mlsanityData to 14 Oct 2026

Training Neural Networks with Local Error Signals

arXiv 1901.06656 ↗First posted 20 Jan 2019stat.ML cs.CV cs.LGcited by 136

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Abstract (arXiv)

Supervised training of neural networks for classification is typically performed with a global loss function. The loss function provides a gradient for the output layer, and this gradient is back-propagated to hidden layers to dictate an update direction for the weights. An alternative approach is to train the network with layer-wise loss functions. In this paper we demonstrate, for the first time, that layer-wise training can approach the state-of-the-art on a variety of image datasets. We use single-layer sub-networks and two different supervised loss functions to generate local error signals for the hidden layers, and we show that the combination of these losses help with optimization in the context of local learning. Using local errors could be a step towards more biologically plausible deep learning because the global error does not have to be transported back to hidden layers. A completely backprop free variant outperforms previously reported results among methods aiming for higher biological plausibility. Code is available https://github.com/anokland/local-loss

Key facts. Cited by 136 papers in the map (data through 14 Oct 2026). First posted on arXiv 20 Jan 2019.

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Citing papers per year: 2021: 27; 2022: 18; 2023: 24; 2024: 26; 2025: 18; 2026: 23.

136 papers.

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  1. 2024Revisiting Zeroth-Order Optimization for Memory-Efficient LLM Fine-Tuning: A Benchmarkcited by 114
  2. 2023Uncovering mesa-optimization algorithms in Transformerscited by 100
  3. 2021Self-Supervised Learning with Kernel Dependence Maximizationcited by 77
  4. 2023DeepZero: Scaling up Zeroth-Order Optimization for Deep Model Trainingcited by 76
  5. 2021Revisiting Locally Supervised Learning: an Alternative to End-to-end Trainingcited by 71
  6. 2022Scaling Forward Gradient With Local Lossescited by 65
  7. 2021The staircase property: How hierarchical structure can guide deep learningcited by 62
  8. 2022Hebbian Deep Learning Without Feedbackcited by 61
  9. 2024Training of Physical Neural Networkscited by 49
  10. 2025MesaNet: Sequence Modeling by Locally Optimal Test-Time Trainingcited by 47
  11. 2023Masked Image Modeling with Local Multi-Scale Reconstructioncited by 43
  12. 2023The Predictive Forward-Forward Algorithmcited by 35
38 more
  1. 2023SG-Former: Self-guided Transformer with Evolving Token Reallocationcited by 32
  2. 2023Can Forward Gradient Match Backpropagation?cited by 26
  3. 2022Signal Propagation: A Framework for Learning and Inference In a Forward Passcited by 24
  4. 2021Reverse Differentiation via Predictive Codingcited by 23
  5. 2021Bottom-up and top-down approaches for the design of neuromorphic processing systems: Tradeoffs and synergies between natural and artificial intelligencecited by 21
  6. 2021Learning to Time-Decode in Spiking Neural Networks Through the Information Bottleneckcited by 15
  7. 2022Gigapixel Whole-Slide Images Classification using Locally Supervised Learningcited by 15
  8. 2024FedImpro: Measuring and Improving Client Update in Federated Learningcited by 15
  9. 2021Predictive Coding Can Do Exact Backpropagation on Convolutional and Recurrent Neural Networkscited by 14
  10. 2021How to Train Your Wide Neural Network Without Backprop: An Input-Weight Alignment Perspectivecited by 13
  11. 2021Towards Biologically Plausible Convolutional Networkscited by 13
  12. 2023Forward Learning with Top-Down Feedback: Empirical and Analytical Characterizationcited by 13
  13. 2022OccamNets: Mitigating Dataset Bias by Favoring Simpler Hypothesescited by 11
  14. 2023Normalization-Equivariant Neural Networks with Application to Image Denoisingcited by 11
  15. 2023Recasting Continual Learning as Sequence Modelingcited by 11
  16. 2025DiffusionBlocks: Block-wise Neural Network Training via Diffusion Interpretationcited by 11
  17. 2023Boosting Learning for LDPC Codes to Improve the Error-Floor Performancecited by 10
  18. 2024Momentum Auxiliary Network for Supervised Local Learningcited by 10
  19. 2024Scaling Supervised Local Learning with Augmented Auxiliary Networkscited by 9
  20. 2021Semantic Clustering based Deduction Learning for Image Recognition and Classificationcited by 8
  21. 2023A General Framework for Interpretable Neural Learning based on Local Information-Theoretic Goal Functionscited by 8
  22. 2023Spiking Neural Networks and Bio-Inspired Supervised Deep Learning: A Surveycited by 8
  23. 2024End-to-End Training Induces Information Bottleneck through Layer-Role Differentiation: A Comparative Analysis with Layer-wise Trainingcited by 8
  24. 2022Low-Variance Forward Gradients using Direct Feedback Alignment and Momentumcited by 7
  25. 2021Decoupled Greedy Learning of CNNs for Synchronous and Asynchronous Distributed Learningcited by 6
  26. 2021Biologically Plausible Training Mechanisms for Self-Supervised Learning in Deep Networkscited by 6
  27. 2023Block-local learning with probabilistic latent representationscited by 6
  28. 2024Advancing Supervised Local Learning Beyond Classification with Long-term Feature Bankcited by 6
  29. 2024PETRA: Parallel End-to-end Training with Reversible Architecturescited by 6
  30. 2021Training Deep Architectures Without End-to-End Backpropagation: A Survey on the Provably Optimal Methodscited by 5
  31. 2021Contrastive Self-supervised Neural Architecture Searchcited by 5
  32. 2021Gradient Forward-Propagation for Large-Scale Temporal Video Modellingcited by 5
  33. 2024LLS: Local Learning Rule for Deep Neural Networks Inspired by Neural Activity Synchronizationcited by 5
  34. 2024MLAAN: Scaling Supervised Local Learning with Multilaminar Leap Augmented Auxiliary Networkcited by 5
  35. 2024HPFF: Hierarchical Locally Supervised Learning with Patch Feature Fusioncited by 5
  36. 2021How much pre-training is enough to discover a good subnetwork?cited by 4
  37. 2022Scaling Laws Beyond Backpropagationcited by 4
  38. 2022Local Learning on Transformers via Feature Reconstructioncited by 4

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