mlsanityData to 14 Oct 2026

Deep Learning without Weight Transport

arXiv 1904.05391 ↗First posted 10 Apr 2019cs.LG stat.MLcited by 87

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Abstract (arXiv)

Current algorithms for deep learning probably cannot run in the brain because they rely on weight transport, where forward-path neurons transmit their synaptic weights to a feedback path, in a way that is likely impossible biologically. An algorithm called feedback alignment achieves deep learning without weight transport by using random feedback weights, but it performs poorly on hard visual-recognition tasks. Here we describe two mechanisms - a neural circuit called a weight mirror and a modification of an algorithm proposed by Kolen and Pollack in 1994 - both of which let the feedback path learn appropriate synaptic weights quickly and accurately even in large networks, without weight transport or complex wiring.Tested on the ImageNet visual-recognition task, these mechanisms outperform both feedback alignment and the newer sign-symmetry method, and nearly match backprop, the standard algorithm of deep learning, which uses weight transport.

Key facts. Cited by 87 papers in the map (data through 14 Oct 2026). First posted on arXiv 10 Apr 2019.

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Citing papers per year: 2021: 16; 2022: 16; 2023: 12; 2024: 15; 2025: 12; 2026: 16.

87 papers.

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  1. 2021Predictive Coding: a Theoretical and Experimental Reviewcited by 77
  2. 2022Scaling Forward Gradient With Local Lossescited by 65
  3. 2022Holomorphic Equilibrium Propagation Computes Exact Gradients Through Finite Size Oscillationscited by 42
  4. 2021Credit Assignment in Neural Networks through Deep Feedback Controlcited by 29
  5. 2021The Backpropagation Algorithm Implemented on Spiking Neuromorphic Hardwarecited by 19
  6. 2022The least-control principle for local learning at equilibriumcited by 16
  7. 2021Latent Equilibrium: A unified learning theory for arbitrarily fast computation with arbitrarily slow neuronscited by 15
  8. 2023Brain-Inspired Machine Intelligence: A Survey of Neurobiologically-Plausible Credit Assignmentcited by 15
  9. 2021Convergence and Alignment of Gradient Descent with Random Backpropagation Weightscited by 14
  10. 2022Meta-Learning Biologically Plausible Plasticity Rules with Random Feedback Pathwayscited by 14
  11. 2023Dual Propagation: Accelerating Contrastive Hebbian Learning with Dyadic Neuronscited by 14
  12. 2021How to Train Your Wide Neural Network Without Backprop: An Input-Weight Alignment Perspectivecited by 13
38 more
  1. 2021Towards Biologically Plausible Convolutional Networkscited by 13
  2. 2022Fusing Event-based Camera and Radar for SLAM Using Spiking Neural Networks with Continual STDP Learningcited by 13
  3. 2023Forward Learning with Top-Down Feedback: Empirical and Analytical Characterizationcited by 13
  4. 2021Meta-Learning Bidirectional Update Rulescited by 10
  5. 2022Minimizing Control for Credit Assignment with Strong Feedbackcited by 10
  6. 2024Backpropagation through space, time, and the braincited by 10
  7. 2024Momentum Auxiliary Network for Supervised Local Learningcited by 10
  8. 2021Benchmarking the Accuracy and Robustness of Feedback Alignment Algorithmscited by 9
  9. 2022Constrained Parameter Inference as a Principle for Learningcited by 9
  10. 2022Is Bio-Inspired Learning Better than Backprop? Benchmarking Bio Learning vs. Backpropcited by 9
  11. 2023Improving equilibrium propagation without weight symmetry through Jacobian homeostasiscited by 9
  12. 2024Scaling Supervised Local Learning with Augmented Auxiliary Networkscited by 9
  13. 2022Learning efficient backprojections across cortical hierarchies in real timecited by 8
  14. 2023Predictive Coding as a Neuromorphic Alternative to Backpropagation: A Critical Evaluationcited by 8
  15. 2022Low-Variance Forward Gradients using Direct Feedback Alignment and Momentumcited by 7
  16. 2021Biologically Plausible Training Mechanisms for Self-Supervised Learning in Deep Networkscited by 6
  17. 2023Block-local learning with probabilistic latent representationscited by 6
  18. 2024Advancing Supervised Local Learning Beyond Classification with Long-term Feature Bankcited by 6
  19. 2021How and When Random Feedback Works: A Case Study of Low-Rank Matrix Factorizationcited by 5
  20. 2022Distinguishing Learning Rules with Brain Machine Interfacescited by 5
  21. 2024Pretraining with Random Noise for Fast and Robust Learning without Weight Transportcited by 5
  22. 2023Synaptic Weight Distributions Depend on the Geometry of Plasticitycited by 4
  23. 2024Towards Interpretable Deep Local Learning with Successive Gradient Reconciliationcited by 4
  24. 2024Towards training digitally-tied analog blocks via hybrid gradient computationcited by 4
  25. 2024Local Loss Optimization in the Infinite Width: Stable Parameterization of Predictive Coding Networks and Target Propagationcited by 4
  26. 2021Target Propagation via Regularized Inversioncited by 3
  27. 2023Correlative Information Maximization: A Biologically Plausible Approach to Supervised Deep Neural Networks without Weight Symmetrycited by 3
  28. 2024Online Pseudo-Zeroth-Order Training of Neuromorphic Spiking Neural Networkscited by 3
  29. 2024Temporal-Difference Learning Using Distributed Error Signalscited by 3
  30. 2025MAN++: Scaling Momentum Auxiliary Network for Supervised Local Learning in Vision Taskscited by 3
  31. 2021BioGrad: Biologically Plausible Gradient-Based Learning for Spiking Neural Networkscited by 2
  32. 2022A Robust Backpropagation-Free Framework for Imagescited by 2
  33. 2023Brain-like Flexible Visual Inference by Harnessing Feedback-Feedforward Alignmentcited by 2
  34. 2024Two Tales of Single-Phase Contrastive Hebbian Learningcited by 2
  35. 2025Closed-Form Feedback-Free Learning with Forward Projectioncited by 2
  36. 2025Training Large Neural Networks With Low-Dimensional Error Feedbackcited by 2
  37. 2025Curl Descent: Non-Gradient Learning Dynamics with Sign-Diverse Plasticitycited by 2
  38. 2026Continual Learning through Control Minimizationcited by 2

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