PMaF: Deep Declarative Layers for Principal Matrix Features

TL;DR

This paper introduces two differentiable deep declarative layers, LESS and IED, for extracting principal matrix features, demonstrating improved efficiency and solution quality over existing methods.

Contribution

The paper presents novel differentiable layers, LESS and IED, with optimized forward and backward passes, advancing deep learning techniques for principal matrix feature extraction.

Findings

Superior solution optimality compared to baselines

Reduced computational complexity in backward pass

Enhanced efficiency with adaptive descent methods

Abstract

We explore two differentiable deep declarative layers, namely least squares on sphere (LESS) and implicit eigen decomposition (IED), for learning the principal matrix features (PMaF). It can be used to represent data features with a low-dimensional vector containing dominant information from a high-dimensional matrix. We first solve the problems with iterative optimization in the forward pass and then backpropagate the solution for implicit gradients under a bi-level optimization framework. Particularly, adaptive descent steps with the backtracking line search method and descent decay in the tangent space are studied to improve the forward pass efficiency of LESS. Meanwhile, exploited data structures are used to greatly reduce the computational complexity in the backward pass of LESS and IED. Empirically, we demonstrate the superiority of our layers over the off-the-shelf baselines by comparing the solution optimality and computational requirements.