# Convolutional Neural Networks Demystified: A Matched Filtering Perspective Based Tutorial

arXiv: https://arxiv.org/abs/2108.11663 · HTML: https://mlsanity.com/paper/2108.11663/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 42 references that are in the map.
- First posted on arXiv 26 Aug 2021.

## Builds on (most cited first, 10 of 10)

- [An Introduction to Convolutional Neural Networks](https://mlsanity.com/paper/1511.08458/) (2015)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Accelerating the Super-Resolution Convolutional Neural Network](https://mlsanity.com/paper/1608.00367/) (2016)
- [1D Convolutional Neural Networks and Applications: A Survey](https://mlsanity.com/paper/1905.03554/) (2019)
- [Graph-based Semi-supervised Learning: A Comprehensive Review](https://mlsanity.com/paper/2102.13303/) (2021)
- [Understanding Convolutional Neural Networks with A Mathematical Model](https://mlsanity.com/paper/1609.04112/) (2016)
- [WaveletKernelNet: An Interpretable Deep Neural Network for Industrial Intelligent Diagnosis](https://mlsanity.com/paper/1911.07925/) (2019)
- [Recent Advances in Convolutional Neural Network Acceleration](https://mlsanity.com/paper/1807.08596/) (2018)
- [Asymmetric CNN for image super-resolution](https://mlsanity.com/paper/2103.13634/) (2021)
- [Understanding the Basis of Graph Convolutional Neural Networks via an Intuitive Matched Filtering Approach](https://mlsanity.com/paper/2108.10751/) (2021)

## Built on by (most cited first, 6 of 6)

- [SHINE: Sequential Hierarchical Integration Network for EEG and MEG](https://mlsanity.com/paper/2602.23960/) (2026)
- [On the benefits of non-linear weight updates](https://mlsanity.com/paper/2207.12505/) (2022)
- [Demystifying CNNs for Images by Matched Filters](https://mlsanity.com/paper/2210.08521/) (2022)
- [Widely Linear Matched Filter: A Lynchpin towards the Interpretability of Complex-valued CNNs](https://mlsanity.com/paper/2401.16729/) (2024)
- [Causal Convolutional Neural Networks as Finite Impulse Response Filters](https://mlsanity.com/paper/2510.24125/) (2025)
- [Frequency Selective Neural Networks as a Foundation Architecture for Time Series Learning](https://mlsanity.com/paper/2608.29012/) (2026)

## Abstract (arXiv)

Deep Neural Networks (DNN) and especially Convolutional Neural Networks (CNN) are a de-facto standard for the analysis of large volumes of signals and images. Yet, their development and underlying principles have been largely performed in an ad-hoc and black box fashion. To help demystify CNNs, we revisit their operation from first principles and a matched filtering perspective. We establish that the convolution operation within CNNs, their very backbone, represents a matched filter which examines the input signal/image for the presence of pre-defined features. This perspective is shown to be physically meaningful, and serves as a basis for a step-by-step tutorial on the operation of CNNs, including pooling, zero padding, various ways of dimensionality reduction. Starting from first principles, both the feed-forward pass and the learning stage (via back-propagation) are illuminated in detail, both through a worked-out numerical example and the corresponding visualizations. It is our hope that this tutorial will help shed new light and physical intuition into the understanding and further development of deep neural networks.