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

Neural echoes provide a unified framework for understanding how neural networks process information by connecting classical signal processing concepts (like impulse responses and filters) to modern deep learning, making network behavior more interpretable across different architectures including CNNs, transformers, and recurrent networks.

The method reveals that neural networks learn interpretable, classical signal processing principles: The analysis of DnCNN showed that the network weights pixels based on spatial and gray value distances, essentially rediscovering bilateral filtering—a well-understood classical technique—which validates that neural networks can learn explainable, principled behaviors rather than operating as "black boxes."

Neural echoes work without requiring network differentiability, making the approach broadly applicable to diverse network types and potentially enabling explanation of systems where gradient-based methods are unavailable or unreliable, expanding the toolkit for responsible AI practitioners.

The framework unifies multiple existing explainability concepts under one umbrella: Saliency maps and adversarial perturbation analysis emerge as special cases of neural echoes in differentiable networks, suggesting this approach could help standardize and simplify how we explain AI systems across different contexts.

Input-dependent, spatially-adaptive explanations improve transparency: Unlike one-size-fits-all explanations, neural echoes adapt to specific input images, potentially providing more accurate and contextual understanding of how networks make decisions on individual cases—important for high-stakes applications requiring detailed accountability.