{"as_of":"2026-08-15T01:10:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1934742d5247dd0a49a96a599f2e541af979c0c2f4aea06bc5d062f8f98ad62b","coverage":[{"denominator":29,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":29,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-29T18:45:27.282354Z","state":"measured"},{"denominator":30,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":30,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T05:07:54.611065Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2605.27673","snapshot_observed_at":"2026-08-01T05:07:54.611065Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimiza- tion,","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.22351","last_updated":"2026-07-24T14:31:54Z","snapshot_observed_at":"2026-08-05T14:57:03.214980Z","submitted_at":"2026-07-24T14:31:54Z","title":"IQ-JEPA: A Joint-Embedding Predictive Architecture with a Hermitian Vision Transformer for Sound Speed and Attenuation Estimation from Ultrasound IQ Data","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-01T05:07:54.611065Z"},"links":{"cited_paper":"/paper/2605.27673","citing_paper":"/paper/2607.22351"},"observation_digest":"sha256:875de9619da8056a8fc1f0f64f94c2b2b7c6395f80a31ad5c503d911bb06f01f","observation_id":"e9103f76-a576-4cb9-a69e-638b17b915fc","resolution":{"observed_at":"2026-08-01T05:07:54.611065Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2605.27673/citation-record","integrity":"/paper/2605.27673/integrity","json":"/paper/2605.27673/citation-record.json","paper":"/paper/2605.27673"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-29T18:45:27.282354Z","title":"Charles Clancy","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:7c9c2fc88def893b4436d3ba2e73267e8e63c82acb161eefde1caf7f96e196b4","observation_id":"67c3f2cd-86e9-4974-8fda-2e2b1c59c6fa","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","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":"2026-06-29T18:45:27.282354Z","title":"Understanding and improving convolutional neural networks via concatenated rectified linear units","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:9562fc543ac3978b4e98ab17d5796625db2b251ae1eede3864864b864e58813e","observation_id":"68193f87-5318-4f3c-8c29-ff7aa8cbfa84","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1711.05101","last_updated":"2019-01-04T21:01:49Z","snapshot_observed_at":"2026-08-14T20:13:52.872565Z","submitted_at":"2017-11-14T14:24:06Z","title":"Decoupled Weight Decay Regularization","version":3},"cited_work":{"arxiv_id":"1711.05101","doi":"10.1137/1.9781611972825.47","metadata_source":"pith","pith_arxiv_id":"1711.05101","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Decoupled Weight Decay Regularization","venue":"cs.LG","work_id":"07ef7360-d385-4033-83f7-8384a6325204","year":2017},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"cited_paper":"/paper/1711.05101","citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:5359872ee39d6e89a904e8e3702fd0f71d66c750a831b20d3059a6e0ebfe9803","observation_id":"b7221820-7401-46a5-befd-5a1d3d52bad8","resolution":{"observed_at":"2026-06-29T18:53:51.700128Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-06-29T18:45:27.282354Z","title":"Springer, 2006","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:a2df8fd241d21635809d87e4e4ba33745281784d1f1b3555f8dff7b3d09ce78f","observation_id":"ea1e2a57-c9cb-4563-a090-b4abac0fd8d4","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1705.09792","last_updated":"2018-02-25T23:42:06Z","snapshot_observed_at":"2026-08-14T20:57:50.619214Z","submitted_at":"2017-05-27T09:04:55Z","title":"Deep Complex Networks","version":4},"cited_work":{"arxiv_id":"1705.09792","doi":null,"metadata_source":"pith","pith_arxiv_id":"1705.09792","snapshot_observed_at":"2026-06-29T18:53:51.696028Z","title":"Deep Complex Networks","venue":"cs.NE","work_id":"a7ca838b-5d6d-469a-9fb4-2b32c3374a0b","year":2017},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"cited_paper":"/paper/1705.09792","citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:1784e1157958171fa8b62831479da46304edb299d3608c9026e396aa968d4894","observation_id":"07f56d95-cbd3-42d6-948a-cb0c83662521","resolution":{"observed_at":"2026-06-29T18:53:51.697136Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-06-29T18:45:27.282354Z","title":"Better than real: Complex-valued neural nets for mri fingerprinting","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:f1952edd7e0c87dd7dad02a61b2f1395de393da3b2dac4f1d5064cbee1157ce4","observation_id":"1c5e0049-8eab-426d-b156-781a64bde254","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","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":"2026-06-29T18:45:27.282354Z","title":"Analysis of deep complex-valued convolutionalneuralnetworksformrireconstructionandphase-focusedapplications.Magneticresonance in medicine, 86(2):1093–1109, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:daf0222cb4badda135f467f565bd7a4ce22509bb275f18ed4c2f5211ff1bc585","observation_id":"ed0de6b1-9ea3-4ad4-b692-5034635441cd","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","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":"2026-06-29T18:45:27.282354Z","title":"Unitary evolution recurrent neural networks","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:38482c37a8604d639eb813bf859597c566d515a403b7234c3ec4c631a69e209d","observation_id":"4e7289d6-9cdf-4401-92c9-3e937a767b5e","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","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":"2026-06-29T18:45:27.282354Z","title":"Full-capacity unitary recurrent neural networks.Advances in neural information processing systems, 29, 2016","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:d3dfab4663c3317e7f2e2477990a2fc61b1341ab941c3977bb8fd7d5db1ae2fc","observation_id":"8fb2c910-e513-47fd-9b42-7e88c2136dbc","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","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":"2026-06-29T18:45:27.282354Z","title":"Group equivariant convolutional networks","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:17996dce2a86e4296af2f822931e7d76784380ca2c18a809288df4109fcbd80b","observation_id":"187da629-1f70-41fe-be5a-f94a7e3c5245","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1612.08498","last_updated":"2016-12-27T04:38:28Z","snapshot_observed_at":"2026-08-14T21:23:38.943981Z","submitted_at":"2016-12-27T04:38:28Z","title":"Steerable CNNs","version":1},"cited_work":{"arxiv_id":"1612.08498","doi":null,"metadata_source":"pith","pith_arxiv_id":"1612.08498","snapshot_observed_at":"2026-07-02T14:37:03.199186Z","title":"Steerable CNNs","venue":"cs.LG","work_id":"b908e68d-144d-4f1b-8164-d073755acabb","year":2016},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"cited_paper":"/paper/1612.08498","citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:fc07f8c3eb89b7354cfd511b7736f1c99d313a67cc04c9c946b878dc8c62d352","observation_id":"e9e452ed-561e-447d-9ada-91518fde4004","resolution":{"observed_at":"2026-06-29T18:53:51.691765Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2104.13478","last_updated":"2021-05-02T16:16:03Z","snapshot_observed_at":"2026-08-12T23:06:05.148534Z","submitted_at":"2021-04-27T21:09:51Z","title":"Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges","version":2},"cited_work":{"arxiv_id":"2104.13478","doi":"10.48550/arxiv.2104.13478","metadata_source":"pith","pith_arxiv_id":"2104.13478","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges","venue":"cs.LG","work_id":"5e909969-dcfb-40f6-9099-241ea6f18350","year":2021},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"cited_paper":"/paper/2104.13478","citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:996d32e693177e03d146b6473f0ac693eada95ec552d59864611127c747192af","observation_id":"03a53eca-fff7-4426-aabe-b8199c218948","resolution":{"observed_at":"2026-06-29T18:53:51.694725Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-06-29T18:45:27.282354Z","title":"Generale(2)-equivariantsteerablecnns.Advancesinneuralinformation processing systems, 32, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:8ffa3902883b9934f2aafeb0f7762d267221463e988bb409fec4cab2ecb640d9","observation_id":"08e50f47-e4bc-4760-beb1-f3386cbff7d1","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","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":"2026-06-29T18:45:27.282354Z","title":"Harmonic networks: Deep translation and rotation equivariance","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:312f431e2061e29b15c946a653e7d8e98edb430f35e895c193c9eb783cb1b7ad","observation_id":"3ad6d09c-f724-4bad-a24e-48a4cc312c09","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","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":"2026-06-29T18:45:27.282354Z","title":"Springer, 2011","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:000cb4b77403fab97ed7eb07e347f7f45a717bfb54345f31a0efc2725eaaf893","observation_id":"3482b372-2947-40f6-9261-52d75fdc0cfe","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1602.09046","last_updated":"2016-02-29T17:13:47Z","snapshot_observed_at":"2026-08-14T22:08:14.409391Z","submitted_at":"2016-02-29T17:13:47Z","title":"On Complex Valued Convolutional Neural Networks","version":1},"cited_work":{"arxiv_id":"1602.09046","doi":null,"metadata_source":"pith","pith_arxiv_id":"1602.09046","snapshot_observed_at":"2026-06-29T18:53:51.681099Z","title":"Guberman, On complex valued convolutional neural networks, arXiv preprint arXiv:1602.09046 (2016)","venue":"cs.NE","work_id":"7101f141-a19f-40b4-bc71-f3adfc43174e","year":2016},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"cited_paper":"/paper/1602.09046","citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:eeb605b66d9498ea558521cec32d7c0ac6838fa8cd947765cd3013989958f683","observation_id":"c2e4a3b9-3402-4a4f-aeae-803740e88b0a","resolution":{"observed_at":"2026-06-29T18:53:51.682996Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-06-29T18:45:27.282354Z","title":"A complex gradient operator and its application in adaptive array theory","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:f6ef1b2b77227f8ecc96114e8833419743c3c70754797af060d9100d3f87d643","observation_id":"f6604aaa-1a91-4fbe-96af-f085cd9e125a","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0906.4835","last_updated":"2009-06-26T03:32:32Z","snapshot_observed_at":"2026-07-06T01:55:47.646403Z","submitted_at":"2009-06-26T03:32:32Z","title":"The Complex Gradient Operator and the CR-Calculus","version":1},"cited_work":{"arxiv_id":"0906.4835","doi":"10.48550/arxiv.0906.4835","metadata_source":"pith","pith_arxiv_id":"0906.4835","snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"The Complex Gradient Operator and the CR-Calculus","venue":"math.OC","work_id":"d67fd52e-8b2f-49da-baba-8350d9824160","year":2009},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"cited_paper":"/paper/0906.4835","citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:8ca1b86a6d4894129e0898258a0ffe34f5886e1635b279690478cc8ab0759039","observation_id":"80c5b49c-20b7-44f5-bb25-dcdc6f6e3a92","resolution":{"observed_at":"2026-06-29T18:53:51.686170Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-06-29T18:45:27.282354Z","title":"Convolutionalradiomodulationrecognition networks","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:4a743232d5d2603ea5111422aea90b920c5eb6b2dc5d2588bdf5a877bad35eb1","observation_id":"cb47fe68-fb5a-42a3-8f7f-db6717ed581d","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","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":"2026-06-29T18:45:27.282354Z","title":"Modulation pattern detection using complex convolutions in deep learning","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:aef6995e2b37c6bbd1fa6c87fa66ac3cafc5e9ff809f00efb789d64b88e5fe1e","observation_id":"3f62af8f-a19c-424f-a22f-5976b5d2d365","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","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":"2026-06-29T18:45:27.282354Z","title":"Complex-valued networks for automatic modulation classification.IEEE Transactions on Vehicular Technology, 69(9):10085–10089, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:216c67f4b384a2b55206c3a29a9affcb53cf25fa7892ec490d2c5a0bd9cf6327","observation_id":"41e52481-cede-4186-95ca-cd8a993599a5","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","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":"2026-06-29T18:45:27.282354Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:fc9b27c57566eb7f2896aa6ee4a078c8d9d2324a9cfdae24d5c13bd9cdc8f670","observation_id":"116537f7-7eb3-4a76-bdd8-a3bdeee91a5d","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","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":"2026-06-29T18:45:27.282354Z","title":"Deep learning with convolutional neural networks for eeg decoding and visualization.Human brain mapping, 38(11):5391–5420, 2017","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:460738b5673859bc03b83ecdd889255669ab599981cb3c3ac11fddda8b42cc63","observation_id":"a491abd7-814c-49d5-af0e-c50ed85f88de","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","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":"2026-06-29T18:45:27.282354Z","title":"Eegnet: acompactconvolutionalneuralnetworkforeeg-basedbrain–computerinterfaces","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:4a48b352fda04c2d6c4e4a71b992011640a45194b818b50ead0f923bd70aff64","observation_id":"d4331b3c-58f9-42aa-9f57-eb35a8a87e3a","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","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":"2026-06-29T18:45:27.282354Z","title":"Measuring phase- amplitude coupling between neuronal oscillations of different frequencies.Journal of neurophysiology, 104(2):1195–1210, 2010","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:afb4a140b84c8b1643fcadfd560a50456c0c85908614cfad5b4d333386bddab9","observation_id":"331db8e6-7db9-4fbb-8fc5-ce1d32a589a1","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","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":"2026-06-29T18:45:27.282354Z","title":"Deep reinforcement learning that matters","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:66c16d366e09315d4019b9ff500ce7b1bbac0ee7fed3750dd1189d28435489bf","observation_id":"c7c072aa-69ff-483b-9f8f-04767d7534dd","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","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":"2026-06-29T18:45:27.282354Z","title":"Are gans created equal? a large-scale study.Advances in neural information processing systems, 31, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:779e2d82d6271a612da2ba60d28c8a0615af4cb6fda4146a45c3f4aea16dd3de","observation_id":"d9ee8436-9f74-4f54-ac66-1d48a0ad924e","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1707.05589","last_updated":"2017-11-20T17:57:58Z","snapshot_observed_at":"2026-08-14T23:27:22.902726Z","submitted_at":"2017-07-18T12:35:53Z","title":"On the State of the Art of Evaluation in Neural Language Models","version":2},"cited_work":{"arxiv_id":"1707.05589","doi":null,"metadata_source":"pith","pith_arxiv_id":"1707.05589","snapshot_observed_at":"2026-06-29T18:53:51.687415Z","title":"On the State of the Art of Evaluation in Neural Language Models","venue":"cs.CL","work_id":"ab688bcb-8407-488a-8445-6ceea09a6665","year":2017},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"cited_paper":"/paper/1707.05589","citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:8e7f3b557e95b150af7c2368a8750377897b88c21067400f6f082cec80b26c6d","observation_id":"3c99588c-8aa1-48f0-a58d-32d658983659","resolution":{"observed_at":"2026-06-29T18:53:51.689041Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-06-29T18:45:27.282354Z","title":"Accounting for variance in machine learning benchmarks.Proceedings of machine learning and systems, 3:747–769, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-06-29T18:45:27.282354Z"},"links":{"citing_paper":"/paper/2605.27673"},"observation_digest":"sha256:2ceb4c8d1a0a49848e3b8c495d79908e3074316d0be58231dba2a27dbdcc57bf","observation_id":"15065440-7f8a-4ed9-a627-a64b960dcc56","resolution":{"observed_at":"2026-06-29T18:45:27.282354Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2605.27673","last_updated":"2026-05-26T20:49:23Z","latest_version":1,"primary_category":"cs.LG","snapshot_observed_at":"2026-07-06T23:37:21.716437Z","submitted_at":"2026-05-26T20:49:23Z","title":"When do complex-valued neural networks help? A study of representation, geometry, and optimization"},"reference_resolution":{"displayed":29,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":22,"verified_exact":7,"verified_fuzzy":0},"total_outbound_references":29},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 1 inbound Pith citation observation for arXiv:2605.27673."}