# The Integrated Forward-Forward Algorithm: Integrating Forward-Forward and Shallow Backpropagation With Local Losses

arXiv: https://arxiv.org/abs/2305.12960 · HTML: https://mlsanity.com/paper/2305.12960/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 22 May 2023.

## Builds on (most cited first, 6 of 6)

- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)
- [Gradients without Backpropagation](https://mlsanity.com/paper/2202.08587/) (2022)
- [Scaling Forward Gradient With Local Losses](https://mlsanity.com/paper/2210.03310/) (2022)
- [Hebbian Deep Learning Without Feedback](https://mlsanity.com/paper/2209.11883/) (2022)
- [Graph Neural Networks Go Forward-Forward](https://mlsanity.com/paper/2302.05282/) (2023)

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

- [Backpropagation-free Spiking Neural Networks with the Forward-Forward Algorithm](https://mlsanity.com/paper/2502.20411/) (2025)
- [CXR-LanIC: Language-Grounded Interpretable Classifier for Chest X-Ray Diagnosis](https://mlsanity.com/paper/2510.21464/) (2025)
- [Forward-Cooperation-Backward (FCB) learning in a Multi-Encoding Uni-Decoding neural network architecture](https://mlsanity.com/paper/2502.20113/) (2025)
- [Emergent Hierarchical Monosemantic Neurons from the Group-Contrastive Forward-Forward Algorithm](https://mlsanity.com/paper/2607.16295/) (2026)

## Abstract (arXiv)

The backpropagation algorithm, despite its widespread use in neural network learning, may not accurately emulate the human cortex's learning process. Alternative strategies, such as the Forward-Forward Algorithm (FFA), offer a closer match to the human cortex's learning characteristics. However, the original FFA paper and related works on the Forward-Forward Algorithm only mentioned very limited types of neural network mechanisms and may limit its application and effectiveness. In response to these challenges, we propose an integrated method that combines the strengths of both FFA and shallow backpropagation, yielding a biologically plausible neural network training algorithm which can also be applied to various network structures. We applied this integrated approach to the classification of the Modified National Institute of Standards and Technology (MNIST) database, where it outperformed FFA and demonstrated superior resilience to noise compared to backpropagation. We show that training neural networks with the Integrated Forward-Forward Algorithm has the potential of generating neural networks with advantageous features like robustness.