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.

翻译：近年来，提升深度神经网络的可解释性日益受到关注，尤其在利用深度学习解决物理学问题时更是如此。可解释性有助于理解模型的泛化能力并揭示其局限性。本文提出一种用于动态系统建模的因果可解释深度结构。该模型利用谐波分析，在保持高时间分辨率和频谱分辨率的前提下，于时频域中建模系统。此外，模型采用阶次递进方式构建，可实现快速、鲁棒且精确的二阶优化，而无需显式计算Hessian矩阵。为解决系统构建块因维度高引发的问题，我们设计了一个神经网络以识别频率间的相互依赖关系。通过音频信号处理任务中所需的非线性系统辨识问题，对所提模型进行了验证与阐释。在声学回声消除场景下，通过众包实验将所提方法与其他前沿方案进行性能对比，结果证实了该方法在实际应用中的有效性。