Interpretable Recurrent Neural Networks Using Sequential Sparse Recovery

TL;DR

This paper introduces an interpretable RNN architecture based on the SISTA algorithm, which models sequential sparse recovery and outperforms traditional black box RNNs in speed and accuracy.

Contribution

The paper presents a novel SISTA-based RNN with interpretable parameters, bridging model-based algorithms and deep learning for sequential sparse recovery.

Findings

SISTA-RNN trains faster than LSTM on a specific task.

SISTA-RNN achieves better performance than black box RNNs.

The model's parameters are directly interpretable as statistical model components.

Abstract

Recurrent neural networks (RNNs) are powerful and effective for processing sequential data. However, RNNs are usually considered "black box" models whose internal structure and learned parameters are not interpretable. In this paper, we propose an interpretable RNN based on the sequential iterative soft-thresholding algorithm (SISTA) for solving the sequential sparse recovery problem, which models a sequence of correlated observations with a sequence of sparse latent vectors. The architecture of the resulting SISTA-RNN is implicitly defined by the computational structure of SISTA, which results in a novel stacked RNN architecture. Furthermore, the weights of the SISTA-RNN are perfectly interpretable as the parameters of a principled statistical model, which in this case include a sparsifying dictionary, iterative step size, and regularization parameters. In addition, on a particular sequential compressive sensing task, the SISTA-RNN trains faster and achieves better performance than conventional state-of-the-art black box RNNs, including long-short term memory (LSTM) RNNs.