{"as_of":"2026-08-20T05:16:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:78e3316869ba57b57e49b35b786b47d88f3c2d8438dac0fac1872fb0ca739aaf","coverage":[{"denominator":23,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":23,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T20:55:55.250912Z","state":"measured"},{"denominator":24,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":24,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+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":"2026-08-15T16:37:56.522303Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-15T18:16:14.067578Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"cited_work":{"arxiv_id":"2505.11692","doi":"10.48550/arxiv.2505.11692","metadata_source":"pith","pith_arxiv_id":"2505.11692","snapshot_observed_at":"2026-08-15T18:16:14.067578Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","venue":"cs.LG","work_id":"0d4f05a8-35e6-4d9a-942b-c7006d1c7bda","year":2025},"citing_paper":{"arxiv_id":"2509.03056","last_updated":"2025-09-04T01:30:08Z","snapshot_observed_at":"2026-08-18T05:13:18.409981Z","submitted_at":"2025-09-03T06:38:22Z","title":"Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-15T16:37:56.522303Z"},"links":{"cited_paper":"/paper/2505.11692","citing_paper":"/paper/2509.03056"},"observation_digest":"sha256:9d0a6c0531492c95c1c29f0f762a3aa81804c7208fe1fc69d5369288331be5aa","observation_id":"a0c98cc1-eee2-4757-9ae4-bff2e0102c37","resolution":{"observed_at":"2026-08-15T16:37:56.702935Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2505.11692/citation-record","integrity":"/paper/2505.11692/integrity","json":"/paper/2505.11692/citation-record.json","paper":"/paper/2505.11692"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T20:55:55.181218Z","title":"Understanding deep neural networks with rectified linear units, 2018","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.181218Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:e3ad70c262a0f660c4afda756d1d2dd82bb487c7047e6e427171b025f6376809","observation_id":"5cc9309a-15c7-4e52-a7ae-f497c3ea9a8b","resolution":{"observed_at":"2026-08-15T20:55:55.181218Z","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":"2026-08-15T20:55:55.468494Z","title":"Bartlett","venue":null,"work_id":"ae230e88-c2cc-43c5-9fb5-2ff5c02ad18c","year":1998},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.185190Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:e66492cb786220e0474155dc0d98d684a5c1476573621586bc7902aadc99e5d2","observation_id":"a6441b2d-0fae-4df6-acc0-5812b94c78f0","resolution":{"observed_at":"2026-08-15T20:55:55.471757Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:55:55.188410Z","title":"A combinatorial theory of dropout: Subnetworks, graph geometry, and generalization, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.188410Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:7735d08a1fa5328d53c21ac727622ce204ac74457b220d9eb29102e2648b8f60","observation_id":"3a19054a-7b7c-4b76-8edf-a370a60d5e17","resolution":{"observed_at":"2026-08-15T20:55:55.188410Z","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":"2026-08-15T20:55:55.453165Z","title":"Neural networks as universal finite-state machines: A constructive deterministic finite automaton theory, 2025","venue":null,"work_id":"bb0426d5-26cb-45bc-a36e-c1f172b4db73","year":2025},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.191650Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:71718c77166fbba64cc6517be45e38525cbaec7a1ed277c654394158043b364d","observation_id":"4057ae10-710a-4a31-8d5d-d638432730a7","resolution":{"observed_at":"2026-08-15T20:55:55.456407Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:55:55.194695Z","title":"The lottery ticket hypothesis: Finding sparse, trainable neural networks, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.194695Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:0130596c941cee292ded5b33890ded29d9a19fd735d0e025206ee20f9d038193","observation_id":"e21063ec-0259-469d-8475-9b3bae75d670","resolution":{"observed_at":"2026-08-15T20:55:55.194695Z","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":"2026-08-15T20:55:55.437211Z","title":"Deep sparse rectifier neural networks","venue":null,"work_id":"9f3cf22e-5943-42a4-bc8f-d551194de558","year":2011},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.198337Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:2caef0c51deb0198221c74f8bfe88e524db4d6d6be0d192488e2e97205273874","observation_id":"11bcba2c-2daf-4cf8-ad50-0997ed8e52c8","resolution":{"observed_at":"2026-08-15T20:55:55.440544Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:55:55.201608Z","title":"Guss and Ruslan Salakhutdinov","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.201608Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:aeb7ede6f173f17634718d669cef450543f6ba273b55be993c76a16f8c79963e","observation_id":"0b7d623d-a732-4eb1-9fc5-4970be1a2ddf","resolution":{"observed_at":"2026-08-15T20:55:55.201608Z","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":"2026-08-15T20:55:55.420669Z","title":"Complexity of linear regions in deep networks","venue":null,"work_id":"ce676281-18cd-4103-86bf-085eda7e9bb9","year":null},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.204473Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:1d0f631c8e9a94e7fa0cb8ba51037f77aa94df91abd4a3cf955c0f69cf635c56","observation_id":"617dac91-d724-4c17-84b8-128dc3b2cc84","resolution":{"observed_at":"2026-08-15T20:55:55.424161Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:55:55.403835Z","title":"Approximating continuous functions by relu nets of minimal width, 2018","venue":null,"work_id":"4b3379d1-b595-49fa-b35f-c3f28669fae0","year":2018},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.210622Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:d1c1fec73cbbbc9f7dd32b133ac4f22e96103f3e2b9e5fafdc3e20366b20211b","observation_id":"d6d92211-ad06-41ca-a75f-3f3964ef3bc6","resolution":{"observed_at":"2026-08-15T20:55:55.407316Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:55:55.393808Z","title":"On the number of linear regions of deep neural networks","venue":null,"work_id":"6b20c722-7c17-43fc-8ff3-6365584c8e74","year":2014},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.213642Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:d732c74440f621aa3c9da48eea59b2b1691a4c0d65eac6a85fe60a4e4f05ff2c","observation_id":"ecc44947-6d2f-4910-a230-ba38856f4c23","resolution":{"observed_at":"2026-08-15T20:55:55.397310Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:55:55.216722Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.216722Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:425451689d7681306ad196e2d36b3e0df8781d3a4eec580cd1431ecdf89b3091","observation_id":"7a38f95d-497e-41d0-9084-ec54d9d0d742","resolution":{"observed_at":"2026-08-15T20:55:55.216722Z","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":"2026-08-15T20:55:55.219906Z","title":"In search of the real inductive bias: On the role of implicit regularization in deep learning, 2015","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.219906Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:75328e7bb64c860601a8ce24743c9e978e58b61a8e150e0740736f2260cfa8d0","observation_id":"99209b28-05b3-427d-9162-b9b2067bd561","resolution":{"observed_at":"2026-08-15T20:55:55.219906Z","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":"2026-08-15T20:55:55.223050Z","title":"Norm-based capacity control in neural networks","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.223050Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:c699d9b2fe6351ce03dce72f82a4d7390a9e6fd22e12d22dd6bc9b0a2d73a5af","observation_id":"4192890c-1eb5-4e88-80b2-8fa584acf127","resolution":{"observed_at":"2026-08-15T20:55:55.223050Z","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":"2026-08-15T20:55:55.364197Z","title":"Abolafia, Jeffrey Pennington, and Jascha Sohl- Dickstein","venue":null,"work_id":"6cce2889-75d1-4ea9-a1df-5adebd52e3e3","year":2018},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.226185Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:b187e00a5ab7fd5d5bfa1ad719081b87b7dbb0fcbbe608dbba66a8dc9ae8cf72","observation_id":"f68ed799-33a6-4ad9-9647-d5a92648c5bf","resolution":{"observed_at":"2026-08-15T20:55:55.367819Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:55:55.354629Z","title":"Pytorch: An imperative style, high- performance deep learning library","venue":null,"work_id":"3c0462c9-8e32-4daa-bdf4-2be3c6289cbe","year":2019},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.229318Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:3ac63b43fb572cb6e8026212010b54df864409849ca13dcadc8d78f40aab32b1","observation_id":"5d9b1354-2e22-4517-bcb0-bf2f4ee8b1ea","resolution":{"observed_at":"2026-08-15T20:55:55.357927Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:55:55.344178Z","title":"Expo- nential expressivity in deep neural networks through transient chaos","venue":null,"work_id":"cb5654c1-eaa4-4a1b-af64-8736c8c558d4","year":2016},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.232241Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:ec7b2f4bf159d26f32b6351a9a4e34f413d9c1a5270aa4ce239b8a59ae5316c1","observation_id":"b6ee4102-6fd0-42a8-b11a-b93b05da5ab3","resolution":{"observed_at":"2026-08-15T20:55:55.348219Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:55:55.332634Z","title":"On the expressive power of deep neural networks, 2017","venue":null,"work_id":"09315269-8859-48ea-91a2-e0e1ea282f7e","year":2017},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.235171Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:184ec176562fa5b4a9721d67bcca0b3f59789909cb434809f21e6976442202c2","observation_id":"2c165f70-01c6-4c52-88c0-5d62d015b6b5","resolution":{"observed_at":"2026-08-15T20:55:55.336475Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:55:55.321787Z","title":"Bounding and counting linear regions of deep neural networks","venue":null,"work_id":"cf8a4302-6b7c-4a8b-99d1-6e49d7d91ff3","year":2018},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.238235Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:b7920e3ed0e160c03cd6dc7debd15ef56773074f8a24af03020af7393980a683","observation_id":"e65edef5-6a0b-4140-bdd1-de798fe798fc","resolution":{"observed_at":"2026-08-15T20:55:55.325545Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:55:55.310319Z","title":"benefits of depth in neural networks","venue":null,"work_id":"57d11cbf-85d6-462b-9c60-5c00686354d5","year":2016},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.241242Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:e46e8c31361ae471002cf305027d5033df9ef5f2b5946619a35eef444cd18f0a","observation_id":"e91560f7-4d1e-4ab1-a79d-703525800f32","resolution":{"observed_at":"2026-08-15T20:55:55.313688Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:55:55.300081Z","title":"Facing up to arrangements: face-count formulas for partitions of space by hyperplanes, volume 1","venue":null,"work_id":"b37c8e32-d104-4678-824c-0f9b9762893b","year":1975},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.244296Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:183bc8e8807e738b536cb3e62795ebadf07b8a3bcd8de08d81dbac7e8acf5b53","observation_id":"95b140b0-0f27-4f6a-84f3-3bd350f84044","resolution":{"observed_at":"2026-08-15T20:55:55.304083Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:55:55.290235Z","title":"Lee, Martin J","venue":null,"work_id":"79a1693b-3924-4edb-b308-a3a9fa307994","year":2015},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.247559Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:bd44ea8b27339076537775ef948f0d73fd0e14516af34e0e60e3720ad0cc19a5","observation_id":"1736ffe8-064a-4457-ab46-bdd0204f9da8","resolution":{"observed_at":"2026-08-15T20:55:55.293450Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:55:55.277217Z","title":"For each such nodev∈ S, the corresponding region Rv contributes little to the function’s global variation due to its low connectivity (few adjacent regions) and likely small volume","venue":null,"work_id":"39adc7c8-11ec-48ce-a5a1-3fa71adfac48","year":null},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.250912Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:c4088b4932f3a94017997c827c9e1cdfa1a65a6a091499f7eefc83537f13ed05","observation_id":"adac6c60-c66b-463f-bf89-45fa71715912","resolution":{"observed_at":"2026-08-15T20:55:55.282729Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T20:55:55.207541Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph","version":2},"reference_index":2604,"source":"pdf_text","source_observed_at":"2026-08-15T20:55:55.207541Z"},"links":{"citing_paper":"/paper/2505.11692"},"observation_digest":"sha256:5872eda67c1a48f1a9e4379f4c9ea93e08b6fab0b00369d031224d891cfdc0ff","observation_id":"0f20cc56-24ea-451f-bad4-82d678c1268b","resolution":{"observed_at":"2026-08-15T20:55:55.207541Z","resolver_source":null,"status":"parse_uncertain"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2505.11692","last_updated":"2025-05-28T21:46:04Z","latest_version":2,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-17T09:23:20.477063Z","submitted_at":"2025-05-16T21:00:56Z","title":"The Geometry of ReLU Networks through the ReLU Transition Graph"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":1,"unresolved":7,"verified_exact":0,"verified_fuzzy":15},"total_outbound_references":23},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 1 inbound Pith citation observation for arXiv:2505.11692."}