This work proposes a quasirandom sequence of quadratures for high-dimensional
mean-field variational inference and a related sparsifying methodology. Each
iterate of the sequence contains two evaluations points that combine to
correctly integrate all univariate quadratic functions, as well as univariate
cubics if the mean-field factors are symmetric. More importantly, averaging
results over short subsequences achieves periodic exactness on a much larger
space of multivariate polynomials of quadratic total degree. This framework is
devised by first considering stochastic blocked mean-field quadratures, which
may be useful in other contexts. By replacing pseudorandom sequences with
quasirandom sequences, over half of all multivariate quadratic basis functions
integrate exactly with only 4 function evaluations, and the exactness dimension
increases for longer subsequences. Analysis shows how these efficient integrals
characterize the dominant log-posterior contributions to mean-field variational
approximations, including diagonal Hessian approximations, to support a robust
sparsifying methodology in deep learning algorithms. A numerical demonstration
of this approach on a simple Convolutional Neural Network for MNIST retains
high test accuracy, 96.9%, while training over 98.9% of parameters to zero in
only 10 epochs, bearing potential to reduce both storage and energy
requirements for deep learning models