Unifying Physical Backpropagation | Paper Citation Record

Observation 9e1388fa-67d4-4edc-a5f5-8c9cb1c2342f · outbound

This paper cites Toward a formal theory for computing machines made out of whatever physics offers.Nature Communications, 14(1):4911, 2023.

Unifying Physical Backpropagation Toward a formal theory for computing machines made out of whatever physics offers.Nature Communications, 14(1):4911, 2023

Reference 1

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Observation 390890aa-ece4-4859-b520-6346e33c4789 · outbound

This paper cites Wave physics as an analog recurrent neural network.Science Advances, 5(12):eaay6946, 2019.

Unifying Physical Backpropagation Wave physics as an analog recurrent neural network.Science Advances, 5(12):eaay6946, 2019

Reference 2

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Observation 76a352bc-44f6-4f8c-9703-0c9b8a940f4b · outbound

This paper cites Analogue computing with metamaterials.Nature Reviews Materials, 6(3):207–225, 2021.

Unifying Physical Backpropagation Analogue computing with metamaterials.Nature Reviews Materials, 6(3):207–225, 2021

Reference 3

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Observation d42fc0af-98a4-4243-8c68-a37e65c213c2 · outbound

This paper cites In- sensor passive speech classification with phononic metamaterials.Advanced Functional Materials, 34(17):2311877, 2024.

Unifying Physical Backpropagation In- sensor passive speech classification with phononic metamaterials.Advanced Functional Materials, 34(17):2311877, 2024

Reference 4

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Observation 53d7cb4f-ea7c-4074-991a-40d292e37af4 · outbound

This paper cites Demonstration of decentralized physics-driven learning.Physical Review Applied, 18(1):014040, 2022.

Unifying Physical Backpropagation Demonstration of decentralized physics-driven learning.Physical Review Applied, 18(1):014040, 2022

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.689360Z

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Observation ae9680dc-0321-415c-9b73-fed30cc69f37 · outbound

This paper cites Memory devices and applications for in-memory computing.Nature Nanotechnology, 15(7):529–544, 2020.

Unifying Physical Backpropagation Memory devices and applications for in-memory computing.Nature Nanotechnology, 15(7):529–544, 2020

Reference 6

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Observation 30a9bd48-367d-4d05-875c-fe0cc682f8c6 · outbound

This paper cites Physics for neuromorphic computing.Nature Reviews Physics, 2(9):499–510, 2020.

Unifying Physical Backpropagation Physics for neuromorphic computing.Nature Reviews Physics, 2(9):499–510, 2020

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.699902Z

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Observation f8723c8b-ad74-4e56-bf23-bd0303be1a5a · outbound

This paper cites Photonics for artificial intelligence and neuro- morphic computing.Nature Photonics, 15(2):102–114, 2021.

Unifying Physical Backpropagation Photonics for artificial intelligence and neuro- morphic computing.Nature Photonics, 15(2):102–114, 2021

Reference 8

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Observation 81ac24da-a5e1-453e-9a86-7999d1f34a84 · outbound

This paper cites Scalable optical learning operator.Nature Computational Science, 1(8):542–549, 2021.

Unifying Physical Backpropagation Scalable optical learning operator.Nature Computational Science, 1(8):542–549, 2021

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.709025Z

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Observation 01d23a7a-dab5-4eab-beb5-32bd07c940a2 · outbound

This paper cites Inference in artificial intelligence with deep optics and photonics.Nature, 588(7836):39–47, 2020.

Unifying Physical Backpropagation Inference in artificial intelligence with deep optics and photonics.Nature, 588(7836):39–47, 2020

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.713783Z

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Observation 20ed9a9b-c7e5-425c-bbb9-a26f305baa71 · outbound

This paper cites All-optical machine learning using diffractive deep neural networks.Science, 361(6406):1004– 1008, 2018.

Unifying Physical Backpropagation All-optical machine learning using diffractive deep neural networks.Science, 361(6406):1004– 1008, 2018

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.718359Z

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Observation 39d062a5-2d47-4776-a7d5-2619d4a2efed · outbound

This paper cites The physics of optical computing.Nature Reviews Physics, 5(12):717–734, 2023.

Unifying Physical Backpropagation The physics of optical computing.Nature Reviews Physics, 5(12):717–734, 2023

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.722972Z

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Observation 4f097ac2-8f69-4f96-b5f0-f6ac8c32ea45 · outbound

This paper cites Arbitrary control over multimode wave propagation for machine learning.Nature Physics, 22:164–171, 2026.

Unifying Physical Backpropagation Arbitrary control over multimode wave propagation for machine learning.Nature Physics, 22:164–171, 2026

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.727183Z

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Observation 0bbb5d47-3c1a-4687-9ecc-970768ce654e · outbound

This paper cites Programmable on-chip nonlinear photonics.Nature, 649(8096):330–337, 2026.

Unifying Physical Backpropagation Programmable on-chip nonlinear photonics.Nature, 649(8096):330–337, 2026

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.731258Z

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Observation 60280dce-5d22-4071-a4f9-5d7087ec8e31 · outbound

This paper cites Recent advances in physical reservoir computing: A review.Neural Networks, 115:100–123, 2019.

Unifying Physical Backpropagation Recent advances in physical reservoir computing: A review.Neural Networks, 115:100–123, 2019

Reference 15

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Observation 439dbfdd-4382-4765-8723-7a84c3149a8a · outbound

This paper cites Training of physical neural networks.Nature, 645(8079):53–61, 2025.

Unifying Physical Backpropagation Training of physical neural networks.Nature, 645(8079):53–61, 2025

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.739200Z

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Observation ce7500e7-f875-4566-bf02-6b98bef6bf76 · outbound

This paper cites Inverse-designed low-index-contrast structures on a silicon photonics platform for vector– matrix multiplication.Nature Photonics, 18(5):501–508, 2024.

Unifying Physical Backpropagation Inverse-designed low-index-contrast structures on a silicon photonics platform for vector– matrix multiplication.Nature Photonics, 18(5):501–508, 2024

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.743289Z

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Observation 5763e534-48e2-44e1-8541-dc7c6930c79c · outbound

This paper cites Deep physical neural networks trained with backpropagation.Nature, 601(7894):549–555, 2022.

Unifying Physical Backpropagation Deep physical neural networks trained with backpropagation.Nature, 601(7894):549–555, 2022

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.747818Z

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Observation 05f81b04-ffc5-418e-a426-4e58ff843b74 · outbound

This paper cites Optical diffusion models for image generation.Advances in Neural Information Processing Systems, 37:59150–59173, 2024.

Unifying Physical Backpropagation Optical diffusion models for image generation.Advances in Neural Information Processing Systems, 37:59150–59173, 2024

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.752125Z

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Observation 50a66671-2cca-4823-baa0-fdd1c9d4b0a6 · outbound

This paper cites Trainable hardware for dynamical computing using error backpropagation through physical media.

Unifying Physical Backpropagation Trainable hardware for dynamical computing using error backpropagation through physical media

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.756170Z

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Observation 692a3931-d99e-4ebf-adaa-f2f0f9edb98b · outbound

This paper cites In situ optical backpropagation training of diffractive optical neural networks.

Unifying Physical Backpropagation In situ optical backpropagation training of diffractive optical neural networks

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.760173Z

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Observation c188d944-052f-4061-b6a1-25d5f118be7a · outbound

This paper cites Threading light through dynamic complex media.Nature Photonics, 19(4):434–440, 2025.

Unifying Physical Backpropagation Threading light through dynamic complex media.Nature Photonics, 19(4):434–440, 2025

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.764139Z

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Observation 4e9fd759-bc2c-46bd-944e-59acdf15e33f · outbound

This paper cites Experimentally realized in situ backpropagation for deep learning in photonic neural networks.Science, 380(6643):398–404, 2023.

Unifying Physical Backpropagation Experimentally realized in situ backpropagation for deep learning in photonic neural networks.Science, 380(6643):398–404, 2023

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.768746Z

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Observation 505b96cf-33c7-4f70-b02a-973eaa9cc50b · outbound

This paper cites Training all-mechanical neural networks for task learning through in situ backpropagation.Nature Communications, 15(1):10528, 2024.

Unifying Physical Backpropagation Training all-mechanical neural networks for task learning through in situ backpropagation.Nature Communications, 15(1):10528, 2024

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.773332Z

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Observation ee0f850b-7327-4018-8b4f-b0835e093bb7 · outbound

This paper cites How to train your resistive net- work: Generalized equilibrium propagation and analytical learning.arXiv preprint arXiv:2602.03546, 2026.

Unifying Physical Backpropagation How to train your resistive net- work: Generalized equilibrium propagation and analytical learning.arXiv preprint arXiv:2602.03546, 2026

Reference 25

Resolution: verified exact; raw_fallback, observed 2026-08-16T00:46:06.820789Z

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Observation a004e595-e3a2-4f9c-94c1-d8270fdbea4e · outbound

This paper cites Self-learning machines based on Hamiltonian echo backpropagation.Physical Review X, 13(3):031020, 2023.

Unifying Physical Backpropagation Self-learning machines based on Hamiltonian echo backpropagation.Physical Review X, 13(3):031020, 2023

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.782236Z

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Observation 50ebd2a2-6be2-49d9-813e-6f9bddc7bcd8 · outbound

This paper cites Routledge, 2018.

Unifying Physical Backpropagation Routledge, 2018

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.787186Z

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Observation 1fcc1974-647f-4d27-8fba-c9a035532395 · outbound

This paper cites Springer Science & Business Media, 2010.

Unifying Physical Backpropagation Springer Science & Business Media, 2010

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.792039Z

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Observation 1f4ff490-52f3-40ea-8231-dc111bd61ee7 · outbound

This paper cites In-situ physical adjoint comput- ing in multiple-scattering electromagnetic environments for wave control.Nature Communications, 16(1):11466, 2025.

Unifying Physical Backpropagation In-situ physical adjoint comput- ing in multiple-scattering electromagnetic environments for wave control.Nature Communications, 16(1):11466, 2025

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.796502Z

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Observation 57d860a0-289e-4ff4-a45d-3303ff35947a · outbound

This paper cites Equilibrium propagation: Bridging the gap between energy- based models and backpropagation.Frontiers in Computational Neuroscience, 11:24, 2017.

Unifying Physical Backpropagation Equilibrium propagation: Bridging the gap between energy- based models and backpropagation.Frontiers in Computational Neuroscience, 11:24, 2017

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.800788Z

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Observation 78ee6357-725f-41ab-bc4c-cd2af153e0d7 · outbound

This paper cites Learning long range dependencies through time reversal symmetry breaking.

Unifying Physical Backpropagation Learning long range dependencies through time reversal symmetry breaking

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.805154Z

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Observation 3192cc96-5d43-4e37-906b-9fa929a9037a · outbound

This paper cites Fully forward mode training for optical neural networks.Nature, 632(8024):280–286, 2024.

Unifying Physical Backpropagation Fully forward mode training for optical neural networks.Nature, 632(8024):280–286, 2024

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.774226Z

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Observation a947b660-a766-42f8-93bb-5360f341d709 · outbound

This paper cites Training of photonic neural networks through in situ backpropagation and gradient measurement.Optica, 5(7):864–871, 2018.

Unifying Physical Backpropagation Training of photonic neural networks through in situ backpropagation and gradient measurement.Optica, 5(7):864–871, 2018

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.759135Z

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Observation a3619e2b-4beb-42fa-aab9-0cd7d48f2988 · outbound

This paper cites Multilayer optical learning networks.Applied Optics, 26(23):5061–5076, 1987.

Unifying Physical Backpropagation Multilayer optical learning networks.Applied Optics, 26(23):5061–5076, 1987

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.743830Z

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Observation 749bbef2-626a-4dc9-98b0-e9be04d04501 · outbound

This paper cites Backpropagation through nonlinear units for the all-optical training of neural networks.Photonics Research, 9(3):B71– B80, 2021.

Unifying Physical Backpropagation Backpropagation through nonlinear units for the all-optical training of neural networks.Photonics Research, 9(3):B71– B80, 2021

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.728618Z

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Observation 0850a9da-0271-45f1-a2eb-0bb449a11797 · outbound

This paper cites Training neural networks with end-to-end optical backpropagation.Advanced Photonics, 7(1):016004, 2025.

Unifying Physical Backpropagation Training neural networks with end-to-end optical backpropagation.Advanced Photonics, 7(1):016004, 2025

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.713689Z

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Observation f75b57b1-16a6-4743-b60a-354b9c18daac · outbound

This paper cites Fully nonlinear neuromorphic computing with linear wave scattering.Nature Physics, 20(9):1434–1440, 2024.

Unifying Physical Backpropagation Fully nonlinear neuromorphic computing with linear wave scattering.Nature Physics, 20(9):1434–1440, 2024

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.698781Z

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Observation 3b303f06-fb83-4e97-a48a-02407dec855e · outbound

This paper cites Topological mechanical neural networks as classifiers through in situ backpropagation learning.

Unifying Physical Backpropagation Topological mechanical neural networks as classifiers through in situ backpropagation learning

Reference 38

Resolution: verified exact; local_arxiv, observed 2026-08-16T00:46:06.725556Z

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Observation a8bae4a4-c628-4ab9-87fe-5f017e560918 · outbound

This paper cites Localization transitions in non-Hermitian quantum mechan- ics.Physical Review Letters, 77(3):570–573, 1996.

Unifying Physical Backpropagation Localization transitions in non-Hermitian quantum mechan- ics.Physical Review Letters, 77(3):570–573, 1996

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.683863Z

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Observation 554567a5-4fa4-4aab-8b73-aef886c7e86c · outbound

This paper cites Supervised learning in physical networks: From machine learning to learning machines.Physical Review X, 11(2):021045, 2021.

Unifying Physical Backpropagation Supervised learning in physical networks: From machine learning to learning machines.Physical Review X, 11(2):021045, 2021

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.668938Z

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Observation ef9aaac2-3884-4719-a08b-dd31537eb2c8 · outbound

This paper cites Learning without neurons in physical systems.Annual Review of Condensed Matter Physics, 14(1):417–441, 2023.

Unifying Physical Backpropagation Learning without neurons in physical systems.Annual Review of Condensed Matter Physics, 14(1):417–441, 2023

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.653877Z

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Observation 1eaadaea-5699-431b-87d5-0afdac308e17 · outbound

This paper cites Machine learning without a processor: Emergent learning in a nonlinear analog network.

Unifying Physical Backpropagation Machine learning without a processor: Emergent learning in a nonlinear analog network

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.639176Z

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Observation f12580a3-b3fc-4531-aa40-838b9dac20a2 · outbound

This paper cites Training self-learning circuits for power-efficient solutions.APL Machine Learning, 2(1):016114, 2024.

Unifying Physical Backpropagation Training self-learning circuits for power-efficient solutions.APL Machine Learning, 2(1):016114, 2024

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.624068Z

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Observation 2b987779-abb5-48d4-86b8-e5ea50fd7cd7 · outbound

This paper cites Coercivity and local convergence of physical learning in linear circuits.arXiv preprint arXiv:2606.15443, 2026.

Unifying Physical Backpropagation Coercivity and local convergence of physical learning in linear circuits.arXiv preprint arXiv:2606.15443, 2026

Reference 44

Resolution: verified exact; raw_fallback, observed 2026-08-16T00:46:06.700817Z

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Observation 238edb60-a8c8-484c-9346-861d962f5aee · outbound

This paper cites Multimodal deep learning using on-chip diffractive optics with in situ training capability.Nature Communications, 15(1):6189, 2024.

Unifying Physical Backpropagation Multimodal deep learning using on-chip diffractive optics with in situ training capability.Nature Communications, 15(1):6189, 2024

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.608323Z

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Observation 5cc3973c-b700-4343-b5d1-29954cf711b6 · outbound

This paper cites Multimodal oscillator networks learn to solve a classification problem.npj Metamaterials, 2(1):3, 2026.

Unifying Physical Backpropagation Multimodal oscillator networks learn to solve a classification problem.npj Metamaterials, 2(1):3, 2026

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.592977Z

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Observation 88177e8b-b945-4c39-ae01-df9d4deaa277 · outbound

This paper cites Forward–forward training of an optical neural network.

Unifying Physical Backpropagation Forward–forward training of an optical neural network

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.578223Z

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Observation c301d3ae-72b7-4e7d-9d13-6c2d1875b071 · outbound

This paper cites Backpropagation-free training of deep physical neural networks.Science, 382(6676):1297–1303, 2023.

Unifying Physical Backpropagation Backpropagation-free training of deep physical neural networks.Science, 382(6676):1297–1303, 2023

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.563475Z

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Observation 32326224-c03d-430b-a550-6a844bb390cb · outbound

This paper cites Training deep physical neural networks with local physical information bottleneck.arXiv preprint arXiv:2602.09569, 2026.

Unifying Physical Backpropagation Training deep physical neural networks with local physical information bottleneck.arXiv preprint arXiv:2602.09569, 2026

Reference 49

Resolution: verified exact; raw_fallback, observed 2026-08-16T00:46:06.606189Z

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Observation 8328d740-a91b-4fa4-8379-a6292a4e101a · outbound

This paper cites Using memristors for robust local learning of hardware restricted Boltzmann machines.Scientific Reports, 9(1):1851, 2019.

Unifying Physical Backpropagation Using memristors for robust local learning of hardware restricted Boltzmann machines.Scientific Reports, 9(1):1851, 2019

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.549099Z

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Observation 0d0e9a17-65b4-45e8-abc6-a1e631ecf16e · outbound

This paper cites an unresolved cited work.

Unifying Physical Backpropagation Unresolved cited work

Reference 51

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:46:07.534127Z

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Observation bde93477-ce26-4af7-85a3-b7bcfff8c27f · outbound

This paper cites Local Learning Rules for Out-of-Equilibrium Physical Generative Models.

Unifying Physical Backpropagation Local Learning Rules for Out-of-Equilibrium Physical Generative Models

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.899468Z

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Observation 94665e02-f2c7-4478-841f-2cdeaa291c87 · outbound

This paper cites Nonlinear Computation with Linear Optics via Source-Position Encoding.

Unifying Physical Backpropagation Nonlinear Computation with Linear Optics via Source-Position Encoding

Reference 53

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.904066Z

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Unavailable: canonical work link unavailable.

Observation 8995debe-bb78-4997-b40d-a4910fc1e758 · outbound

This paper cites Nonlinear optical encoding enabled by recurrent linear scattering.Nature Photonics, 18(10):1067–1075, 2024.

Unifying Physical Backpropagation Nonlinear optical encoding enabled by recurrent linear scattering.Nature Photonics, 18(10):1067–1075, 2024

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.519296Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 195a060a-4933-4e83-92a9-9d31b527349d · outbound

This paper cites Nonlinear processing with linear optics.Nature Photonics, 18(10):1076–1082, 2024.

Unifying Physical Backpropagation Nonlinear processing with linear optics.Nature Photonics, 18(10):1076–1082, 2024

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.503984Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation edeab902-72ae-42b2-abb7-bcd209690470 · outbound

This paper cites Giles and Niles A.

Unifying Physical Backpropagation Giles and Niles A

Reference 56

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.489024Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 821fb53f-9b43-4696-898e-774607be9530 · outbound

This paper cites an unresolved cited work.

Unifying Physical Backpropagation Unresolved cited work

Reference 57

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:46:07.473800Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 3ebc2fd8-2071-4698-a0db-85e575f6fedf · outbound

This paper cites Dutton, and Shanhui Fan.

Unifying Physical Backpropagation Dutton, and Shanhui Fan

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.458801Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation af87eca3-4d14-414d-98eb-81634cde922b · outbound

This paper cites an unresolved cited work.

Unifying Physical Backpropagation Unresolved cited work

Reference 59

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:46:07.444135Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 79b9c01d-f373-48c9-acc1-08c5f2d4db9c · outbound

This paper cites Optimal control of PDEs in a complex space setting: Application to the Schr¨ odinger equation.SIAM Journal on Control and Optimization, 57(2):1390–1412, 2019.

Unifying Physical Backpropagation Optimal control of PDEs in a complex space setting: Application to the Schr¨ odinger equation.SIAM Journal on Control and Optimization, 57(2):1390–1412, 2019

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.430331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 16c8f897-3230-4c95-89fc-14c4d23fbd51 · outbound

This paper cites an unresolved cited work.

Unifying Physical Backpropagation Unresolved cited work

Reference 61

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:46:07.415728Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4bd3ec84-a8fc-4737-82ab-ce013e93e14f · outbound

This paper cites Complex-valued matrix differentiation: Techniques and key results.IEEE Transactions on Signal Processing, 55(6):2740–2746, 2007.

Unifying Physical Backpropagation Complex-valued matrix differentiation: Techniques and key results.IEEE Transactions on Signal Processing, 55(6):2740–2746, 2007

Reference 62

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.400856Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7f1c2edd-c7d8-448d-b799-f3c2ef3c7579 · outbound

This paper cites Unconstrained optimization of real functions in complex variables.SIAM Journal on Optimization, 22(3):879–898, 2012.

Unifying Physical Backpropagation Unconstrained optimization of real functions in complex variables.SIAM Journal on Optimization, 22(3):879–898, 2012

Reference 63

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.385593Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8435d6bb-f50e-48e0-829b-ff865826fdb2 · outbound

This paper cites Springer Netherlands, 2009.

Unifying Physical Backpropagation Springer Netherlands, 2009

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.371041Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8c9b545d-c999-4b8a-9365-5b69453dbc43 · outbound

This paper cites Training overdamped dynamics.arXiv preprint arXiv:2602.19122, 2026.

Unifying Physical Backpropagation Training overdamped dynamics.arXiv preprint arXiv:2602.19122, 2026

Reference 65

Resolution: verified exact; raw_fallback, observed 2026-08-16T00:46:06.496495Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 447a349e-3302-4b4c-a838-e3377c9a5be1 · outbound

This paper cites Equilibrium Propagation for Dissipative Dynamics.

Unifying Physical Backpropagation Equilibrium Propagation for Dissipative Dynamics

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.963030Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ca56bbf5-6df2-4f4e-9131-db17485e4117 · outbound

This paper cites Holomorphic equilibrium propagation computes exact gradi- ents through finite size oscillations.Advances in Neural Information Processing Systems, 35:12950– 12963, 2022.

Unifying Physical Backpropagation Holomorphic equilibrium propagation computes exact gradi- ents through finite size oscillations.Advances in Neural Information Processing Systems, 35:12950– 12963, 2022

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.357149Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f81da60f-1d69-4808-ac96-16ea337ff137 · outbound

This paper cites Training nonlinear optical neural networks with Scattering Backpropagation.

Unifying Physical Backpropagation Training nonlinear optical neural networks with Scattering Backpropagation

Reference 68

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.973046Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 56ab3b59-ff39-4601-9649-f93a9dfc20b0 · outbound

This paper cites Near-equilibrium propagation training in nonlinear wave systems.arXiv preprint arXiv:2510.16084, 2025.

Unifying Physical Backpropagation Near-equilibrium propagation training in nonlinear wave systems.arXiv preprint arXiv:2510.16084, 2025

Reference 69

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.977788Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3a5ff6f6-3e8e-4944-9273-6da0ab2db595 · outbound

This paper cites Generalization of Equilibrium Propagation to Vector Field Dynamics.

Unifying Physical Backpropagation Generalization of Equilibrium Propagation to Vector Field Dynamics

Reference 70

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.982267Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 13440c67-405e-4b43-af1f-29db97d3d10b · outbound

This paper cites Improving equilibrium propagation without weight symmetry through Jacobian homeostasis.

Unifying Physical Backpropagation Improving equilibrium propagation without weight symmetry through Jacobian homeostasis

Reference 71

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.341615Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a6514f2c-e84e-4b45-8d02-cbab3d0a0de5 · outbound

This paper cites Equilibrium Propagation for Non-Conservative Systems.

Unifying Physical Backpropagation Equilibrium Propagation for Non-Conservative Systems

Reference 72

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.991596Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0702e99d-78ff-4a76-8c31-7735c30d45dd · outbound

This paper cites Agnostic Physics-Driven Deep Learning.

Unifying Physical Backpropagation Agnostic Physics-Driven Deep Learning

Reference 73

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:05.996422Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 233e277a-b10e-4463-818b-7472e4faeb7f · outbound

This paper cites Reciprocal relations in irreversible processes.

Unifying Physical Backpropagation Reciprocal relations in irreversible processes

Reference 74

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.326899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation dd5878f1-c8f3-4399-8e08-0bed7b2923d3 · outbound

This paper cites Fluctuations and irreversible processes.Physical Review, 91(6):1505–1512, 1953.

Unifying Physical Backpropagation Fluctuations and irreversible processes.Physical Review, 91(6):1505–1512, 1953

Reference 75

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.311481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 339ca949-da9e-4b12-8cfa-8eb07698b381 · outbound

This paper cites Topological mechanics of gyroscopic metamaterials.Proceedings of the National Academy of Sciences, 112(47):14495–14500, 2015.

Unifying Physical Backpropagation Topological mechanics of gyroscopic metamaterials.Proceedings of the National Academy of Sciences, 112(47):14495–14500, 2015

Reference 76

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.296883Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation cbaa2982-725e-44e8-9964-2bef625484a1 · outbound

This paper cites Observation of PT phase transition in a simple mechanical system.American Journal of Physics, 81(3):173–179, 2013.

Unifying Physical Backpropagation Observation of PT phase transition in a simple mechanical system.American Journal of Physics, 81(3):173–179, 2013

Reference 77

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.283561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b17f11b2-c0ce-47d8-be06-fed64e592b3a · outbound

This paper cites Time reversal of ultrasonic fields.

Unifying Physical Backpropagation Time reversal of ultrasonic fields

Reference 78

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.267883Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e49d490e-1376-42df-855c-4bbeb5b6cc30 · outbound

This paper cites Lagrangian-based Equilibrium Propagation: generalisation to arbitrary boundary conditions & equivalence with Hamiltonian Echo Learning.

Unifying Physical Backpropagation Lagrangian-based Equilibrium Propagation: generalisation to arbitrary boundary conditions & equivalence with Hamiltonian Echo Learning

Reference 79

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:06.025279Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4ed3ec33-de91-475f-b1a9-6743b52de51f · outbound

This paper cites an unresolved cited work.

Unifying Physical Backpropagation Unresolved cited work

Reference 80

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:46:07.253047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 150c1501-62ce-4abb-aac0-e92d6a32a0f8 · outbound

This paper cites Scaling equilibrium propagation to deep convnets by drastically reducing its gradient estimator bias.Frontiers in Neuroscience, 15:633674, 2021.

Unifying Physical Backpropagation Scaling equilibrium propagation to deep convnets by drastically reducing its gradient estimator bias.Frontiers in Neuroscience, 15:633674, 2021

Reference 81

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.238766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d28915eb-8e5f-4934-b1e0-12381ae629f7 · outbound

This paper cites Equilibrium propagation for learning in Lagrangian dynamical systems.Physical Review E, 112(3):035304, 2025.

Unifying Physical Backpropagation Equilibrium propagation for learning in Lagrangian dynamical systems.Physical Review E, 112(3):035304, 2025

Reference 82

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.224163Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8f707fd7-c1bb-479d-af54-7e64e05c0883 · outbound

This paper cites Springer Science & Business Media, 1991.

Unifying Physical Backpropagation Springer Science & Business Media, 1991

Reference 83

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.208800Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 93d14549-4456-4522-9b98-94cb7800308b · outbound

This paper cites A short tutorial on Wirtinger Calculus with applications in quantum information.

Unifying Physical Backpropagation A short tutorial on Wirtinger Calculus with applications in quantum information

Reference 84

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:06.046428Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ca8384b6-1708-4544-b1fa-8f2c26c38205 · outbound

This paper cites Integrated photonic neural network with on-chip backpropagation training.Nature, 651(8107):927–932, 2026.

Unifying Physical Backpropagation Integrated photonic neural network with on-chip backpropagation training.Nature, 651(8107):927–932, 2026

Reference 85

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.194144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 90ae2b03-5a70-47c2-a8d8-d2feffeb4f42 · outbound

This paper cites Training End-to-End Analog Neural Networks with Equilibrium Propagation.

Unifying Physical Backpropagation Training End-to-End Analog Neural Networks with Equilibrium Propagation

Reference 86

Resolution: unresolved; no resolver link, observed 2026-08-16T00:46:06.054589Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 76a1151c-2b73-4eb4-aea3-8081200b7ddb · outbound

This paper cites Training an Ising machine with equilibrium propagation.Nature Communications, 15(1):3671, 2024.

Unifying Physical Backpropagation Training an Ising machine with equilibrium propagation.Nature Communications, 15(1):3671, 2024

Reference 87

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.178878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 3fc0bcfd-8e07-4fc0-839e-6679f0e9065b · outbound

This paper cites Equivalence of equilibrium propagation and recurrent back- propagation.Neural Computation, 31(2):312–329, 2019.

Unifying Physical Backpropagation Equivalence of equilibrium propagation and recurrent back- propagation.Neural Computation, 31(2):312–329, 2019

Reference 88

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.164079Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ce00a984-62df-4183-a3f5-9ac44af1ae4d · outbound

This paper cites Updates of equilibrium prop match gradients of backprop through time in an RNN with static input.Advances in Neural Information Processing Systems, 32, 2019.

Unifying Physical Backpropagation Updates of equilibrium prop match gradients of backprop through time in an RNN with static input.Advances in Neural Information Processing Systems, 32, 2019

Reference 89

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.148938Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5e98f556-17f6-4f7c-96b3-83801e1cb2b6 · outbound

This paper cites Frequency propagation: Multimechanism learning in nonlinear physical networks.Neural Computation, 36(4):596–620, 2024.

Unifying Physical Backpropagation Frequency propagation: Multimechanism learning in nonlinear physical networks.Neural Computation, 36(4):596–620, 2024

Reference 90

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.133741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a8ab75d8-791f-4c7d-a45f-7b18a7075f7d · outbound

This paper cites Training coupled phase oscillators as a neuromorphic platform using equilibrium propagation.Neuromorphic Computing and Engineering, 4(3):034014, 2024.

Unifying Physical Backpropagation Training coupled phase oscillators as a neuromorphic platform using equilibrium propagation.Neuromorphic Computing and Engineering, 4(3):034014, 2024

Reference 91

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.119150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 157d1eeb-ac3b-405a-84ae-f380bffddc68 · outbound

This paper cites Generalized bulk–boundary correspondence in non-Hermitian topolectrical circuits.Nature Physics, 16(7):747– 750, 2020.

Unifying Physical Backpropagation Generalized bulk–boundary correspondence in non-Hermitian topolectrical circuits.Nature Physics, 16(7):747– 750, 2020

Reference 92

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.104681Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e3c54856-4d7d-4d6a-893f-b7e88ed60b30 · outbound

This paper cites Topological funneling of light.Science, 368(6488):311–314, 2020.

Unifying Physical Backpropagation Topological funneling of light.Science, 368(6488):311–314, 2020

Reference 93

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.089730Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5dc0e373-235d-4765-a390-6f51c8993368 · outbound

This paper cites Sound isolation and giant linear nonreciprocity in a compact acoustic circulator.Science, 343(6170):516–519, 2014.

Unifying Physical Backpropagation Sound isolation and giant linear nonreciprocity in a compact acoustic circulator.Science, 343(6170):516–519, 2014

Reference 94

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.074399Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b2e53d59-41de-4251-a6bd-2f17d5371455 · outbound

This paper cites Odd elasticity.Nature Physics, 16(4):475–480, 2020.

Unifying Physical Backpropagation Odd elasticity.Nature Physics, 16(4):475–480, 2020

Reference 95

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.058277Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b0bafa6d-7c27-4745-abab-54af78674ba8 · outbound

This paper cites On Onsager’s principle of microscopic reversibility.Reviews of Modern Physics, 17(2-3):343–350, 1945.

Unifying Physical Backpropagation On Onsager’s principle of microscopic reversibility.Reviews of Modern Physics, 17(2-3):343–350, 1945

Reference 96

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.043100Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation df0bd6df-2fe8-4d49-932b-7b7d01837bb0 · outbound

This paper cites Symmetry and topology in non-Hermitian physics.Physical Review X, 9(4):041015, 2019.

Unifying Physical Backpropagation Symmetry and topology in non-Hermitian physics.Physical Review X, 9(4):041015, 2019

Reference 97

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.028033Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 602965f6-e642-4273-bfe7-45bbf84eb7cd · outbound

This paper cites Non-reciprocal robotic metamaterials.Nature Communications, 10(1):4608, 2019.

Unifying Physical Backpropagation Non-reciprocal robotic metamaterials.Nature Communications, 10(1):4608, 2019

Reference 98

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:07.012305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ff8fbc27-cff2-49a5-b823-1b6077a0024f · outbound

This paper cites Observation of non-Hermitian topology and its bulk–edge correspondence in an active mechanical metamaterial.

Unifying Physical Backpropagation Observation of non-Hermitian topology and its bulk–edge correspondence in an active mechanical metamaterial

Reference 99

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:06.996375Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 50cc25b8-d88c-42a5-9623-44c932676803 · outbound

This paper cites Adjoint computation of Berry phase gradients.Journal of Sound and Vibration, 619:119357, 2025.

Unifying Physical Backpropagation Adjoint computation of Berry phase gradients.Journal of Sound and Vibration, 619:119357, 2025

Reference 100

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T00:46:06.981345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Coverage vector

Reference resolution

Outbound references

Pith citing papers