# Interpretable Convolutional Neural Networks via Feedforward Design

arXiv: https://arxiv.org/abs/1810.02786 · HTML: https://mlsanity.com/paper/1810.02786/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2018.

## Built on by (most cited first, 30 of 49)

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- [A Survey on Understanding, Visualizations, and Explanation of Deep Neural Networks](https://mlsanity.com/paper/2102.01792/) (2021)
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- [Interpretability of Machine Learning: Recent Advances and Future Prospects](https://mlsanity.com/paper/2305.00537/) (2023)
- [Successive Subspace Learning: An Overview](https://mlsanity.com/paper/2103.00121/) (2021)
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- [Geo-DefakeHop: High-Performance Geographic Fake Image Detection](https://mlsanity.com/paper/2110.09795/) (2021)
- [TGHop: An Explainable, Efficient and Lightweight Method for Texture Generation](https://mlsanity.com/paper/2107.04020/) (2021)
- [Segmentation of Cardiac Structures via Successive Subspace Learning with Saab Transform from Cine MRI](https://mlsanity.com/paper/2107.10718/) (2021)
- [GSIP: Green Semantic Segmentation of Large-Scale Indoor Point Clouds](https://mlsanity.com/paper/2109.11835/) (2021)
- [A-PixelHop: A Green, Robust and Explainable Fake-Image Detector](https://mlsanity.com/paper/2111.04012/) (2021)
- [A Survey of Neural Trees](https://mlsanity.com/paper/2209.03415/) (2022)
- [DefakeHop++: An Enhanced Lightweight Deepfake Detector](https://mlsanity.com/paper/2205.00211/) (2022)
- [PAGER: Progressive Attribute-Guided Extendable Robust Image Generation](https://mlsanity.com/paper/2206.00162/) (2022)
- [Bridging Gap between Image Pixels and Semantics via Supervision: A Survey](https://mlsanity.com/paper/2107.13757/) (2021)
- [GreenPCO: An Unsupervised Lightweight Point Cloud Odometry Method](https://mlsanity.com/paper/2112.04054/) (2021)
- [Subspace Learning Machine (SLM): Methodology and Performance](https://mlsanity.com/paper/2205.05296/) (2022)
- [GENHOP: An Image Generation Method Based on Successive Subspace Learning](https://mlsanity.com/paper/2210.03689/) (2022)
- [Design of Supervision-Scalable Learning Systems: Methodology and Performance Benchmarking](https://mlsanity.com/paper/2206.09061/) (2022)
- [S3I-PointHop: SO(3)-Invariant PointHop for 3D Point Cloud Classification](https://mlsanity.com/paper/2302.11506/) (2023)
- [Enhancing Edge Intelligence with Highly Discriminant LNT Features](https://mlsanity.com/paper/2312.14968/) (2023)
- [Towards Explaining Hypercomplex Neural Networks](https://mlsanity.com/paper/2403.17929/) (2024)
- [Acceleration of Subspace Learning Machine via Particle Swarm Optimization and Parallel Processing](https://mlsanity.com/paper/2208.07023/) (2022)
- [Learn to Enhance the Negative Information in Convolutional Neural Network](https://mlsanity.com/paper/2306.10536/) (2023)

## Abstract (arXiv)

The model parameters of convolutional neural networks (CNNs) are determined by backpropagation (BP). In this work, we propose an interpretable feedforward (FF) design without any BP as a reference. The FF design adopts a data-centric approach. It derives network parameters of the current layer based on data statistics from the output of the previous layer in a one-pass manner. To construct convolutional layers, we develop a new signal transform, called the Saab (Subspace Approximation with Adjusted Bias) transform. It is a variant of the principal component analysis (PCA) with an added bias vector to annihilate activation's nonlinearity. Multiple Saab transforms in cascade yield multiple convolutional layers. As to fully-connected (FC) layers, we construct them using a cascade of multi-stage linear least squared regressors (LSRs). The classification and robustness (against adversarial attacks) performances of BP- and FF-designed CNNs applied to the MNIST and the CIFAR-10 datasets are compared. Finally, we comment on the relationship between BP and FF designs.