# The Pontryagin Maximum Principle for Training Convolutional Neural Networks

Source: [The Pontryagin Maximum Principle for Training Convolutional Neural Networks](<https://www.sota2.com/research/paper/68fa5e141e209131ce9df1d1>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T05:41:12.037Z

Authors: Sebastian Hofmann, Alfio Borz\\\`i

Published: 2025-04-15T22:20:54.000Z

## Abstract

A novel batch sequential quadratic Hamiltonian (bSQH) algorithm for training convolutional neural networks (CNNs) with $L^0$-based regularization is presented. This methodology is based on a discrete-time Pontryagin maximum principle (PMP). It uses forward and backward sweeps together with the layerwise approximate maximization of an augmented Hamiltonian function, where the augmentation parameter is chosen adaptively.   A technique for determining this augmentation parameter is proposed, and the loss-reduction and convergence properties of the bSQH algorithm are analysed theoretically and validated numerically. Results of numerical experiments in the context of image classification with a sparsity enforcing $L^0$-based regularizer demonstrate the effectiveness of the proposed method in full-batch and mini-batch modes.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2504.11647>)

[PDF](<https://arxiv.org/pdf/2504.11647.pdf>)