in [0, p− 1] and polynomials of degree les...