mlsanityData to 13 Oct 2026

Backpropagation-free Training of Deep Physical Neural Networks

arXiv 2304.11042 ↗First posted 20 Apr 2023cs.LG cs.NE physics.app-phcited by 42

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Abstract (arXiv)

Recent years have witnessed the outstanding success of deep learning in various fields such as vision and natural language processing. This success is largely indebted to the massive size of deep learning models that is expected to increase unceasingly. This growth of the deep learning models is accompanied by issues related to their considerable energy consumption, both during the training and inference phases, as well as their scalability. Although a number of work based on unconventional physical systems have been proposed which addresses the issue of energy efficiency in the inference phase, efficient training of deep learning models has remained unaddressed. So far, training of digital deep learning models mainly relies on backpropagation, which is not suitable for physical implementation as it requires perfect knowledge of the computation performed in the so-called forward pass of the neural network. Here, we tackle this issue by proposing a simple deep neural network architecture augmented by a biologically plausible learning algorithm, referred to as "model-free forward-forward training". The proposed architecture enables training deep physical neural networks consisting of layers of physical nonlinear systems, without requiring detailed knowledge of the nonlinear physical layers' properties. We show that our method outperforms state-of-the-art hardware-aware training methods by improving training speed, decreasing digital computations, and reducing power consumption in physical systems. We demonstrate the adaptability of the proposed method, even in systems exposed to dynamic or unpredictable external perturbations. To showcase the universality of our approach, we train diverse wave-based physical neural networks that vary in the underlying wave phenomenon and the type of non-linearity they use, to perform vowel and image classification tasks experimentally.

Key facts. Cited by 42 papers in the map (data through 13 Oct 2026). Builds on 20 of its 87 references that are in the map. First posted on arXiv 20 Apr 2023.

Builds on

20 of 87 references.

References · 20

  1. 2021Carbon Emissions and Large Neural Network Trainingcited by 565
  2. 2014On the Number of Linear Regions of Deep Neural Networkscited by 380
  3. 2022The Forward-Forward Algorithm: Some Preliminary Investigationscited by 263
  4. 2016Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagationcited by 255
  5. 2018All-Optical Machine Learning Using Diffractive Deep Neural Networkscited by 177
  6. 2021Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systemscited by 126
  7. 2018Training of photonic neural networks through in situ backpropagationcited by 45
  8. 2022Experimentally realized in situ backpropagation for deep learning in nanophotonic neural networkscited by 44
  9. 2019Wave Physics as an Analog Recurrent Neural Networkcited by 43
  10. 2017Reinforcement Learning in a large scale photonic Recurrent Neural Networkcited by 30
  11. 2021An optical neural network using less than 1 photon per multiplicationcited by 30
  12. 2023SymBa: Symmetric Backpropagation-Free Contrastive Learning with Forward-Forward Algorithm for Optimizing Convergencecited by 27
8 more
  1. 2017Vowel recognition with four coupled spin-torque nano-oscillatorscited by 22
  2. 2023Blockwise Self-Supervised Learning at Scalecited by 22
  3. 2020Scalable Optical Learning Operatorcited by 19
  4. 2020Interlocking Backpropagation: Improving depthwise model-parallelismcited by 17
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  6. 2021Wave-based extreme deep learning based on non-linear time-Floquet entanglementcited by 6
  7. 2023On the Tacit Linearity Assumption in Common Cascaded Models of RIS-Parametrized Wireless Channelscited by 6
  8. 2023Physics-inspired Neuroacoustic Computing Based on Tunable Nonlinear Multiple-scatteringcited by 4

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Citing papers per year: 2023: 4; 2024: 14; 2025: 13; 2026: 11.

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  1. 2024Training of Physical Neural Networkscited by 48
  2. 2023Training an Ising Machine with Equilibrium Propagationcited by 29
  3. 2023Forward-Forward Training of an Optical Neural Networkcited by 19
  4. 2024Self-Contrastive Forward-Forward Algorithmcited by 16
  5. 2023Nonlinear optical encoding enabled by recurrent linear scatteringcited by 15
  6. 2024Quantum Equilibrium Propagation for efficient training of quantum systems based on Onsager reciprocitycited by 9
  7. 2024Ornstein-Uhlenbeck Adaptation as a Mechanism for Learning in Brains and Machinescited by 6
  8. 2023A universal approximation theorem for nonlinear resistive networkscited by 5
  9. 2024Noise-Aware Training of Neuromorphic Dynamic Device Networkscited by 5
  10. 2026End-to-end autonomous scientific discovery on a real optical platformcited by 5
  11. 2024FLOPS: Forward Learning with OPtimal Samplingcited by 4
  12. 2024Asymmetrical estimator for training encapsulated deep photonic neural networkscited by 3
30 more
  1. 2024Towards training digitally-tied analog blocks via hybrid gradient computationcited by 3
  2. 2025Iterative Quantum Feature Mapscited by 3
  3. 2025Near-Equilibrium Propagation training in nonlinear wave systemscited by 3
  4. 2024Training Spiking Neural Networks via Augmented Direct Feedback Alignmentcited by 2
  5. 2024Noise-based Local Learning using Stochastic Magnetic Tunnel Junctionscited by 2
  6. 2025Blending Optimal Control and Biologically Plausible Learning for Noise-Robust Physical Neural Networkscited by 2
  7. 2025Nonlinear Computation with Linear Optics via Source-Position Encodingcited by 2
  8. 2025Model-free Optical Processors using In Situ Reinforcement Learning with Proximal Policy Optimizationcited by 2
  9. 2025Function regression using the forward forward training and inferring paradigmcited by 2
  10. 2024Learning Using a Single Forward Passcited by 1
  11. 2024Harnessing Nonidealities in Analog In-Memory Computing Circuits: A Physical Modeling Approach for Neuromorphic Systemscited by 1
  12. 2025One-Time Soft Alignment Enables Resilient Learning without Weight Transportcited by 1
  13. 2026Training deep physical neural networks with local physical information bottleneckcited by 1
  14. 2026Local learning for stable backpropagation-free neural network training towards physical learningcited by 1
  15. 2026Physical Foundation Models: Fixed hardware implementations of large-scale neural networkscited by 1
  16. 2024Thermal Crosstalk Modelling and Compensation Methods for Programmable Photonic Integrated Circuitscited by 0
  17. 2024Generalizing Deep Surrogate Solvers for Broadband Electromagnetic Field Prediction at Unseen Wavelengthscited by 0
  18. 2025Thermodynamic cost of inference and learning in physical neural networkscited by 0
  19. 2025Programmable metasurfaces for future photonic artificial intelligencecited by 0
  20. 2025Machine Intelligence on Wireless Edge Networkscited by 0
  21. 2025Evolutionary chemical learning in dimerization networkscited by 0
  22. 2025A Solvable Molecular Switch Model for Stable Temporal Information Processingcited by 0
  23. 2025Analog Physical Systems Can Exhibit Double Descentcited by 0
  24. 2026Laser interferometry as a robust neuromorphic platform for machine learningcited by 0
  25. 2026Can Local Learning Match Self-Supervised Backpropagation?cited by 0
  26. 2026Toward all-optical unsupervised Hebbian learning in deep photonic neuromorphic networkscited by 0
  27. 2026Training single-electron and single-photon stochastic physical neural networkscited by 0
  28. 2026Fully Analog Resonant Recurrent Neural Network via Metacircuitcited by 0
  29. 2026Pre-training Enables Extraordinary All-optical Image Denoisingcited by 0
  30. 2026Low-power analogue neural networks with trainable nonlinear connections for continuous controlcited by 0