Neural Harmonium: An Interpretable Deep Structure for Nonlinear Dynamic System Identification with Application to Audio Processing

TL;DR

Neural Harmonium introduces an interpretable deep learning model for nonlinear dynamic system identification, leveraging harmonic analysis in the time-frequency domain, optimized efficiently, and validated on audio processing tasks like acoustic echo cancellation.

Contribution

The paper presents a novel causal, interpretable deep structure that models dynamic systems using harmonic analysis, with efficient second order optimization and neural network-based frequency dependency identification.

Findings

Effective in nonlinear system identification for audio processing

Outperforms state-of-the-art solutions in acoustic echo cancellation

Provides high temporal and spectral resolution with interpretability

Abstract

Improving the interpretability of deep neural networks has recently gained increased attention, especially when the power of deep learning is leveraged to solve problems in physics. Interpretability helps us understand a model's ability to generalize and reveal its limitations. In this paper, we introduce a causal interpretable deep structure for modeling dynamic systems. Our proposed model makes use of the harmonic analysis by modeling the system in a time-frequency domain while maintaining high temporal and spectral resolution. Moreover, the model is built in an order recursive manner which allows for fast, robust, and exact second order optimization without the need for an explicit Hessian calculation. To circumvent the resulting high dimensionality of the building blocks of our system, a neural network is designed to identify the frequency interdependencies. The proposed model is illustrated and validated on nonlinear system identification problems as required for audio signal processing tasks. Crowd-sourced experimentation contrasting the performance of the proposed approach to other state-of-the-art solutions on an acoustic echo cancellation scenario confirms the effectiveness of our method for real-life applications.