{"as_of":"2026-08-18T22:10:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4ac344dcbe722271f1a8b0bad27b8334796d4914787fd4c7867cf442ff7d744a","coverage":[{"denominator":109,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":100,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T00:46:06.117939Z","state":"measured"},{"denominator":100,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":100,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2608.11585/citation-record","integrity":"/paper/2608.11585/integrity","json":"/paper/2608.11585/citation-record.json","paper":"/paper/2608.11585"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.668781Z","title":"Toward a formal theory for computing machines made out of whatever physics offers.Nature Communications, 14(1):4911, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.668781Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:c7126b59a1607ddc67d77c457a243b8ca93deb700a24bcc62a455c08cb11d5fe","observation_id":"9e1388fa-67d4-4edc-a5f5-8c9cb1c2342f","resolution":{"observed_at":"2026-08-16T00:46:05.668781Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.674358Z","title":"Wave physics as an analog recurrent neural network.Science Advances, 5(12):eaay6946, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.674358Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:83cf6556cd156688b0649997538e22d97411cdb63c24853b3a537946870a5501","observation_id":"390890aa-ece4-4859-b520-6346e33c4789","resolution":{"observed_at":"2026-08-16T00:46:05.674358Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.679450Z","title":"Analogue computing with metamaterials.Nature Reviews Materials, 6(3):207–225, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.679450Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:aea14e09499c6da4c46d5ff9d3f39135766fc5b3304225f6788ba3e79385395b","observation_id":"76a352bc-44f6-4f8c-9703-0c9b8a940f4b","resolution":{"observed_at":"2026-08-16T00:46:05.679450Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.684462Z","title":"In- sensor passive speech classification with phononic metamaterials.Advanced Functional Materials, 34(17):2311877, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.684462Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:f4f5cba0877f94900d201b4272c8f247e87b9fbea1275230355b920d5bfee5b6","observation_id":"d42fc0af-98a4-4243-8c68-a37e65c213c2","resolution":{"observed_at":"2026-08-16T00:46:05.684462Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.689360Z","title":"Demonstration of decentralized physics-driven learning.Physical Review Applied, 18(1):014040, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.689360Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:985a16333f18a37882c1ef20febfabe213039c3ca5abfb035fcd4c0d98b1c5fb","observation_id":"53d7cb4f-ea7c-4074-991a-40d292e37af4","resolution":{"observed_at":"2026-08-16T00:46:05.689360Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.694295Z","title":"Memory devices and applications for in-memory computing.Nature Nanotechnology, 15(7):529–544, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.694295Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:792374ccc3aabf5d2ca4aa88e13b35c0a40c8b891a93e27c571033b3ff891ebc","observation_id":"ae9680dc-0321-415c-9b73-fed30cc69f37","resolution":{"observed_at":"2026-08-16T00:46:05.694295Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.699902Z","title":"Physics for neuromorphic computing.Nature Reviews Physics, 2(9):499–510, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.699902Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:1ddb524899f5d550652830a11425425094ff240a25cebf1805845671629a31ae","observation_id":"30a9bd48-367d-4d05-875c-fe0cc682f8c6","resolution":{"observed_at":"2026-08-16T00:46:05.699902Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.704410Z","title":"Photonics for artificial intelligence and neuro- morphic computing.Nature Photonics, 15(2):102–114, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.704410Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:5948d583156f4d5de4129030717c2c8b65b2c694c6a576499ce1e47f654d4858","observation_id":"f8723c8b-ad74-4e56-bf23-bd0303be1a5a","resolution":{"observed_at":"2026-08-16T00:46:05.704410Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.709025Z","title":"Scalable optical learning operator.Nature Computational Science, 1(8):542–549, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.709025Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:6a98af31e51fda9b8b0b140f90f09708870afc9fb16a6d3fd5ff7acb34c85db4","observation_id":"81ac24da-a5e1-453e-9a86-7999d1f34a84","resolution":{"observed_at":"2026-08-16T00:46:05.709025Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.713783Z","title":"Inference in artificial intelligence with deep optics and photonics.Nature, 588(7836):39–47, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.713783Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:0d3f234f630cf9f1fe991c0429e01709be54afb63dff7f0d1a1ebb247a8c69ae","observation_id":"01d23a7a-dab5-4eab-beb5-32bd07c940a2","resolution":{"observed_at":"2026-08-16T00:46:05.713783Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.718359Z","title":"All-optical machine learning using diffractive deep neural networks.Science, 361(6406):1004– 1008, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.718359Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:f4f2baffc4e9edf6b9ca81ffe7a071bff78c91f617c8df22bae12f8bf59ac8e9","observation_id":"20ed9a9b-c7e5-425c-bbb9-a26f305baa71","resolution":{"observed_at":"2026-08-16T00:46:05.718359Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.722972Z","title":"The physics of optical computing.Nature Reviews Physics, 5(12):717–734, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.722972Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:58eec2146de7420f71719c239fe16c160e842890e9409e550c3c9b0805d74129","observation_id":"39d062a5-2d47-4776-a7d5-2619d4a2efed","resolution":{"observed_at":"2026-08-16T00:46:05.722972Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.727183Z","title":"Arbitrary control over multimode wave propagation for machine learning.Nature Physics, 22:164–171, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.727183Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:3931b227fa485a55b9e9a708816ed6b8e9d41c67cd2b804e3d1009fec49c02fb","observation_id":"4f097ac2-8f69-4f96-b5f0-f6ac8c32ea45","resolution":{"observed_at":"2026-08-16T00:46:05.727183Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.731258Z","title":"Programmable on-chip nonlinear photonics.Nature, 649(8096):330–337, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.731258Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:034940e213b135835083d48cb404510e35ffba5206418fe8ecd15b4ba344d67e","observation_id":"0bbb5d47-3c1a-4687-9ecc-970768ce654e","resolution":{"observed_at":"2026-08-16T00:46:05.731258Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.735169Z","title":"Recent advances in physical reservoir computing: A review.Neural Networks, 115:100–123, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.735169Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:6e9592331746f10ebc739b32c64fa00bacb239894416c13a15b354d1e36e1820","observation_id":"60280dce-5d22-4071-a4f9-5d7087ec8e31","resolution":{"observed_at":"2026-08-16T00:46:05.735169Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.739200Z","title":"Training of physical neural networks.Nature, 645(8079):53–61, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.739200Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:2621f560e1238daa5a591dbc8f43571a24b9305d206784e75a5456c9dc0ce8d4","observation_id":"439dbfdd-4382-4765-8723-7a84c3149a8a","resolution":{"observed_at":"2026-08-16T00:46:05.739200Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.743289Z","title":"Inverse-designed low-index-contrast structures on a silicon photonics platform for vector– matrix multiplication.Nature Photonics, 18(5):501–508, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.743289Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:79024e20d4e1742aca1fed0b295d3a0f1ac4d9b0fec96219834698bd1a1536f6","observation_id":"ce7500e7-f875-4566-bf02-6b98bef6bf76","resolution":{"observed_at":"2026-08-16T00:46:05.743289Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.747818Z","title":"Deep physical neural networks trained with backpropagation.Nature, 601(7894):549–555, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.747818Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:09f268a1b96af4d424a9021677e47d40d1caac2d823e0b55ac779ddeb5b3a128","observation_id":"5763e534-48e2-44e1-8541-dc7c6930c79c","resolution":{"observed_at":"2026-08-16T00:46:05.747818Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.752125Z","title":"Optical diffusion models for image generation.Advances in Neural Information Processing Systems, 37:59150–59173, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.752125Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:6120a29dfbb66936eb547083eb48197c37fcb8ad1e41b13541210a0442c2250a","observation_id":"05f81b04-ffc5-418e-a426-4e58ff843b74","resolution":{"observed_at":"2026-08-16T00:46:05.752125Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.756170Z","title":"Trainable hardware for dynamical computing using error backpropagation through physical media","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.756170Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:a3f054741c557041d2485a8078ac2555a5ffdca7e0a1f7845da5e4c61df62bef","observation_id":"50a66671-2cca-4823-baa0-fdd1c9d4b0a6","resolution":{"observed_at":"2026-08-16T00:46:05.756170Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.760173Z","title":"In situ optical backpropagation training of diffractive optical neural networks","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.760173Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:09f31fb0e87a4aaa91da172a074f6f6d24f1370d38230f18730102f4c9b344c0","observation_id":"692a3931-d99e-4ebf-adaa-f2f0f9edb98b","resolution":{"observed_at":"2026-08-16T00:46:05.760173Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.764139Z","title":"Threading light through dynamic complex media.Nature Photonics, 19(4):434–440, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.764139Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:6690b3d1e4095a4f94def4b4d6e62c3c7e9d7b3cb83b8355461f8c48fd75a701","observation_id":"c188d944-052f-4061-b6a1-25d5f118be7a","resolution":{"observed_at":"2026-08-16T00:46:05.764139Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.768746Z","title":"Experimentally realized in situ backpropagation for deep learning in photonic neural networks.Science, 380(6643):398–404, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.768746Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:21d1788772de47195c84b7e1ad31ac40c55752e7277ec63c90a954f238c469a4","observation_id":"4e9fd759-bc2c-46bd-944e-59acdf15e33f","resolution":{"observed_at":"2026-08-16T00:46:05.768746Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.773332Z","title":"Training all-mechanical neural networks for task learning through in situ backpropagation.Nature Communications, 15(1):10528, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.773332Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:802ac5dce6f66a867a8cb71a4cef5e860b900b395eebc1bce0bb6e7dbb44be18","observation_id":"505b96cf-33c7-4f70-b02a-973eaa9cc50b","resolution":{"observed_at":"2026-08-16T00:46:05.773332Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2602.03546","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:06.812418Z","title":"How to train your resistive net- work: Generalized equilibrium propagation and analytical learning.arXiv preprint arXiv:2602.03546, 2026","venue":null,"work_id":"d93ed329-deb2-4123-b268-ce74a408145b","year":2026},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.777764Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:47c78f5c416ca58f9cadfde2534c5c9f3320ac5bb7e3115b5cd9273ecb8179a8","observation_id":"ee0f850b-7327-4018-8b4f-b0835e093bb7","resolution":{"observed_at":"2026-08-16T00:46:06.820789Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.782236Z","title":"Self-learning machines based on Hamiltonian echo backpropagation.Physical Review X, 13(3):031020, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.782236Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:79af18b019ad2b05c44e2ec88fb19139ce32fdfe18b13ac6dbdec034a7989ad6","observation_id":"a004e595-e3a2-4f9c-94c1-d8270fdbea4e","resolution":{"observed_at":"2026-08-16T00:46:05.782236Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.787186Z","title":"Routledge, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.787186Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:d63981921dbf04fa46ea491ebd10001c9a91822fad1b673a3406b54fa8b9fa42","observation_id":"50ebd2a2-6be2-49d9-813e-6f9bddc7bcd8","resolution":{"observed_at":"2026-08-16T00:46:05.787186Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.792039Z","title":"Springer Science & Business Media, 2010","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.792039Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:9ee1e46133036056210553a72ac8fe3f1a16f1193058f56637e1cfdb0ed38ac0","observation_id":"1fcc1974-647f-4d27-8fba-c9a035532395","resolution":{"observed_at":"2026-08-16T00:46:05.792039Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.796502Z","title":"In-situ physical adjoint comput- ing in multiple-scattering electromagnetic environments for wave control.Nature Communications, 16(1):11466, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.796502Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:5fc2181c132031b5dcc4ff1c99613b90fc9129c4353214cdce0ebbbfb104be93","observation_id":"1f4ff490-52f3-40ea-8231-dc111bd61ee7","resolution":{"observed_at":"2026-08-16T00:46:05.796502Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.800788Z","title":"Equilibrium propagation: Bridging the gap between energy- based models and backpropagation.Frontiers in Computational Neuroscience, 11:24, 2017","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.800788Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:54fefd66a7a3af52528b28eaf7a8b60ccf256228c6960b7a38756e08d5122086","observation_id":"57d860a0-289e-4ff4-a45d-3303ff35947a","resolution":{"observed_at":"2026-08-16T00:46:05.800788Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.05259","last_updated":"2025-06-05T17:20:39Z","snapshot_observed_at":"2026-08-18T03:32:03.352493Z","submitted_at":"2025-06-05T17:20:39Z","title":"Learning long range dependencies through time reversal symmetry breaking","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.05259","snapshot_observed_at":"2026-08-16T00:46:05.805154Z","title":"Learning long range dependencies through time reversal symmetry breaking.arXiv preprint arXiv:2506.05259, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.805154Z"},"links":{"cited_paper":"/paper/2506.05259","citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:cc636a98b66d6e1355be3eca44f775955004f5fdd6ab6d14996a3b3f41c308d7","observation_id":"78ee6357-725f-41ab-bc4c-cd2af153e0d7","resolution":{"observed_at":"2026-08-16T00:46:05.805154Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.769115Z","title":"Fully forward mode training for optical neural networks.Nature, 632(8024):280–286, 2024","venue":null,"work_id":"9afbe2d0-2a65-41a2-b6e1-9dff4517e004","year":2024},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.809993Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:c224fd303e989b328f2f547d646575033f4fa560e5ef862287ec65b69e39a7da","observation_id":"3192cc96-5d43-4e37-906b-9fa929a9037a","resolution":{"observed_at":"2026-08-16T00:46:07.774226Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.754042Z","title":"Training of photonic neural networks through in situ backpropagation and gradient measurement.Optica, 5(7):864–871, 2018","venue":null,"work_id":"0ad5d0e8-36b8-447d-9b55-004db2f768a6","year":2018},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.814375Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:b60524184d5af4ed9314a4a42cbbbf4a3ce20e5172983de92575ab6796de993a","observation_id":"a947b660-a766-42f8-93bb-5360f341d709","resolution":{"observed_at":"2026-08-16T00:46:07.759135Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.738804Z","title":"Multilayer optical learning networks.Applied Optics, 26(23):5061–5076, 1987","venue":null,"work_id":"804c34b9-948f-4e99-accd-1795acf3988d","year":1987},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.818879Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:b51f2f9adf9fa63bc52be4f557cbb8537581d7cec6fbb5774fa286a53a7d511f","observation_id":"a3619e2b-4beb-42fa-aab9-0cd7d48f2988","resolution":{"observed_at":"2026-08-16T00:46:07.743830Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.723851Z","title":"Backpropagation through nonlinear units for the all-optical training of neural networks.Photonics Research, 9(3):B71– B80, 2021","venue":null,"work_id":"e5562749-3bb7-4255-9355-ab608a66fc7c","year":2021},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.823634Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:f13b0b2c128e64343558461ef3b192408080e4a38236262363cc1a9368d593a7","observation_id":"749bbef2-626a-4dc9-98b0-e9be04d04501","resolution":{"observed_at":"2026-08-16T00:46:07.728618Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.708972Z","title":"Training neural networks with end-to-end optical backpropagation.Advanced Photonics, 7(1):016004, 2025","venue":null,"work_id":"3fb86387-33ec-4260-9fc5-bf2459bdc5cf","year":2025},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.827946Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:4e5f77993999c07389d2af4302e3895b5b410e60dda82de40172faf66030f5c8","observation_id":"0850a9da-0271-45f1-a2eb-0bb449a11797","resolution":{"observed_at":"2026-08-16T00:46:07.713689Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.693517Z","title":"Fully nonlinear neuromorphic computing with linear wave scattering.Nature Physics, 20(9):1434–1440, 2024","venue":null,"work_id":"fe04f475-2d2d-42f2-9414-a3bc371aa7a4","year":2024},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.832389Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:b345c823939f602fac4f5d926b9116a07179ed3938bb8c1e6d913badfc9455a8","observation_id":"f75b57b1-16a6-4743-b60a-354b9c18daac","resolution":{"observed_at":"2026-08-16T00:46:07.698781Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.07796","last_updated":"2025-03-10T19:25:29Z","snapshot_observed_at":"2026-08-18T16:12:01.570841Z","submitted_at":"2025-03-10T19:25:29Z","title":"Topological mechanical neural networks as classifiers through in situ backpropagation learning","version":1},"cited_work":{"arxiv_id":"2503.07796","doi":null,"metadata_source":"pith","pith_arxiv_id":"2503.07796","snapshot_observed_at":"2026-08-16T00:46:06.720325Z","title":"Topological mechanical neural networks as classifiers through in situ backpropagation learning","venue":"cond-mat.dis-nn","work_id":"585f6c30-cf71-485a-af2d-250a2417a661","year":2025},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.836754Z"},"links":{"cited_paper":"/paper/2503.07796","citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:ee27f1b34ccea5d3ae8af70cd3866e2ad3c17dc1c627d33bca40087304e4711c","observation_id":"3b303f06-fb83-4e97-a48a-02407dec855e","resolution":{"observed_at":"2026-08-16T00:46:06.725556Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.679048Z","title":"Localization transitions in non-Hermitian quantum mechan- ics.Physical Review Letters, 77(3):570–573, 1996","venue":null,"work_id":"6bb0e9cf-a5a1-40af-877c-9b08201007b6","year":1996},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.841572Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:11cf92f3ae26fa66b5af809d2fadd3c31dd0189608d23a2dd1435a3843f3c11f","observation_id":"a8bae4a4-c628-4ab9-87fe-5f017e560918","resolution":{"observed_at":"2026-08-16T00:46:07.683863Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.664162Z","title":"Supervised learning in physical networks: From machine learning to learning machines.Physical Review X, 11(2):021045, 2021","venue":null,"work_id":"d387ba10-6d8f-4758-a254-1aa6d11f2874","year":2021},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.846312Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:569cbfff2df72ca83be539b37b246e36cee7d47441f943adc7c584d6eba94e8d","observation_id":"554567a5-4fa4-4aab-8b73-aef886c7e86c","resolution":{"observed_at":"2026-08-16T00:46:07.668938Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.648670Z","title":"Learning without neurons in physical systems.Annual Review of Condensed Matter Physics, 14(1):417–441, 2023","venue":null,"work_id":"8a9f438f-5b60-49bf-89b5-d1bd79b68fe9","year":2023},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.850950Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:2a9688cd3c9302abb1731947c0932d325c9ebbf7931680acb59cd4a0cf417e84","observation_id":"ef9aaac2-3884-4719-a08b-dd31537eb2c8","resolution":{"observed_at":"2026-08-16T00:46:07.653877Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.634110Z","title":"Machine learning without a processor: Emergent learning in a nonlinear analog network","venue":null,"work_id":"91c37ec4-95ff-44d2-9bad-2d7abb8370be","year":2024},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.855456Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:127e9d8854b05c4b38ef680d456ccdd8e4c05006ca74e120be45bb5ca93f3b9a","observation_id":"1eaadaea-5699-431b-87d5-0afdac308e17","resolution":{"observed_at":"2026-08-16T00:46:07.639176Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.618505Z","title":"Training self-learning circuits for power-efficient solutions.APL Machine Learning, 2(1):016114, 2024","venue":null,"work_id":"25ddb42f-599c-48dc-95e6-7078765a9411","year":2024},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.860305Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:0ff16a382036a96b7bba4ca801f9d97d1c5359dc4a1e28fb800ab3d50a52235c","observation_id":"f12580a3-b3fc-4531-aa40-838b9dac20a2","resolution":{"observed_at":"2026-08-16T00:46:07.624068Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2606.15443","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:06.693346Z","title":"Coercivity and local convergence of physical learning in linear circuits.arXiv preprint arXiv:2606.15443, 2026","venue":null,"work_id":"4b540601-e10c-4e8b-b39b-942568269180","year":2026},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.864538Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:ce64135a1a3813fe3a6eef147f75af2b2319917e08576e28683a68ec56146777","observation_id":"2b987779-abb5-48d4-86b8-e5ea50fd7cd7","resolution":{"observed_at":"2026-08-16T00:46:06.700817Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.603017Z","title":"Multimodal deep learning using on-chip diffractive optics with in situ training capability.Nature Communications, 15(1):6189, 2024","venue":null,"work_id":"9f14f184-e8af-4ac4-8771-8db32291f532","year":2024},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.868953Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:45aec3dfb06020e7327df2bffa620738194a62b698402e5e16be81f45175b503","observation_id":"238edb60-a8c8-484c-9346-861d962f5aee","resolution":{"observed_at":"2026-08-16T00:46:07.608323Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.588138Z","title":"Multimodal oscillator networks learn to solve a classification problem.npj Metamaterials, 2(1):3, 2026","venue":null,"work_id":"70daaed9-e6c8-485d-ac20-e22a3c451857","year":2026},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.873525Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:2d0de6004fbf94a2f843ea43c94d206ca2a05c986e095f5f73048c42345fce3c","observation_id":"5cc3973c-b700-4343-b5d1-29954cf711b6","resolution":{"observed_at":"2026-08-16T00:46:07.592977Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.573360Z","title":"Forward–forward training of an optical neural network","venue":null,"work_id":"463f4823-d130-4bfb-a343-0bcd513a9537","year":2023},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.878428Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:7647b25271c19bcb457a744c40556b8ca5cdde5393c1886bebc72aac0edcb406","observation_id":"88177e8b-b945-4c39-ae01-df9d4deaa277","resolution":{"observed_at":"2026-08-16T00:46:07.578223Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.558638Z","title":"Backpropagation-free training of deep physical neural networks.Science, 382(6676):1297–1303, 2023","venue":null,"work_id":"bafd2bcb-bcad-403e-b006-012ebe94e61a","year":2023},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.882587Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:7acffbe500ef9c8a7be7ffe0983d457164679ccc35956a725fdef78f70f5b984","observation_id":"c301d3ae-72b7-4e7d-9d13-6c2d1875b071","resolution":{"observed_at":"2026-08-16T00:46:07.563475Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2602.09569","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:06.598292Z","title":"Training deep physical neural networks with local physical information bottleneck.arXiv preprint arXiv:2602.09569, 2026","venue":null,"work_id":"e536256f-9d4d-46de-ac4f-563d7ada1371","year":2026},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.887082Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:12639bce2f62641f64e0bdf1da854e7d3edf191ce5ad4fbac156185b4008ade5","observation_id":"32326224-c03d-430b-a550-6a844bb390cb","resolution":{"observed_at":"2026-08-16T00:46:06.606189Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.544194Z","title":"Using memristors for robust local learning of hardware restricted Boltzmann machines.Scientific Reports, 9(1):1851, 2019","venue":null,"work_id":"085b0f5e-043c-417f-909d-5fc052989d89","year":2019},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.891088Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:9acdb677e4cdefbf7c57e41b5b44c505aed820ebe1bea836cd2c3dcde625988f","observation_id":"8328d740-a91b-4fa4-8379-a6292a4e101a","resolution":{"observed_at":"2026-08-16T00:46:07.549099Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.529552Z","title":null,"venue":null,"work_id":"d56b17c1-90f4-4adc-ae68-6ada2ec42737","year":2026},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.895409Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:fed4ed0837d2d054a302207bf2db05231c96de39490ef90e194ac398a2f4bdff","observation_id":"0d0e9a17-65b4-45e8-abc6-a1e631ecf16e","resolution":{"observed_at":"2026-08-16T00:46:07.534127Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.19136","last_updated":"2026-07-03T15:09:41Z","snapshot_observed_at":"2026-08-17T08:23:51.722795Z","submitted_at":"2025-06-23T21:11:40Z","title":"Local Learning Rules for Out-of-Equilibrium Physical Generative Models","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.19136","snapshot_observed_at":"2026-08-16T00:46:05.899468Z","title":"Local learning rules for out-of-equilibrium physical generative models.arXiv preprint arXiv:2506.19136, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.899468Z"},"links":{"cited_paper":"/paper/2506.19136","citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:6893f072bfe256e4e63621dfa9f0484d03609b10508a1c931146860fb7a39963","observation_id":"bde93477-ce26-4af7-85a3-b7bcfff8c27f","resolution":{"observed_at":"2026-08-16T00:46:05.899468Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2504.20401","last_updated":"2025-08-01T15:35:41Z","snapshot_observed_at":"2026-08-18T11:56:55.645663Z","submitted_at":"2025-04-29T03:55:05Z","title":"Nonlinear Computation with Linear Optics via Source-Position Encoding","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.20401","snapshot_observed_at":"2026-08-16T00:46:05.904066Z","title":"Nonlinear computation with linear optics via source-position encoding.arXiv preprint arXiv:2504.20401, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.904066Z"},"links":{"cited_paper":"/paper/2504.20401","citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:710bb48a6e1f215dec1202d43ecbfaced240e356e124798ab946e402c128123b","observation_id":"94665e02-f2c7-4478-841f-2cdeaa291c87","resolution":{"observed_at":"2026-08-16T00:46:05.904066Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.514300Z","title":"Nonlinear optical encoding enabled by recurrent linear scattering.Nature Photonics, 18(10):1067–1075, 2024","venue":null,"work_id":"6a01b86c-c2da-4cff-a345-c9e18ab422ac","year":2024},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.908418Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:2d9c1db9b7ec6f783f15c7e89ac65ed1cc1ce6ce8ae09d835bfa8fb8a40d6389","observation_id":"8995debe-bb78-4997-b40d-a4910fc1e758","resolution":{"observed_at":"2026-08-16T00:46:07.519296Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.498929Z","title":"Nonlinear processing with linear optics.Nature Photonics, 18(10):1076–1082, 2024","venue":null,"work_id":"8ad6c24c-b5d0-45e6-80cf-ae68cc7d8380","year":2024},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.912296Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:fdc198b68315415777e32ba065ae3ee5d4b9c79ae7a616d2b91d5b4a26e12afe","observation_id":"195a060a-4933-4e83-92a9-9d31b527349d","resolution":{"observed_at":"2026-08-16T00:46:07.503984Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.483736Z","title":"Giles and Niles A","venue":null,"work_id":"70bbcc43-b95d-45ff-9508-9e0cecc674c9","year":2000},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.916872Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:920a4da4ea7a77e2b106e57984def65412a19f8c649b492af42d3049afca0836","observation_id":"edeab902-72ae-42b2-abb7-bcd209690470","resolution":{"observed_at":"2026-08-16T00:46:07.489024Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.468700Z","title":null,"venue":null,"work_id":"36cb83ab-23c1-40b8-b18e-40c7239a52b4","year":2006},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.921441Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:c1840d6da52fe784ec6cc5900c5ed5a830d1b48ae90787571be0919f162c9e17","observation_id":"821fb53f-9b43-4696-898e-774607be9530","resolution":{"observed_at":"2026-08-16T00:46:07.473800Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.453470Z","title":"Dutton, and Shanhui Fan","venue":null,"work_id":"ce81baa5-5551-436a-8694-90ace3ba609a","year":2004},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.926116Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:ba262e88283534c0178fb29eba45fa1b664fad2def73b2a65f642a2c54f966b5","observation_id":"3ebc2fd8-2071-4698-a0db-85e575f6fedf","resolution":{"observed_at":"2026-08-16T00:46:07.458801Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.439670Z","title":null,"venue":null,"work_id":"813adf64-cbcf-43e6-96cf-de314ef18804","year":2007},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.930783Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:63ae4e43c697218c6a04bc6caa6eff79049647e165e4e1a400ca21bfc394b186","observation_id":"af87eca3-4d14-414d-98eb-81634cde922b","resolution":{"observed_at":"2026-08-16T00:46:07.444135Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.425887Z","title":"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","venue":null,"work_id":"2fed841b-68e3-4185-9c5e-35c94aa719e8","year":2019},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.935322Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:4ce1addd1258dc75fb0d71bff0319e422e2e27157ad4d6fd12105334d720f73d","observation_id":"79b9c01d-f373-48c9-acc1-08c5f2d4db9c","resolution":{"observed_at":"2026-08-16T00:46:07.430331Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.410748Z","title":null,"venue":null,"work_id":"e3c41f13-419a-4d73-a08c-829934ec4449","year":1983},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.939731Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:c1fb9638973ce47920474d491f1fc95731e8eea662d8dc51decb71fa8566b23f","observation_id":"16c8f897-3230-4c95-89fc-14c4d23fbd51","resolution":{"observed_at":"2026-08-16T00:46:07.415728Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.395148Z","title":"Complex-valued matrix differentiation: Techniques and key results.IEEE Transactions on Signal Processing, 55(6):2740–2746, 2007","venue":null,"work_id":"6cff6b16-622e-4ff3-a10b-8d3222fa35fb","year":2007},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.944453Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:1839c806fda7ec732dd66a08d325021c7f9a7adeb1556eca475e1218e6b1f537","observation_id":"4bd3ec84-a8fc-4737-82ab-ce013e93e14f","resolution":{"observed_at":"2026-08-16T00:46:07.400856Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.380888Z","title":"Unconstrained optimization of real functions in complex variables.SIAM Journal on Optimization, 22(3):879–898, 2012","venue":null,"work_id":"4e9702e8-5601-41b2-9def-7f7ce55fd7e3","year":2012},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.949079Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:490aec8aadc0570ae8919a1bae87ce1ef6da0880dd6d9f274cf1b14196e14fd3","observation_id":"7f1c2edd-c7d8-448d-b799-f3c2ef3c7579","resolution":{"observed_at":"2026-08-16T00:46:07.385593Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.366467Z","title":"Springer Netherlands, 2009","venue":null,"work_id":"0050ce0f-4987-46e2-970b-e83218522176","year":2009},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.953746Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:034108dd8cb86d8d09a64ee36c1a14575bb6fd5e7d1499c43d5b89907f8bc2ee","observation_id":"8435d6bb-f50e-48e0-829b-ff865826fdb2","resolution":{"observed_at":"2026-08-16T00:46:07.371041Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2602.19122","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:06.486938Z","title":"Training overdamped dynamics.arXiv preprint arXiv:2602.19122, 2026","venue":null,"work_id":"c2755aa3-e117-49dc-ab4f-c44b9f79a168","year":2026},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.958437Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:aed84d3e6a753136dbd9cbf59aa55dec787dc6c4acbe8333e14d3e5bed7d1b49","observation_id":"8c9b545d-c999-4b8a-9365-5b69453dbc43","resolution":{"observed_at":"2026-08-16T00:46:06.496495Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.20402","last_updated":"2025-08-08T04:52:40Z","snapshot_observed_at":"2026-08-14T18:27:46.991911Z","submitted_at":"2025-06-25T13:16:52Z","title":"Equilibrium Propagation for Dissipative Dynamics","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.20402","snapshot_observed_at":"2026-08-16T00:46:05.963030Z","title":"Equilibrium propagation for dissipative dynamics.arXiv preprint arXiv:2506.20402, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.963030Z"},"links":{"cited_paper":"/paper/2506.20402","citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:8a687aa1e60a835ddb16aad242ad113472cc55dd9c76f0c5ee7faa1999a336e0","observation_id":"447a349e-3302-4b4c-a838-e3377c9a5be1","resolution":{"observed_at":"2026-08-16T00:46:05.963030Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.352428Z","title":"Holomorphic equilibrium propagation computes exact gradi- ents through finite size oscillations.Advances in Neural Information Processing Systems, 35:12950– 12963, 2022","venue":null,"work_id":"ad320fa9-e325-4b7e-890b-b4d31a35b4e7","year":2022},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.968550Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:4dc7559c15c8f1fd4e03cb156c8c20d45b99a0637cee80e7b5fde894df01b6c9","observation_id":"ca56bbf5-6df2-4f4e-9131-db17485e4117","resolution":{"observed_at":"2026-08-16T00:46:07.357149Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2508.11750","last_updated":"2025-08-15T18:00:05Z","snapshot_observed_at":"2026-08-14T07:10:05.934970Z","submitted_at":"2025-08-15T18:00:05Z","title":"Training nonlinear optical neural networks with Scattering Backpropagation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.11750","snapshot_observed_at":"2026-08-16T00:46:05.973046Z","title":"Training nonlinear optical neural networks with scattering backpropagation.arXiv preprint arXiv:2508.11750, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.973046Z"},"links":{"cited_paper":"/paper/2508.11750","citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:30067e861afbc2b0928d86cdb79ce3482873bfda2b43d29328bbacff101a992c","observation_id":"f81da60f-1d69-4808-ac96-16ea337ff137","resolution":{"observed_at":"2026-08-16T00:46:05.973046Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:05.977788Z","title":"Near-equilibrium propagation training in nonlinear wave systems.arXiv preprint arXiv:2510.16084, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.977788Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:b0d565a1163184862f8d683e164fc220ed0b04bfc146e733918d3226a193ccdc","observation_id":"56ab3b59-ff39-4601-9649-f93a9dfc20b0","resolution":{"observed_at":"2026-08-16T00:46:05.977788Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1808.04873","last_updated":"2018-08-14T19:41:12Z","snapshot_observed_at":"2026-08-17T10:31:24.297521Z","submitted_at":"2018-08-14T19:41:12Z","title":"Generalization of Equilibrium Propagation to Vector Field Dynamics","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1808.04873","snapshot_observed_at":"2026-08-16T00:46:05.982267Z","title":"Gen- eralization of equilibrium propagation to vector field dynamics.arXiv preprint arXiv:1808.04873, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.982267Z"},"links":{"cited_paper":"/paper/1808.04873","citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:d1895da673c857260acedebc6edab75f05e5c5952f23c53e9e3d7c5c013dbb68","observation_id":"3a5ff6f6-3e8e-4944-9273-6da0ab2db595","resolution":{"observed_at":"2026-08-16T00:46:05.982267Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.336545Z","title":"Improving equilibrium propagation without weight symmetry through Jacobian homeostasis","venue":null,"work_id":"3caa2da1-9370-4efc-9b92-13d66d52f5d3","year":2024},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.987035Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:793c49b54b09f8fab614446d5a8f7862098cc088cd4399175ee7a16e464209bd","observation_id":"13440c67-405e-4b43-af1f-29db97d3d10b","resolution":{"observed_at":"2026-08-16T00:46:07.341615Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2602.03670","last_updated":"2026-06-01T15:49:57Z","snapshot_observed_at":"2026-08-17T07:07:24.052976Z","submitted_at":"2026-02-03T15:52:23Z","title":"Equilibrium Propagation for Non-Conservative Systems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2602.03670","snapshot_observed_at":"2026-08-16T00:46:05.991596Z","title":"Equilibrium propagation for non-conservative systems.arXiv preprint arXiv:2602.03670, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.991596Z"},"links":{"cited_paper":"/paper/2602.03670","citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:82a28a5e1444baa4bccd26a1b321800eba40da95a7deec1dd04b83ca87d23668","observation_id":"a6514f2c-e84e-4b45-8d02-cbab3d0a0de5","resolution":{"observed_at":"2026-08-16T00:46:05.991596Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2205.15021","last_updated":"2022-05-30T12:02:53Z","snapshot_observed_at":"2026-08-16T16:56:42.081415Z","submitted_at":"2022-05-30T12:02:53Z","title":"Agnostic Physics-Driven Deep Learning","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2205.15021","snapshot_observed_at":"2026-08-16T00:46:05.996422Z","title":"Agnostic physics-driven deep learning.arXiv preprint arXiv:2205.15021, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:05.996422Z"},"links":{"cited_paper":"/paper/2205.15021","citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:dca4eb78d380f0ffa6642742a9a2ab5778962385e6724a83ed1878dcf4b6b837","observation_id":"0702e99d-78ff-4a76-8c31-7735c30d45dd","resolution":{"observed_at":"2026-08-16T00:46:05.996422Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.321779Z","title":"Reciprocal relations in irreversible processes","venue":null,"work_id":"bb01a82e-06b9-451d-96fc-a6d5b656ccf0","year":1931},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.001356Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:f21c804a28cf4d8d8481a98c9de83361e1fd2f231242875ced4572ec932af9cd","observation_id":"233e277a-b10e-4463-818b-7472e4faeb7f","resolution":{"observed_at":"2026-08-16T00:46:07.326899Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.306701Z","title":"Fluctuations and irreversible processes.Physical Review, 91(6):1505–1512, 1953","venue":null,"work_id":"fbec5499-6051-4bc8-af36-cf1dfcc02668","year":1953},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.006772Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:0de2aa0acedf79c9f8941b5b0f46a91c4ec07bea0367c93c0a76348188a2283c","observation_id":"dd5878f1-c8f3-4399-8e08-0bed7b2923d3","resolution":{"observed_at":"2026-08-16T00:46:07.311481Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.292590Z","title":"Topological mechanics of gyroscopic metamaterials.Proceedings of the National Academy of Sciences, 112(47):14495–14500, 2015","venue":null,"work_id":"cfe3ea1d-cb09-4c8c-a452-6e526094a543","year":2015},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.011635Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:73bc1543cf3688eecc0ea5935a488e40b75dcbb3963e6b62d3d93f33b4c411d0","observation_id":"339ca949-da9e-4b12-8cfa-8eb07698b381","resolution":{"observed_at":"2026-08-16T00:46:07.296883Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.278838Z","title":"Observation of PT phase transition in a simple mechanical system.American Journal of Physics, 81(3):173–179, 2013","venue":null,"work_id":"adac56fc-9e6c-4177-8100-4d5d8277904a","year":2013},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.016356Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:bee4127b4ecc2b6665abf207e08375fee81436eb9164f4c2aa49b51c1322c779","observation_id":"cbaa2982-725e-44e8-9964-2bef625484a1","resolution":{"observed_at":"2026-08-16T00:46:07.283561Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.263208Z","title":"Time reversal of ultrasonic fields","venue":null,"work_id":"63e45012-13c2-4574-8698-10311f984e41","year":1992},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.020788Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:e8dec9e26833011282e9b945f402c7d59d6100fa520ba5f40144eaad06184e06","observation_id":"b17f11b2-c0ce-47d8-be06-fed64e592b3a","resolution":{"observed_at":"2026-08-16T00:46:07.267883Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.06248","last_updated":"2026-04-13T10:47:48Z","snapshot_observed_at":"2026-08-15T15:14:57.250998Z","submitted_at":"2025-06-06T17:17:40Z","title":"Lagrangian-based Equilibrium Propagation: generalisation to arbitrary boundary conditions & equivalence with Hamiltonian Echo Learning","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.06248","snapshot_observed_at":"2026-08-16T00:46:06.025279Z","title":"Lagrangian-based equilib- rium propagation: generalisation to arbitrary boundary conditions & equivalence with Hamiltonian echo learning.arXiv preprint arXiv:2506.06248, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.025279Z"},"links":{"cited_paper":"/paper/2506.06248","citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:3c4725fa8e3d345adc00595c25f9d5d123e747303eb115805fdb5ecd89e9c091","observation_id":"e49d490e-1376-42df-855c-4bbeb5b6cc30","resolution":{"observed_at":"2026-08-16T00:46:06.025279Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.248975Z","title":null,"venue":null,"work_id":"5159044e-39f3-46a3-b9be-1de30c0d996d","year":1965},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.030076Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:20f3fe43daf2c8fb8b8f5d0c88933cd701ecedd965027c5a0cf1ba211e500fed","observation_id":"4ed3ec33-de91-475f-b1a9-6743b52de51f","resolution":{"observed_at":"2026-08-16T00:46:07.253047Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.233993Z","title":"Scaling equilibrium propagation to deep convnets by drastically reducing its gradient estimator bias.Frontiers in Neuroscience, 15:633674, 2021","venue":null,"work_id":"0204b6ce-f719-4a27-a334-890f38845abf","year":2021},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":81,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.034069Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:5af49db992ca5c94943db563dc1abc9bd94b34f07105d939b3d411f15a8b8b26","observation_id":"150c1501-62ce-4abb-aac0-e92d6a32a0f8","resolution":{"observed_at":"2026-08-16T00:46:07.238766Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.218916Z","title":"Equilibrium propagation for learning in Lagrangian dynamical systems.Physical Review E, 112(3):035304, 2025","venue":null,"work_id":"8d3d5fe1-5499-4a63-8a25-4f7ae27aed8f","year":2025},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.038029Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:f86bab261ab4097ad45f1ebb00ce4cd48252d4a86f283b21a131828f38706819","observation_id":"d28915eb-8e5f-4934-b1e0-12381ae629f7","resolution":{"observed_at":"2026-08-16T00:46:07.224163Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.204133Z","title":"Springer Science & Business Media, 1991","venue":null,"work_id":"99778f81-696b-4520-98ed-8fbeb224369e","year":1991},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":83,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.042357Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:cee4ab5027324aa52a481c872dce09768506cd76e9c8a23a43894a4c28f02c4a","observation_id":"8f707fd7-c1bb-479d-af54-7e64e05c0883","resolution":{"observed_at":"2026-08-16T00:46:07.208800Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2312.04858","last_updated":"2023-12-08T06:26:04Z","snapshot_observed_at":"2026-08-18T20:44:03.659316Z","submitted_at":"2023-12-08T06:26:04Z","title":"A short tutorial on Wirtinger Calculus with applications in quantum information","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.04858","snapshot_observed_at":"2026-08-16T00:46:06.046428Z","title":"A short tutorial on Wirtinger calculus with applications in quantum information.arXiv preprint arXiv:2312.04858, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":84,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.046428Z"},"links":{"cited_paper":"/paper/2312.04858","citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:65a5fe640eabc28fcf375025eabf718ddfdecda95a8c9c0e833f1fa6b2f98931","observation_id":"93d14549-4456-4522-9b98-94cb7800308b","resolution":{"observed_at":"2026-08-16T00:46:06.046428Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.188999Z","title":"Integrated photonic neural network with on-chip backpropagation training.Nature, 651(8107):927–932, 2026","venue":null,"work_id":"6980ca31-f54b-4f36-bee9-10ef4bb92e1b","year":2026},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":85,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.050664Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:92bce34e5000e548e72000b0449943b206d5705558d361f1f5115ec7030993a5","observation_id":"ca8384b6-1708-4544-b1fa-8f2c26c38205","resolution":{"observed_at":"2026-08-16T00:46:07.194144Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2006.01981","last_updated":"2020-06-09T22:26:05Z","snapshot_observed_at":"2026-08-10T18:05:12.198187Z","submitted_at":"2020-06-02T23:38:35Z","title":"Training End-to-End Analog Neural Networks with Equilibrium Propagation","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2006.01981","snapshot_observed_at":"2026-08-16T00:46:06.054589Z","title":"Training end-to-end analog neural networks with equilibrium propagation.arXiv preprint arXiv:2006.01981, 2020","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":86,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.054589Z"},"links":{"cited_paper":"/paper/2006.01981","citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:496a0d489b0cbc41858bba6f7dcb298dfb405ef90cf1c2004b1b8e186fe95629","observation_id":"90ae2b03-5a70-47c2-a8d8-d2feffeb4f42","resolution":{"observed_at":"2026-08-16T00:46:06.054589Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.174182Z","title":"Training an Ising machine with equilibrium propagation.Nature Communications, 15(1):3671, 2024","venue":null,"work_id":"8d2b3a89-f058-4f20-97a7-1ea8c104d439","year":2024},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":87,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.058717Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:be9c75d4a2d2e4a2899bb0020ae4f92aecd53db48dfe47e5661abcde879e35b4","observation_id":"76a1151c-2b73-4eb4-aea3-8081200b7ddb","resolution":{"observed_at":"2026-08-16T00:46:07.178878Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.158969Z","title":"Equivalence of equilibrium propagation and recurrent back- propagation.Neural Computation, 31(2):312–329, 2019","venue":null,"work_id":"4c9058d0-8d47-41d1-839a-afcef3dec194","year":2019},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":88,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.062633Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:e486fddcdd7532d2e8f51da614971ecaf7d587ce8b64a71e7e9d0a37d03547e4","observation_id":"3fc0bcfd-8e07-4fc0-839e-6679f0e9065b","resolution":{"observed_at":"2026-08-16T00:46:07.164079Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.144071Z","title":"Updates of equilibrium prop match gradients of backprop through time in an RNN with static input.Advances in Neural Information Processing Systems, 32, 2019","venue":null,"work_id":"efaf712e-8058-46a4-9b25-1c45e2273786","year":2019},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":89,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.067153Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:9b2479e27be9e1808480b2b179954d117c9df097bb3612c89ca9124450c7e7b2","observation_id":"ce00a984-62df-4183-a3f5-9ac44af1ae4d","resolution":{"observed_at":"2026-08-16T00:46:07.148938Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.128827Z","title":"Frequency propagation: Multimechanism learning in nonlinear physical networks.Neural Computation, 36(4):596–620, 2024","venue":null,"work_id":"50d5fcd2-dd7f-49a9-9674-7307f2d0025c","year":2024},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":90,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.071873Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:b0a6f3dd92951a97ce1f14ab78c3491d8488f015acc5ae02c21aa9a21f8729f4","observation_id":"5e98f556-17f6-4f7c-96b3-83801e1cb2b6","resolution":{"observed_at":"2026-08-16T00:46:07.133741Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.114479Z","title":"Training coupled phase oscillators as a neuromorphic platform using equilibrium propagation.Neuromorphic Computing and Engineering, 4(3):034014, 2024","venue":null,"work_id":"29fb7549-616e-410e-8e64-836b9ef0c89f","year":2024},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":91,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.076518Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:ee80b2459864643b60535aced20994e094b172289d7233a5d3ffd4d235d5bef6","observation_id":"a8ab75d8-791f-4c7d-a45f-7b18a7075f7d","resolution":{"observed_at":"2026-08-16T00:46:07.119150Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.099921Z","title":"Generalized bulk–boundary correspondence in non-Hermitian topolectrical circuits.Nature Physics, 16(7):747– 750, 2020","venue":null,"work_id":"40054fe4-83db-498a-ac7e-2ed8faa7ed74","year":2020},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":92,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.081204Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:5c0b801390d5c7b883cd85f551b59702fcbb0db74848c3a5c16acc0defc6b1f6","observation_id":"157d1eeb-ac3b-405a-84ae-f380bffddc68","resolution":{"observed_at":"2026-08-16T00:46:07.104681Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.085154Z","title":"Topological funneling of light.Science, 368(6488):311–314, 2020","venue":null,"work_id":"e6637aa5-3a21-4884-a162-333479dae184","year":2020},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":93,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.085506Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:91dbe85ebc421d7943e6d6f71bbbbffb304a579a241a4989173f6e2f2e2d309f","observation_id":"e3c54856-4d7d-4d6a-893f-b7e88ed60b30","resolution":{"observed_at":"2026-08-16T00:46:07.089730Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.069097Z","title":"Sound isolation and giant linear nonreciprocity in a compact acoustic circulator.Science, 343(6170):516–519, 2014","venue":null,"work_id":"09499bd2-3919-4755-aeb8-1bc4ea1fb2cd","year":2014},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":94,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.090155Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:27d16a3baeb19587159133e62aee92c989dbf395eb8cf395d64de41f680dddcd","observation_id":"5dc0e373-235d-4765-a390-6f51c8993368","resolution":{"observed_at":"2026-08-16T00:46:07.074399Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.053388Z","title":"Odd elasticity.Nature Physics, 16(4):475–480, 2020","venue":null,"work_id":"23226814-7c05-40d1-81af-8a0325b29035","year":2020},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":95,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.094767Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:6b7f38a8d1980d21547263c3d6009047ed80ec7242d114a1d9465cde339e93b3","observation_id":"b2e53d59-41de-4251-a6bd-2f17d5371455","resolution":{"observed_at":"2026-08-16T00:46:07.058277Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.038257Z","title":"On Onsager’s principle of microscopic reversibility.Reviews of Modern Physics, 17(2-3):343–350, 1945","venue":null,"work_id":"ca0ba044-6c67-4ad1-972e-a487502650ad","year":1945},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":96,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.099445Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:5c2473767c67fced554687aafbc5733d3d09c3279ba31c26c6d7136daffa52f3","observation_id":"b0bafa6d-7c27-4745-abab-54af78674ba8","resolution":{"observed_at":"2026-08-16T00:46:07.043100Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.022909Z","title":"Symmetry and topology in non-Hermitian physics.Physical Review X, 9(4):041015, 2019","venue":null,"work_id":"459725e5-3c8f-4a0a-9f0a-8a7850b33c97","year":2019},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":97,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.104192Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:3978101c99c64bf7ec0d4356c2d4f398b93c209005979a7296af82f7b8774b21","observation_id":"df0bd6df-2fe8-4d49-932b-7b7d01837bb0","resolution":{"observed_at":"2026-08-16T00:46:07.028033Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:07.007179Z","title":"Non-reciprocal robotic metamaterials.Nature Communications, 10(1):4608, 2019","venue":null,"work_id":"f92a7804-bfe7-4d21-a602-26567f3baaa8","year":2019},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":98,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.108772Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:f3be1248ef62922b14c9930c6fa5f49ffe20d393535e1e5342209738fa545cd3","observation_id":"602965f6-e642-4273-bfe7-45bbf84eb7cd","resolution":{"observed_at":"2026-08-16T00:46:07.012305Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:06.991386Z","title":"Observation of non-Hermitian topology and its bulk–edge correspondence in an active mechanical metamaterial","venue":null,"work_id":"61114c6e-e842-45a2-b43e-8d93f534492a","year":2020},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":99,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.113279Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:ae325238b4144aefc6251025bcd15dd5d17a61c9d8584c0f07820195c5b182fb","observation_id":"ff8fbc27-cff2-49a5-b823-1b6077a0024f","resolution":{"observed_at":"2026-08-16T00:46:06.996375Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T00:46:06.975783Z","title":"Adjoint computation of Berry phase gradients.Journal of Sound and Vibration, 619:119357, 2025","venue":null,"work_id":"faa33609-586b-405f-baa9-94347b2140aa","year":2025},"citing_paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation","version":1},"reference_index":100,"source":"pdf_text","source_observed_at":"2026-08-16T00:46:06.117939Z"},"links":{"citing_paper":"/paper/2608.11585"},"observation_digest":"sha256:c0d8e8b6cd29927e62c7361815bc67e50ac3cc44dedcca1d2a749c8d3a6e5cb7","observation_id":"50cc25b8-d88c-42a5-9623-44c932676803","resolution":{"observed_at":"2026-08-16T00:46:06.981345Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.11585","last_updated":"2026-08-12T02:53:39Z","latest_version":1,"primary_category":"cond-mat.dis-nn","snapshot_observed_at":"2026-08-18T17:54:47.057808Z","submitted_at":"2026-08-12T02:53:39Z","title":"Unifying Physical Backpropagation"},"reference_resolution":{"displayed":100,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":46,"verified_exact":5,"verified_fuzzy":49},"total_outbound_references":109},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 100 of 109 outbound references and 0 inbound Pith citation observations for arXiv:2608.11585."}