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Improving the interpretability of deep neural networks has recently gainedincreased attention, especially when the power of deep learning is leveraged tosolve problems in physics. Interpretability helps us understand a model'sability to generalize and reveal its limitations. In this paper, we introduce acausal interpretable deep structure for modeling dynamic systems. Our proposedmodel makes use of the harmonic analysis by modeling the system in atime-frequency domain while maintaining high temporal and spectral resolution.Moreover, the model is built in an order recursive manner which allows forfast, robust, and exact second order optimization without the need for anexplicit Hessian calculation. To circumvent the resulting high dimensionalityof the building blocks of our system, a neural network is designed to identifythe frequency interdependencies. The proposed model is illustrated andvalidated on nonlinear system identification problems as required for audiosignal processing tasks. Crowd-sourced experimentation contrasting theperformance of the proposed approach to other state-of-the-art solutions on anacoustic echo cancellation scenario confirms the effectiveness of our methodfor real-life applications.

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