PMaF: Deep Declarative Layers for Principal Matrix Features
This work addresses the challenge of efficient matrix feature extraction in machine learning, offering incremental improvements in optimization and computational efficiency for domain-specific applications.
The paper tackles the problem of learning principal matrix features from high-dimensional data by introducing two differentiable deep declarative layers, LESS and IED, which improve solution optimality and reduce computational complexity compared to baselines.
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.