# Function regression using the forward forward training and inferring paradigm

arXiv: https://arxiv.org/abs/2510.06762 · HTML: https://mlsanity.com/paper/2510.06762/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 18 references that are in the map.
- First posted on arXiv 8 Oct 2025.

## Builds on (most cited first, 8 of 8)

- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)
- [Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systems](https://mlsanity.com/paper/2104.13386/) (2021)
- [Brain-inspired computing: We need a master plan](https://mlsanity.com/paper/2104.14517/) (2021)
- [Backpropagation-free Training of Deep Physical Neural Networks](https://mlsanity.com/paper/2304.11042/) (2023)
- [Layer Collaboration in the Forward-Forward Algorithm](https://mlsanity.com/paper/2305.12393/) (2023)
- [Training Convolutional Neural Networks with the Forward-Forward algorithm](https://mlsanity.com/paper/2312.14924/) (2023)
- [Distance-Forward Learning: Enhancing the Forward-Forward Algorithm Towards High-Performance On-Chip Learning](https://mlsanity.com/paper/2408.14925/) (2024)

## Built on by (most cited first, 2 of 2)

- [Local learning for stable backpropagation-free neural network training towards physical learning](https://mlsanity.com/paper/2603.24790/) (2026)
- [FFR: Forward-Forward Learning for Regression](https://mlsanity.com/paper/2606.03927/) (2026)

## Abstract (arXiv)

Function regression/approximation is a fundamental application of machine learning. Neural networks (NNs) can be easily trained for function regression using a sufficient number of neurons and epochs. The forward-forward learning algorithm is a novel approach for training neural networks without backpropagation, and is well suited for implementation in neuromorphic computing and physical analogs for neural networks. To the best of the authors' knowledge, the Forward Forward paradigm of training and inferencing NNs is currently only restricted to classification tasks. This paper introduces a new methodology for approximating functions (function regression) using the Forward-Forward algorithm. Furthermore, the paper evaluates the developed methodology on univariate and multivariate functions, and provides preliminary studies of extending the proposed Forward-Forward regression to Kolmogorov Arnold Networks, and Deep Physical Neural Networks.