The Neural Echo: A Signal Processing Perspective for Understanding Neural Networks

2026-08-05

AI Summary

This work addresses the limited interpretability of local response behavior in existing neural networks for image tasks. It introduces the “Neural Echo” framework, which systematically adapts the concept of impulse response from signal processing to interpretable AI by employing input-adaptive local kernels to characterize network dynamics. Built upon affine mappings, the method constructs input-dependent local impulse responses that are applicable across diverse architectures—including convolutional, fully connected, recurrent, and Transformer-based models—without requiring differentiability. Experiments on DnCNN reveal that its pixel-weighting mechanism closely resembles bilateral filtering, not only recovering key properties of classical denoising models but also offering a unified theoretical perspective on adversarial perturbations and saliency maps.

Abstract

We introduce the neural echo as a tool for understanding the behavior of neural networks. It generalizes the model-based concepts of impulse responses, diffusion echoes, and filter echoes to learning-based methods. It provides local, space-adaptive impulse responses and filter kernels for a neural network, its so-called echoes. These echoes depend on the input image and can be visualized to understand the learned dynamics of the network via an affine mapping. Neural echoes build a bridge from classical signal processing to modern explainable AI. They are very general and can be applied to both image-to-image and classification networks, with convolutional or fully connected structure, of feedforward or recurrent type, including modern transformer networks. Network differentiability is not required. In the differentiable case, neural echoes comprise concepts based on the network Jacobian, such as saliency maps and the analysis of adversarial perturbations, as special instances. As a simple blueprint to explain our framework, we derive neural echoes for the denoising convolutional neural network (DnCNN). Our experiments suggest that this network weights pixels based on their spatial and gray value distances. This not only clarifies its behavior, but also shows that it can reproduce key concepts of classical model-based denoisers such as bilateral filtering.

Problem

• neural networks
• explainable AI
• signal processing
• impulse response
• model interpretability

Innovation

• Neural Echo
• Explainable AI
• Signal Processing
• Impulse Response
• Jacobian Analysis