Training Neural Networks with Local Error Signals
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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.
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50 newest of 136 All 136 (JSON)
- 2024Revisiting Zeroth-Order Optimization for Memory-Efficient LLM Fine-Tuning: A Benchmarkcited by 114
- 2023Uncovering mesa-optimization algorithms in Transformerscited by 100
- 2021Self-Supervised Learning with Kernel Dependence Maximizationcited by 77
- 2023DeepZero: Scaling up Zeroth-Order Optimization for Deep Model Trainingcited by 76
- 2021Revisiting Locally Supervised Learning: an Alternative to End-to-end Trainingcited by 71
- 2022Scaling Forward Gradient With Local Lossescited by 65
- 2021The staircase property: How hierarchical structure can guide deep learningcited by 62
- 2022Hebbian Deep Learning Without Feedbackcited by 61
- 2024Training of Physical Neural Networkscited by 49
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- 2026LocalTrain: Integer-Only Local Learning for Energy-Efficient CNN Training on Edge FPGAs12 Oct 2026
- 2026Increasing Width Allows Greedy Layer-wise Training to Rival End-to-End Backpropagation in Self-Supervised Learning30 Sep 2026
- 2026SOLO: Pretraining Billion-Parameter Language Models with Shared-Output Local Learning28 Sep 2026
- 2026ProtoSeam: Lifting Classifier Training with Latent Gaussian Mixture Models28 Sep 2026
- 2026The Price of Locality: Why Forward-Forward Underperforms Backpropagation?27 Sep 2026
- 2026LocalProp: Neuro-Localized Memory-Efficient Backpropagation26 Sep 2026
- 2026Toward On-Chip Training of Spiking Neural Networks for Dense Event-Based Vision26 Sep 2026
- 2026The Drift Contract: Spectral Updates for Depth-Robust Local Learning16 Sep 2026
- 2026LoCA: Forward-Only LLM Tuning after One-Shot Calibration with Local Credit Assignment4 Aug 2026
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- 2026Conditioned Direct Feedback Alignment via Activity and Error Geometry20 Jul 2026
- 2026Gauge-Fixing the Forward-Forward Objective: A Whitened Goodness Derived from a Likelihood-Ratio Account14 Jul 2026
12 newest of 133 All 133 (JSON)