# Minimizing Control for Credit Assignment with Strong Feedback

arXiv: https://arxiv.org/abs/2204.07249 · HTML: https://mlsanity.com/paper/2204.07249/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 47 references that are in the map.
- First posted on arXiv 14 Apr 2022.

## Builds on (most cited first, 16 of 16)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [Difference Target Propagation](https://mlsanity.com/paper/1412.7525/) (2014)
- [Dendritic cortical microcircuits approximate the backpropagation algorithm](https://mlsanity.com/paper/1810.11393/) (2018)
- [Deep Learning without Weight Transport](https://mlsanity.com/paper/1904.05391/) (2019)
- [A Theoretical Framework for Target Propagation](https://mlsanity.com/paper/2006.14331/) (2020)
- [Credit Assignment in Neural Networks through Deep Feedback Control](https://mlsanity.com/paper/2106.07887/) (2021)
- [Learning to solve the credit assignment problem](https://mlsanity.com/paper/1906.00889/) (2019)
- [Deriving Differential Target Propagation from Iterating Approximate Inverses](https://mlsanity.com/paper/2007.15139/) (2020)
- [Predicting non-linear dynamics by stable local learning in a recurrent spiking neural network](https://mlsanity.com/paper/1702.06463/) (2017)
- [The brain as an efficient and robust adaptive learner](https://mlsanity.com/paper/1705.08031/) (2017)
- [Biological credit assignment through dynamic inversion of feedforward networks](https://mlsanity.com/paper/2007.05112/) (2020)
- [Learning arbitrary dynamics in efficient, balanced spiking networks using local plasticity rules](https://mlsanity.com/paper/1705.08026/) (2017)

## Built on by (most cited first, 10 of 10)

- [The least-control principle for local learning at equilibrium](https://mlsanity.com/paper/2207.01332/) (2022)
- [Backpropagation through space, time, and the brain](https://mlsanity.com/paper/2403.16933/) (2024)
- [Improving equilibrium propagation without weight symmetry through Jacobian homeostasis](https://mlsanity.com/paper/2309.02214/) (2023)
- [Bio-Inspired, Task-Free Continual Learning through Activity Regularization](https://mlsanity.com/paper/2212.04316/) (2022)
- [Continual Learning through Control Minimization](https://mlsanity.com/paper/2602.04542/) (2026)
- [A feedback control optimizer for online and hardware-aware training of Spiking Neural Networks](https://mlsanity.com/paper/2602.13261/) (2026)
- [Credit Assignment via Neural Manifold Noise Correlation](https://mlsanity.com/paper/2601.02636/) (2026)
- [Self-supervised local learning rules learn the hidden hierarchical structure of high-dimensional data](https://mlsanity.com/paper/2605.18557/) (2026)
- [Dis-inhibitory neuronal circuits can control the sign of synaptic plasticity](https://mlsanity.com/paper/2310.19614/) (2023)
- [Can Local Learning Match Self-Supervised Backpropagation?](https://mlsanity.com/paper/2601.21683/) (2026)

## Abstract (arXiv)

The success of deep learning ignited interest in whether the brain learns hierarchical representations using gradient-based learning. However, current biologically plausible methods for gradient-based credit assignment in deep neural networks need infinitesimally small feedback signals, which is problematic in biologically realistic noisy environments and at odds with experimental evidence in neuroscience showing that top-down feedback can significantly influence neural activity. Building upon deep feedback control (DFC), a recently proposed credit assignment method, we combine strong feedback influences on neural activity with gradient-based learning and show that this naturally leads to a novel view on neural network optimization. Instead of gradually changing the network weights towards configurations with low output loss, weight updates gradually minimize the amount of feedback required from a controller that drives the network to the supervised output label. Moreover, we show that the use of strong feedback in DFC allows learning forward and feedback connections simultaneously, using learning rules fully local in space and time. We complement our theoretical results with experiments on standard computer-vision benchmarks, showing competitive performance to backpropagation as well as robustness to noise. Overall, our work presents a fundamentally novel view of learning as control minimization, while sidestepping biologically unrealistic assumptions.