# Reshaping the Forward-Forward Algorithm with a Similarity-Based Objective

arXiv: https://arxiv.org/abs/2509.08697 · HTML: https://mlsanity.com/paper/2509.08697/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 20 references that are in the map.
- First posted on arXiv 29 Aug 2025.

## Builds on (most cited first, 12 of 12)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [In Defense of the Triplet Loss for Person Re-Identification](https://mlsanity.com/paper/1703.07737/) (2017)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)
- [Infinite Mixture Prototypes for Few-Shot Learning](https://mlsanity.com/paper/1902.04552/) (2019)
- [SymBa: Symmetric Backpropagation-Free Contrastive Learning with Forward-Forward Algorithm for Optimizing Convergence](https://mlsanity.com/paper/2303.08418/) (2023)
- [A Theoretically Sound Upper Bound on the Triplet Loss for Improving the Efficiency of Deep Distance Metric Learning](https://mlsanity.com/paper/1904.08720/) (2019)
- [Convolutional Channel-wise Competitive Learning for the Forward-Forward Algorithm](https://mlsanity.com/paper/2312.12668/) (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)
- [The Trifecta: Three simple techniques for training deeper Forward-Forward networks](https://mlsanity.com/paper/2311.18130/) (2023)

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

- [Learning without Global Backpropagation via Synergistic Information Distillation](https://mlsanity.com/paper/2510.03273/) (2025)

## Abstract (arXiv)

Backpropagation is the pivotal algorithm underpinning the success of artificial neural networks, yet it has critical limitations such as biologically implausible backward locking and global error propagation. To circumvent these constraints, the Forward-Forward algorithm was proposed as a more biologically plausible method that replaces the backward pass with an additional forward pass. Despite this advantage, the Forward-Forward algorithm significantly trails backpropagation in accuracy, and its optimal form exhibits low inference efficiency due to multiple forward passes required. In this work, the Forward-Forward algorithm is reshaped through its integration with similarity learning frameworks, eliminating the need for multiple forward passes during inference. This proposed algorithm is named Forward-Forward Algorithm Unified with Similarity-based Tuplet loss (FAUST). Empirical evaluations on MNIST, Fashion-MNIST, and CIFAR-10 datasets indicate that FAUST substantially improves accuracy, narrowing the gap with backpropagation. On CIFAR-10, FAUST achieves 56.22% accuracy with a simple multi-layer perceptron architecture, approaching the backpropagation benchmark of 57.63% accuracy.