# Error-driven Input Modulation: Solving the Credit Assignment Problem without a Backward Pass

arXiv: https://arxiv.org/abs/2201.11665 · HTML: https://mlsanity.com/paper/2201.11665/

## Key facts

- Cited by 63 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2022.

## Built on by (most cited first, 30 of 63)

- [The Predictive Forward-Forward Algorithm](https://mlsanity.com/paper/2301.01452/) (2023)
- [Brain-inspired Computational Intelligence via Predictive Coding](https://mlsanity.com/paper/2308.07870/) (2023)
- [Training Convolutional Neural Networks with the Forward-Forward algorithm](https://mlsanity.com/paper/2312.14924/) (2023)
- [Forward Learning with Top-Down Feedback: Empirical and Analytical Characterization](https://mlsanity.com/paper/2302.05440/) (2023)
- [The Trifecta: Three simple techniques for training deeper Forward-Forward networks](https://mlsanity.com/paper/2311.18130/) (2023)
- [Training Machine Learning models at the Edge: A Survey](https://mlsanity.com/paper/2403.02619/) (2024)
- [Momentum Auxiliary Network for Supervised Local Learning](https://mlsanity.com/paper/2407.05623/) (2024)
- [Improving equilibrium propagation without weight symmetry through Jacobian homeostasis](https://mlsanity.com/paper/2309.02214/) (2023)
- [Graph Neural Networks Go Forward-Forward](https://mlsanity.com/paper/2302.05282/) (2023)
- [Extending the Forward Forward Algorithm](https://mlsanity.com/paper/2307.04205/) (2023)
- [FFCL: Forward-Forward Net with Cortical Loops, Training and Inference on Edge Without Backpropagation](https://mlsanity.com/paper/2405.12443/) (2024)
- [Advancing Supervised Local Learning Beyond Classification with Long-term Feature Bank](https://mlsanity.com/paper/2406.00446/) (2024)
- [Beyond Backpropagation: Optimization with Multi-Tangent Forward Gradients](https://mlsanity.com/paper/2410.17764/) (2024)
- [On-device Online Learning and Semantic Management of TinyML Systems](https://mlsanity.com/paper/2405.07601/) (2024)
- [LLS: Local Learning Rule for Deep Neural Networks Inspired by Neural Activity Synchronization](https://mlsanity.com/paper/2405.15868/) (2024)
- [MLAAN: Scaling Supervised Local Learning with Multilaminar Leap Augmented Auxiliary Network](https://mlsanity.com/paper/2406.16633/) (2024)
- [HPFF: Hierarchical Locally Supervised Learning with Patch Feature Fusion](https://mlsanity.com/paper/2407.05638/) (2024)
- [Counter-Current Learning: A Biologically Plausible Dual Network Approach for Deep Learning](https://mlsanity.com/paper/2409.19841/) (2024)
- [Poor Man's Training on MCUs: A Memory-Efficient Quantized Back-Propagation-Free Approach](https://mlsanity.com/paper/2411.05873/) (2024)
- [Backpropagation-free Spiking Neural Networks with the Forward-Forward Algorithm](https://mlsanity.com/paper/2502.20411/) (2025)
- [Towards Interpretable Deep Local Learning with Successive Gradient Reconciliation](https://mlsanity.com/paper/2406.05222/) (2024)
- [Towards training digitally-tied analog blocks via hybrid gradient computation](https://mlsanity.com/paper/2409.03306/) (2024)
- [Mono-Forward: Revisiting Forward-Forward through Objective-Locality Decomposition](https://mlsanity.com/paper/2501.09238/) (2025)
- [TESS: A Scalable Temporally and Spatially Local Learning Rule for Spiking Neural Networks](https://mlsanity.com/paper/2502.01837/) (2025)
- [Feed-Forward Optimization With Delayed Feedback for Neural Network Training](https://mlsanity.com/paper/2304.13372/) (2023)
- [LightFF: Lightweight Inference for Forward-Forward Algorithm](https://mlsanity.com/paper/2404.05241/) (2024)
- [Temporal-Difference Learning Using Distributed Error Signals](https://mlsanity.com/paper/2411.03604/) (2024)
- [MAN++: Scaling Momentum Auxiliary Network for Supervised Local Learning in Vision Tasks](https://mlsanity.com/paper/2507.16279/) (2025)
- [Adaptive Spatial Goodness Encoding: Advancing and Scaling Forward-Forward Learning Without Backpropagation](https://mlsanity.com/paper/2509.12394/) (2025)
- [LANCE: Low Rank Activation Compression for Efficient On-Device Continual Learning](https://mlsanity.com/paper/2509.21617/) (2025)

## Abstract (arXiv)

Supervised learning in artificial neural networks typically relies on backpropagation, where the weights are updated based on the error-function gradients and sequentially propagated from the output layer to the input layer. Although this approach has proven effective in a wide domain of applications, it lacks biological plausibility in many regards, including the weight symmetry problem, the dependence of learning on non-local signals, the freezing of neural activity during error propagation, and the update locking problem. Alternative training schemes have been introduced, including sign symmetry, feedback alignment, and direct feedback alignment, but they invariably rely on a backward pass that hinders the possibility of solving all the issues simultaneously. Here, we propose to replace the backward pass with a second forward pass in which the input signal is modulated based on the error of the network. We show that this novel learning rule comprehensively addresses all the above-mentioned issues and can be applied to both fully connected and convolutional models. We test this learning rule on MNIST, CIFAR-10, and CIFAR-100. These results help incorporate biological principles into machine learning.