Exploring how deep learning decodes anomalous diffusion via Grad-CAM

TL;DR

This study uses the Gradient-weighted Class Activation Map to investigate how deep learning recognizes the distinctive features of a particular anomalous diffusion model from the raw trajectory data, and shows that Grad-CAM reveals the portions of the trajectory that hold crucial information about the underlying mechanism of anomalous diffusion.

Abstract

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.

Figures (12)

• Figure 1: Schematic illustration of model classification via ResAnDi and evaluation of the Grad-CAM score. Processing a time series representing a two-dimensional particle trajectory via $18$ layers, ResAnDi yields a vector whose components indicate the probabilities that the trajectory belongs to each of the eight classes of diffusion mechanisms described in the main text. Moreover, by calculating which nodes of the last convolutional layer contribute more to correct classification, the Grad-CAM score is assigned to each subinterval of the trajectory.
• Figure 2: Examples of particle trajectories in the $xy$-plane whose subintervals are erased (top) by targeting the top $10\%$ of the Grad-CAM score (indicated by the color scale) or (bottom) by random choice.
• Figure 3: Classification accuracy of ResAnDi after targeted erasure of subintervals corresponding to each decile of the Grad-CAM score. Removing subintervals with a higher Grad-CAM score results in lower accuracy. For comparison, the effect of random erasure is also shown by a dashed line.
• Figure 4: Schematic illustrations of dataset augmentation method. (Top) Using targeted augmentation, trajectories with high a mean Grad-CAM score are rotated by random angles to build the augmented dataset. (Bottom) Using random augmentation, the trajectories to be rotated are chosen at random.
• Figure 5: Effects of noise in the unseen test data on the classification accuracy. Targeted augmentation using trajectories belonging to the top $60\%$ of the mean Grad-CAM score exhibits more robust performance against increased noise level. The statistics are obtained from $5$ models trained using each augmentation scheme, with the standard errors indicated by shaded regions. (Inset) Enhanced accuracy due to the use of targeted augmentation.