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

arXiv: https://arxiv.org/abs/2310.07032 · HTML: https://mlsanity.com/paper/2310.07032/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 48 references that are in the map.
- First posted on arXiv 10 Oct 2023.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [Explainable Artificial Intelligence: Understanding, Visualizing and Interpreting Deep Learning Models](https://mlsanity.com/paper/1708.08296/) (2017)
- [Riemannian metrics for neural networks I: feedforward networks](https://mlsanity.com/paper/1303.0818/) (2013)
- [Low-Complexity, Real-Time Joint Neural Echo Control and Speech Enhancement Based On PercepNet](https://mlsanity.com/paper/2102.05245/) (2021)
- [ICASSP 2022 Acoustic Echo Cancellation Challenge](https://mlsanity.com/paper/2202.13290/) (2022)
- [ICASSP 2021 Acoustic Echo Cancellation Challenge: Datasets, Testing Framework, and Results](https://mlsanity.com/paper/2009.04972/) (2020)
- [System identification using Bayesian neural networks with nonparametric noise models](https://mlsanity.com/paper/2104.12119/) (2021)

## Abstract (arXiv)

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.