# Analytic Learning of Convolutional Neural Network For Pattern Recognition

arXiv: https://arxiv.org/abs/2202.06504 · HTML: https://mlsanity.com/paper/2202.06504/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 39 references that are in the map.
- First posted on arXiv 14 Feb 2022.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [Deeply supervised salient object detection with short connections](https://mlsanity.com/paper/1611.04849/) (2016)
- [Interventional Few-Shot Learning](https://mlsanity.com/paper/2009.13000/) (2020)
- [The Singular Values of Convolutional Layers](https://mlsanity.com/paper/1805.10408/) (2018)
- [Interpretable Convolutional Neural Networks via Feedforward Design](https://mlsanity.com/paper/1810.02786/) (2018)
- [A Gentle Introduction to Deep Learning in Medical Image Processing](https://mlsanity.com/paper/1810.05401/) (2018)
- [Parallel Multi Channel Convolution using General Matrix Multiplication](https://mlsanity.com/paper/1704.04428/) (2017)
- [Learning from the Kernel and the Range Space](https://mlsanity.com/paper/1810.09071/) (2018)
- [Stacking-Based Deep Neural Network: Deep Analytic Network for Pattern Classification](https://mlsanity.com/paper/1811.07184/) (2018)
- [PILAE: A Non-gradient Descent Learning Scheme for Deep Feedforward Neural Networks](https://mlsanity.com/paper/1811.01545/) (2018)
- [Analytic Network Learning](https://mlsanity.com/paper/1811.08227/) (2018)

## Built on by (most cited first, 1 of 1)

- [GACL: Exemplar-Free Generalized Analytic Continual Learning](https://mlsanity.com/paper/2403.15706/) (2024)

## Abstract (arXiv)

Training convolutional neural networks (CNNs) with back-propagation (BP) is time-consuming and resource-intensive particularly in view of the need to visit the dataset multiple times. In contrast, analytic learning attempts to obtain the weights in one epoch. However, existing attempts to analytic learning considered only the multilayer perceptron (MLP). In this article, we propose an analytic convolutional neural network learning (ACnnL). Theoretically we show that ACnnL builds a closed-form solution similar to its MLP counterpart, but differs in their regularization constraints. Consequently, we are able to answer to a certain extent why CNNs usually generalize better than MLPs from the implicit regularization point of view. The ACnnL is validated by conducting classification tasks on several benchmark datasets. It is encouraging that the ACnnL trains CNNs in a significantly fast manner with reasonably close prediction accuracies to those using BP. Moreover, our experiments disclose a unique advantage of ACnnL under the small-sample scenario when training data are scarce or expensive.