Exploring how deep learning decodes anomalous diffusion via Grad-CAM

While deep learning has been successfully applied to the data-driven classification of anomalous diffusion mechanisms, how the algorithm achieves the feat still remains a mystery. In this study, we use a well-known technique aimed at achieving explainable AI, namely the Gradient-weighted Class Activation Map (Grad-CAM), to investigate how deep learning (implemented by ResNets) recognizes the distinctive features of a particular anomalous diffusion model from the raw trajectory data. Our results show that Grad-CAM reveals the portions of the trajectory that hold crucial information about the underlying mechanism of anomalous diffusion, which can be utilized to enhance the robustness of the trained classifier against the measurement noise. Moreover, we observe that deep learning distills unique statistical characteristics of different diffusion mechanisms at various spatiotemporal scales, with larger-scale (smaller-scale) features identified at higher (lower) layers.

From Empirical Observations to Universality: Dynamics of Deep Learning with Inputs Built on Gaussian mixture

This study broadens the scope of theoretical frameworks in deep learning by delving into the dynamics of neural networks with inputs that demonstrate the structural characteristics to Gaussian Mixture (GM). We analyzed how the dynamics of neural networks under GM-structured inputs diverge from the predictions of conventional theories based on simple Gaussian structures. A revelation of our work is the observed convergence of neural network dynamics towards conventional theory even with standardized GM inputs, highlighting an unexpected universality. We found that standardization, especially in conjunction with certain nonlinear functions, plays a critical role in this phenomena. Consequently, despite the complex and varied nature of GM distributions, we demonstrate that neural networks exhibit asymptotic behaviors in line with predictions under simple Gaussian frameworks.