Training Deep Networks with Structured Layers by Matrix Backpropagation

TL;DR

This paper introduces a novel matrix backpropagation method enabling the integration of global structured matrix computations into deep neural networks, demonstrated through improved visual segmentation results.

Contribution

It develops a mathematical framework for backpropagation through structured matrix layers, allowing end-to-end training of deep networks with global computation modules.

Findings

Deep networks with structured matrix layers outperform traditional models.

Matrix backpropagation enables efficient training of global computation layers.

Experimental results on segmentation benchmarks show improved accuracy.

Abstract

Deep neural network architectures have recently produced excellent results in a variety of areas in artificial intelligence and visual recognition, well surpassing traditional shallow architectures trained using hand-designed features. The power of deep networks stems both from their ability to perform local computations followed by pointwise non-linearities over increasingly larger receptive fields, and from the simplicity and scalability of the gradient-descent training procedure based on backpropagation. An open problem is the inclusion of layers that perform global, structured matrix computations like segmentation (e.g. normalized cuts) or higher-order pooling (e.g. log-tangent space metrics defined over the manifold of symmetric positive definite matrices) while preserving the validity and efficiency of an end-to-end deep training framework. In this paper we propose a sound mathematical apparatus to formally integrate global structured computation into deep computation architectures. At the heart of our methodology is the development of the theory and practice of backpropagation that generalizes to the calculus of adjoint matrix variations. The proposed matrix backpropagation methodology applies broadly to a variety of problems in machine learning or computational perception. Here we illustrate it by performing visual segmentation experiments using the BSDS and MSCOCO benchmarks, where we show that deep networks relying on second-order pooling and normalized cuts layers, trained end-to-end using matrix backpropagation, outperform counterparts that do not take advantage of such global layers.