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.

提出一种用于建模动态系统的因果可解释深度结构，通过在时频域建模系统并保持高时域和频谱分辨率，通过一种顺序递归的方式构建模型，以实现快速、强健和精确的二阶优化，无需显式的Hessian计算，利用神经网络识别频率之间的相互依赖，通过非线性系统识别问题进行验证，对于音频信号处理任务具有广泛实际应用。

神经谐振盒：一种可解释的非线性动态系统识别的深度结构及其在音频处理中的应用