# Generalised Perceptron Learning

arXiv: https://arxiv.org/abs/2012.03642 · HTML: https://mlsanity.com/paper/2012.03642/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2020.

## Built on by (most cited first, 4 of 4)

- [Lifted Bregman Training of Neural Networks](https://mlsanity.com/paper/2208.08772/) (2022)
- [A Lifted Bregman Formulation for the Inversion of Deep Neural Networks](https://mlsanity.com/paper/2303.01965/) (2023)
- [Heterogeneous virus classification using a functional deep learning model based on transmission electron microscopy images (Preprint)](https://mlsanity.com/paper/2405.15563/) (2024)
- [Analog-Friendly Predictive Coding without Activation Derivatives](https://mlsanity.com/paper/2609.32350/) (2026)

## Abstract (arXiv)

We present a generalisation of Rosenblatt's traditional perceptron learning algorithm to the class of proximal activation functions and demonstrate how this generalisation can be interpreted as an incremental gradient method applied to a novel energy function. This novel energy function is based on a generalised Bregman distance, for which the gradient with respect to the weights and biases does not require the differentiation of the activation function. The interpretation as an energy minimisation algorithm paves the way for many new algorithms, of which we explore a novel variant of the iterative soft-thresholding algorithm for the learning of sparse perceptrons.