# Two Routes to Scalable Credit Assignment without Weight Symmetry

arXiv: https://arxiv.org/abs/2003.01513 · HTML: https://mlsanity.com/paper/2003.01513/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2020.

## Built on by (most cited first, 19 of 19)

- [Credit Assignment in Neural Networks through Deep Feedback Control](https://mlsanity.com/paper/2106.07887/) (2021)
- [Beyond Geometry: Comparing the Temporal Structure of Computation in Neural Circuits with Dynamical Similarity Analysis](https://mlsanity.com/paper/2306.10168/) (2023)
- [On the relationship between predictive coding and backpropagation](https://mlsanity.com/paper/2106.13082/) (2021)
- [Latent Equilibrium: A unified learning theory for arbitrarily fast computation with arbitrarily slow neurons](https://mlsanity.com/paper/2110.14549/) (2021)
- [Meta-Learning Biologically Plausible Plasticity Rules with Random Feedback Pathways](https://mlsanity.com/paper/2210.16414/) (2022)
- [Benchmarking the Accuracy and Robustness of Feedback Alignment Algorithms](https://mlsanity.com/paper/2108.13446/) (2021)
- [Training Deep Architectures Without End-to-End Backpropagation: A Survey on the Provably Optimal Methods](https://mlsanity.com/paper/2101.03419/) (2021)
- [How and When Random Feedback Works: A Case Study of Low-Rank Matrix Factorization](https://mlsanity.com/paper/2111.08706/) (2021)
- [Target Propagation via Regularized Inversion](https://mlsanity.com/paper/2112.01453/) (2021)
- [Temporal-Difference Learning Using Distributed Error Signals](https://mlsanity.com/paper/2411.03604/) (2024)
- [Brain-like Flexible Visual Inference by Harnessing Feedback-Feedforward Alignment](https://mlsanity.com/paper/2310.20599/) (2023)
- [Overcoming Rank Collapse in Feedback Alignment](https://mlsanity.com/paper/2606.11123/) (2026)
- [Implicit Regularization in Feedback Alignment Learning Mechanisms for Neural Networks](https://mlsanity.com/paper/2306.01870/) (2023)
- [Oja's plasticity rule overcomes several challenges of training neural networks under biological constraints](https://mlsanity.com/paper/2408.08408/) (2024)
- [Credit Assignment via Neural Manifold Noise Correlation](https://mlsanity.com/paper/2601.02636/) (2026)
- [Frozen Backpropagation: Relaxing Weight Symmetry in Deep Spiking Neural Networks](https://mlsanity.com/paper/2505.13741/) (2025)
- [Forward Only Learning for Orthogonal Neural Networks of any Depth](https://mlsanity.com/paper/2512.20668/) (2025)
- [Can Local Learning Match Self-Supervised Backpropagation?](https://mlsanity.com/paper/2601.21683/) (2026)
- [Weight Feedback Computes the Jacobian Transpose Locally in Modern Deep Networks](https://mlsanity.com/paper/2607.13380/) (2026)

## Abstract (arXiv)

The neural plausibility of backpropagation has long been disputed, primarily for its use of non-local weight transport - the biologically dubious requirement that one neuron instantaneously measure the synaptic weights of another. Until recently, attempts to create local learning rules that avoid weight transport have typically failed in the large-scale learning scenarios where backpropagation shines, e.g. ImageNet categorization with deep convolutional networks. Here, we investigate a recently proposed local learning rule that yields competitive performance with backpropagation and find that it is highly sensitive to metaparameter choices, requiring laborious tuning that does not transfer across network architecture. Our analysis indicates the underlying mathematical reason for this instability, allowing us to identify a more robust local learning rule that better transfers without metaparameter tuning. Nonetheless, we find a performance and stability gap between this local rule and backpropagation that widens with increasing model depth. We then investigate several non-local learning rules that relax the need for instantaneous weight transport into a more biologically-plausible "weight estimation" process, showing that these rules match state-of-the-art performance on deep networks and operate effectively in the presence of noisy updates. Taken together, our results suggest two routes towards the discovery of neural implementations for credit assignment without weight symmetry: further improvement of local rules so that they perform consistently across architectures and the identification of biological implementations for non-local learning mechanisms.