Training of Physical Neural Networks
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Abstract (arXiv)
Physical neural networks (PNNs) are a class of neural-like networks that leverage the properties of physical systems to perform computation. While PNNs are so far a niche research area with small-scale laboratory demonstrations, they are arguably one of the most underappreciated important opportunities in modern AI. Could we train AI models 1000x larger than current ones? Could we do this and also have them perform inference locally and privately on edge devices, such as smartphones or sensors? Research over the past few years has shown that the answer to all these questions is likely "yes, with enough research": PNNs could one day radically change what is possible and practical for AI systems. To do this will however require rethinking both how AI models work, and how they are trained - primarily by considering the problems through the constraints of the underlying hardware physics. To train PNNs at large scale, many methods including backpropagation-based and backpropagation-free approaches are now being explored. These methods have various trade-offs, and so far no method has been shown to scale to the same scale and performance as the backpropagation algorithm widely used in deep learning today. However, this is rapidly changing, and a diverse ecosystem of training techniques provides clues for how PNNs may one day be utilized to create both more efficient realizations of current-scale AI models, and to enable unprecedented-scale models.
Key facts. Cited by 47 papers in the map (data through 7 Oct 2026). Builds on 104 of its 240 references that are in the map. First posted on arXiv 5 Jun 2024.
Builds on
104 of 240 references.
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50 most cited of 104 All 104 (JSON)
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Citing papers per year: 2024: 6; 2025: 21; 2026: 20.
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- 2025Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computationcited by 120
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- 2024Self-Contrastive Forward-Forward Algorithmcited by 15
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- 2025Blending Optimal Control and Biologically Plausible Learning for Noise-Robust Physical Neural Networkscited by 2
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- 2025Harnessing uncertainty when learning through Equilibrium Propagation in neural networkscited by 0
- 2025Programmable metasurfaces for future photonic artificial intelligencecited by 0
- 2025Mechanical in-sensor computing: a programmable meta-sensor for structural damage classification without external electronic powercited by 0
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- 2025Neural networks for neurocomputing circuits: a computational study of tolerance to noise and activation function non-uniformity when machine learning materials propertiescited by 0
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- 2026Training single-electron and single-photon stochastic physical neural networkscited by 0
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- 2026Analog-Friendly Predictive Coding without Activation Derivatives26 Sep 2026
- 2026Physical policy gradient theorem for in situ stochastic-adjoint training5 Sep 2026
- 2026Multi-layer MIMO Relay as Deep Physical Neural Networks: Power Amplifiers as Activation Functions20 Jul 2026
- 2026Towards transferable lightweight neuromorphic computing through a model-free temporal-switch framework1 Jul 2026
- 2026Optical Implementation of Equilibrium Propagation Using Spatial Photonic Ising Machines11 Jun 2026
- 2026Perturbative Contrastive Physical Learning8 Jun 2026
- 2026A physical adaptive material motor unit neural network: a hygromorph composite material machine5 Jun 2026
- 2026Training a Predictive Coding Network on ImageNet using Equilibrium Propagation2 Jun 2026
- 2026Measurement-Adapted Eigentask Representations for Photon-Limited Optical Readout11 May 2026
- 2026Pre-training Enables Extraordinary All-optical Image Denoising8 May 2026
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- 2026Physical Foundation Models: Fixed hardware implementations of large-scale neural networks30 Apr 2026
- 2026Training single-electron and single-photon stochastic physical neural networks12 Apr 2026
- 2026The Phase Is the Gradient: Equilibrium Propagation for Frequency Learning in Kuramoto Networks11 Apr 2026
- 2026Local learning for stable backpropagation-free neural network training towards physical learning25 Mar 2026
- 2026Training deep physical neural networks with local physical information bottleneck10 Feb 2026
- 2026On the Infinite Width and Depth Limits of Predictive Coding Networks7 Feb 2026
- 2026Physical Analogue Kolmogorov-Arnold Networks based on Reconfigurable Nonlinear-Processing Units7 Feb 2026
- 2026Laser interferometry as a robust neuromorphic platform for machine learning26 Jan 2026
- 2025Analog Physical Systems Can Exhibit Double Descent21 Nov 2025
- 2025Near-Equilibrium Propagation training in nonlinear wave systems17 Oct 2025
- 2025Neural networks for neurocomputing circuits: a computational study of tolerance to noise and activation function non-uniformity when machine learning materials properties13 Oct 2025
- 2025MeSH: Memory-as-State-Highways for Recursive Transformers9 Oct 2025
- 2025Low-rank surrogate modeling and stochastic zero-order optimization for training of neural networks with black-box layers18 Sep 2025
- 2025Self-Organising Memristive Networks as Physical Learning Systems31 Aug 2025
- 2025Learning with springs and sticks26 Aug 2025
- 2025Higher-Order Kuramoto Oscillator Network for Dense Associative Memory29 Jul 2025
- 2025Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computation14 Jul 2025
- 2025Model-free Optical Processors using In Situ Reinforcement Learning with Proximal Policy Optimization8 Jul 2025
- 2025Towards the Training of Deeper Predictive Coding Neural Networks30 Jun 2025
- 2025Local Learning Rules for Out-of-Equilibrium Physical Generative Models23 Jun 2025
- 2025Machine Intelligence on Wireless Edge Networks13 Jun 2025
- 2025Learning long range dependencies through time reversal symmetry breaking5 Jun 2025
- 2025Mechanical in-sensor computing: a programmable meta-sensor for structural damage classification without external electronic power24 May 2025
- 2025Programmable metasurfaces for future photonic artificial intelligence16 May 2025
- 2025Harnessing uncertainty when learning through Equilibrium Propagation in neural networks28 Mar 2025
- 2025Thermodynamic cost of inference and learning in physical neural networks13 Mar 2025
- 2025Blending Optimal Control and Biologically Plausible Learning for Noise-Robust Physical Neural Networks26 Feb 2025
- 2025Analog In-memory Training on General Non-ideal Resistive Elements: The Impact of Response Functions10 Feb 2025
- 2025Scaling of hardware-compatible perturbative training algorithms26 Jan 2025
- 2024Self-Contrastive Forward-Forward Algorithm17 Sep 2024
- 2024Towards training digitally-tied analog blocks via hybrid gradient computation5 Sep 2024
- 2024Streamlined optical training of large-scale modern deep learning architectures with direct feedback alignment1 Sep 2024
- 2024Knowledge Mechanisms in Large Language Models: A Survey and Perspective22 Jul 2024
- 2024Towards Exact Gradient-based Training on Analog In-memory Computing18 Jun 2024
- 2024Quantum Equilibrium Propagation for efficient training of quantum systems based on Onsager reciprocity10 Jun 2024
- 2025Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computationcited by 120
- 2024Knowledge Mechanisms in Large Language Models: A Survey and Perspectivecited by 50
- 2024Self-Contrastive Forward-Forward Algorithmcited by 15
- 2024Quantum Equilibrium Propagation for efficient training of quantum systems based on Onsager reciprocitycited by 9
- 2025MeSH: Memory-as-State-Highways for Recursive Transformerscited by 8
- 2025Towards the Training of Deeper Predictive Coding Neural Networkscited by 7
- 2024Towards Exact Gradient-based Training on Analog In-memory Computingcited by 6
- 2025Learning long range dependencies through time reversal symmetry breakingcited by 6
- 2025Analog In-memory Training on General Non-ideal Resistive Elements: The Impact of Response Functionscited by 4
- 2024Towards training digitally-tied analog blocks via hybrid gradient computationcited by 3
- 2024Streamlined optical training of large-scale modern deep learning architectures with direct feedback alignmentcited by 3
- 2025Blending Optimal Control and Biologically Plausible Learning for Noise-Robust Physical Neural Networkscited by 2
12 most cited of 46 All 46 (JSON)
- 2026Physical Muon: Orthogonalization as an Equilibrium Computation29 Sep 2026
- 2026Making Analog Training Scale: Co-Designing Mapping, Optimizer, and Converters29 Sep 2026
- 2026Analog-Friendly Predictive Coding without Activation Derivatives26 Sep 2026
- 2026Physical policy gradient theorem for in situ stochastic-adjoint training5 Sep 2026
- 2026Multi-layer MIMO Relay as Deep Physical Neural Networks: Power Amplifiers as Activation Functions20 Jul 2026
- 2026Towards transferable lightweight neuromorphic computing through a model-free temporal-switch framework1 Jul 2026
- 2026Optical Implementation of Equilibrium Propagation Using Spatial Photonic Ising Machines11 Jun 2026
- 2026Perturbative Contrastive Physical Learning8 Jun 2026
- 2026A physical adaptive material motor unit neural network: a hygromorph composite material machine5 Jun 2026
- 2026Training a Predictive Coding Network on ImageNet using Equilibrium Propagation2 Jun 2026
- 2026Measurement-Adapted Eigentask Representations for Photon-Limited Optical Readout11 May 2026
- 2026Pre-training Enables Extraordinary All-optical Image Denoising8 May 2026
12 newest of 46 All 46 (JSON)