Neural Harmonium: An Interpretable Deep Structure for Nonlinear Dynamic System Identification with Application to Audio Processing
This addresses the need for interpretable models in physics-based applications like audio processing, though it appears incremental as it builds on existing harmonic analysis and neural network techniques.
The paper tackles the problem of interpretability in deep neural networks for dynamic system identification by introducing a causal interpretable deep structure that models systems in the time-frequency domain, and validates it on audio processing tasks with crowd-sourced experimentation showing effectiveness in real-life applications like acoustic echo cancellation.
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.