{"as_of":"2026-08-16T23:42:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f4cb736aba24b9a2380322d198f55b41dae2630d19106c096896b2354fa2f044","coverage":[{"denominator":28,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":28,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T14:46:14.645227Z","state":"measured"},{"denominator":28,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":28,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+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/1908.02747/citation-record","integrity":"/paper/1908.02747/integrity","json":"/paper/1908.02747/citation-record.json","paper":"/paper/1908.02747"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:46:15.584351Z","title":"Distributed optimization in sen sor networks,","venue":null,"work_id":"fd8c51ad-2ad7-47cb-bcd8-84f1e5f7d85b","year":2004},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.405337Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:70ed06723e288da2740b6d776450f3643a54fb624963559c895bf3e2119dee2e","observation_id":"feba2a95-02fb-471d-a837-648c3a39f2e6","resolution":{"observed_at":"2026-08-14T14:46:15.591286Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:46:15.557442Z","title":"Diffusion adaptation strategie s for distributed optimization and learning over networks,","venue":null,"work_id":"1c47e698-c8dc-44ec-af10-738cabdcba61","year":2012},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.417801Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:a4058bbc9ea489ee7df24164e6d8c72f21a9c31948fbeb08355c513304e1cc08","observation_id":"7ed93cc2-665a-4b87-83bc-1c921136931d","resolution":{"observed_at":"2026-08-14T14:46:15.567399Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:46:15.518944Z","title":"An overview of recent pr ogress in the study of distributed multi-agent coordination,","venue":null,"work_id":"245dd540-8a52-49cb-8a4f-e4bc6aed7f89","year":2012},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.432495Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:407362fd4a05022e936b1e973f086bb2e3632a5a2cc1d7312f682187d7c18850","observation_id":"85aa1e90-4219-4296-9da3-d6f25a4c9fcf","resolution":{"observed_at":"2026-08-14T14:46:15.525743Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:46:15.492546Z","title":"D istributed optimization and statistical learning via the alternating direction method of multipliers,","venue":null,"work_id":"5bec6a0f-5920-48da-811e-da914c23af3a","year":2011},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.439859Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:d2d500c591c74339a6234ce8d4d8c02299d9cf412d38bb9a19aba454cc0be5dc","observation_id":"111eadcb-7282-4d3f-ba0c-45a91abe2fb2","resolution":{"observed_at":"2026-08-14T14:46:15.502303Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1901.00214","last_updated":"2019-01-01T22:01:10Z","snapshot_observed_at":"2026-08-14T17:36:09.331081Z","submitted_at":"2019-01-01T22:01:10Z","title":"Clustering with Distributed Data","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1901.00214","snapshot_observed_at":"2026-08-14T14:46:14.450230Z","title":"Clustering with distributed data ,","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.450230Z"},"links":{"cited_paper":"/paper/1901.00214","citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:d0682d632eae33911a3e15302d319cd9085ce52aade0531921fc9b1448b6f530","observation_id":"c328482a-c6d6-4037-9a2e-9650a1261a72","resolution":{"observed_at":"2026-08-14T14:46:14.450230Z","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":"2026-08-14T14:46:15.456110Z","title":"Distributed subgradient met hods for multi- agent optimization,","venue":null,"work_id":"707e2c1a-1d68-40a3-87a8-7bdcd5cbbe71","year":2009},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.457789Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:a59068a96299cec0b0c20416773d2e9bf02b74ca7af7ddfa54888b6d09b5f650","observation_id":"6e73d378-d596-43a9-a03b-8c29615a33bf","resolution":{"observed_at":"2026-08-14T14:46:15.468292Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:46:15.426315Z","title":"A distributed quasi-n ewton algo- rithm for empirical risk minimization with nonsmooth regul arization,","venue":null,"work_id":"9d04d469-9073-4b8d-82aa-6efed0854b3b","year":2018},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.475325Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:35daa6accca54cc06d89b4d32c5d6f42ad59d73f439963e06452fe2dfcb3f905","observation_id":"966d0913-b6a8-4943-b970-c9880ff89c65","resolution":{"observed_at":"2026-08-14T14:46:15.432136Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:46:15.399113Z","title":"Distributed nonconvex opt imization over networks,","venue":null,"work_id":"fbbd01a5-80d2-4a65-9521-fd436f998a83","year":2015},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.481418Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:93b262ef9e68a1e4fe7603411203c425e8800acca2b451b7ea55acc638eaf2aa","observation_id":"c798571b-07f1-4daa-b0c6-e2e3551b899a","resolution":{"observed_at":"2026-08-14T14:46:15.408409Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:46:15.366194Z","title":"Distributed nonconv ex multiagent optimization over time-varying networks,","venue":null,"work_id":"3a6bbec8-2874-448c-899a-0f9429605409","year":2016},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.488122Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:7af5d53e3644a341f19ab61169056df1831154d90fb51b3c286e533108cc3fa7","observation_id":"cac629c5-4bda-4858-b366-05c4f66c4efd","resolution":{"observed_at":"2026-08-14T14:46:15.374384Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1903.04133","last_updated":"2020-07-15T17:27:58Z","snapshot_observed_at":"2026-08-14T17:04:30.135154Z","submitted_at":"2019-03-11T05:40:14Z","title":"Distributed Non-convex Optimization of Multi-agent Systems Using Boosting Functions to Escape Local Optima: Theory and Applications","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1903.04133","snapshot_observed_at":"2026-08-14T14:46:14.496490Z","title":"Distributed non-con vex optimization of multi-agent systems using boosting functions to escape l ocal optima,","venue":null,"work_id":null,"year":1903},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.496490Z"},"links":{"cited_paper":"/paper/1903.04133","citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:3c7cf562105a95c411b438e9b99daeefb8eb6a881284b63c6cbf2d843cf584ab","observation_id":"663c5b02-0735-4e24-bbd0-484ed282b16a","resolution":{"observed_at":"2026-08-14T14:46:14.496490Z","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":"2026-08-14T14:46:15.342143Z","title":"Convergence of a multi-a gent projected stochastic gradient algorithm for non-convex optimizatio n,","venue":null,"work_id":"5ae622e2-12d1-4e4c-a017-c99eb431164b","year":2012},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.505909Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:d19176243c09d577c8d8cf56d9cbd991fda27be45bd1f789df57b7a1f9e45513","observation_id":"f8ad49a3-258f-45ae-a685-e727987136de","resolution":{"observed_at":"2026-08-14T14:46:15.349918Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:46:15.319161Z","title":"Next: In-network nonconv ex optimiza- tion,","venue":null,"work_id":"307a5092-2ca6-450e-918c-089499918acd","year":2016},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.511645Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:8838559d080c66af52421d0d847797850c163ae2d425770220d2915f740a826c","observation_id":"be5cd77b-25b9-4725-8d77-34c0920c3bb3","resolution":{"observed_at":"2026-08-14T14:46:15.325880Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:46:15.285756Z","title":"Identifying and attacking the saddle point prob lem in high- dimensional non-convex optimization,","venue":null,"work_id":"752cd74a-c77b-4848-a6a1-2334c2687217","year":2014},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.524168Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:0b33b108881b7651bb29e197651750400fac2aa3af7f5b812d370c65b79301cb","observation_id":"f2fc5e41-5345-48d4-a92d-c74eea202e6f","resolution":{"observed_at":"2026-08-14T14:46:15.297484Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:46:15.249477Z","title":"Gra dient descent only converges to minimizers,","venue":null,"work_id":"c8ce7aa4-f0c9-4b76-b8df-2b7bc06d1eed","year":2016},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.535397Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:041b8128b46e929b0f6064a14cc5609710b1dd6ff49316f6d2cffe5d6d0f2d63","observation_id":"4e735da1-0abd-42b9-a744-172874fd40c0","resolution":{"observed_at":"2026-08-14T14:46:15.255436Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:46:15.227439Z","title":"First-order methods almost always avoid strict s addle points,","venue":null,"work_id":"1e85bf53-fb6d-4217-a8d8-377bfea9ed94","year":2019},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.546876Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:c5d03654af31a68ea752c1a3331bc7df92d672946d77eb41cd2f0d47b617e904","observation_id":"ab79da0b-5640-4240-bb40-381049f26634","resolution":{"observed_at":"2026-08-14T14:46:15.235482Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:46:15.194554Z","title":"Revisiting normaliz ed gradient descent: Fast evasion of saddle points,","venue":null,"work_id":"82996c0c-8165-4992-92c5-2b03ebb68acc","year":2019},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.556465Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:a59c2887bd4cd14904ad232d42a29ff0ac8bec622c305d578de5c00e384e0427","observation_id":"89e7a80e-4767-417a-98e7-b858bf61e981","resolution":{"observed_at":"2026-08-14T14:46:15.208483Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:46:15.149513Z","title":"Shub, Global stability of dynamical systems","venue":null,"work_id":"00a79022-aa17-4a14-835e-2d681da7ca51","year":2013},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.565320Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:578c1068f02e05a22ad4cf7c46be79399faa39d03a23a26c82acbc687c289f53","observation_id":"929ab326-f125-4187-89b2-ba5b1a9e6f06","resolution":{"observed_at":"2026-08-14T14:46:15.156416Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:46:14.573980Z","title":null,"venue":null,"work_id":null,"year":1955},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.573980Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:95b8e8e8d88242e27bcb992658c8e964fe08a6f7c6dc504cb29a7589d0cf80c8","observation_id":"b0fb7aef-fca9-446a-9003-da0aa722e516","resolution":{"observed_at":"2026-08-14T14:46:14.573980Z","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":"2026-08-14T14:46:15.102891Z","title":"Anneal ing for distributed global optimization,","venue":null,"work_id":"0681ef88-a629-48ae-9bf3-c900309b7920","year":2019},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.579549Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:26f1d7533d91543a464b3be24dacb4c8568aae40a363e2730b8de494703a8043","observation_id":"bc87bf5d-2bc1-45c6-b279-fae6e53ac2a6","resolution":{"observed_at":"2026-08-14T14:46:15.114848Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:46:15.064809Z","title":"Non-convex distributed opt imization,","venue":null,"work_id":"b052c41d-81d4-4b6f-9cce-d0852d704a5f","year":2017},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.586229Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:65aa8cbef1ea435848d6c1a949d907fc111cb3e233d67921ea5999798ae58c1f","observation_id":"c873bbbf-946b-438a-b136-436609096c6f","resolution":{"observed_at":"2026-08-14T14:46:15.071366Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1809.08694","last_updated":"2020-05-25T16:53:35Z","snapshot_observed_at":"2026-08-14T18:24:41.972871Z","submitted_at":"2018-09-23T23:06:39Z","title":"Second-order Guarantees of Distributed Gradient Algorithms","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1809.08694","snapshot_observed_at":"2026-08-14T14:46:14.593383Z","title":"Second- order guarantees of distributed gradient algorithms,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.593383Z"},"links":{"cited_paper":"/paper/1809.08694","citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:faa17189688e9c63f283cf05f7ea3b9e0990e3b59c8f0040f9c8124eb9f6f3dd","observation_id":"7ed19cbd-b533-41ab-923b-c48755dfd309","resolution":{"observed_at":"2026-08-14T14:46:14.593383Z","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":"2026-08-14T14:46:15.041097Z","title":"Distributed parame ter estimation in sensor networks: Nonlinear observation models and imper fect com- munication,","venue":null,"work_id":"7571a249-13a9-4c99-bc65-4d4d01537645","year":2012},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.598907Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:845918ce69e5e9594bb17e4b4f79eaba845b964ce8eaf62117fed4713aae005d","observation_id":"ec08c84f-f25e-4a19-8eff-c8a9ab796e44","resolution":{"observed_at":"2026-08-14T14:46:15.049829Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:46:15.008771Z","title":"Constrained consensus and optimization in multi-agent networks,","venue":null,"work_id":"fc440848-e894-4646-871a-d89a320b9477","year":2010},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.606017Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:356640d15c0512312e17c9147fafd945b761f94b6517fd65c4c41cd4b61b8d04","observation_id":"d68341dc-5808-469c-841d-5ff3b4d127fd","resolution":{"observed_at":"2026-08-14T14:46:15.019179Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:46:14.959905Z","title":"Distributed optimization over time-varying directed graphs,","venue":null,"work_id":"095ba2db-ef1d-4cb1-b4d6-92882a5a6665","year":2014},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.614698Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:ca4214220a9f2f50a44c38a866b70b0c395a615956364c5fe9bf5821fbcc67bd","observation_id":"fcb55e3b-2207-4330-b8aa-5fe7cd724dcc","resolution":{"observed_at":"2026-08-14T14:46:14.972024Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:46:14.913603Z","title":"Gradient primal- dual al- gorithm converges to second-order stationary solutions fo r nonconvex distributed optimization,","venue":null,"work_id":"5ae8a0df-982f-433d-8b87-a14e6e179875","year":2018},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.621347Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:c1e150e0909c20b084f83d13711bf2304175f16fcb6064abc31849fedb8c652e","observation_id":"122f1847-bd54-4f74-9fc9-2998f8a45ee8","resolution":{"observed_at":"2026-08-14T14:46:14.929726Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:46:14.627430Z","title":null,"venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.627430Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:0354a9d73727b74187e692a8735704b7d2a45c7d0f8a3482e8ff29f9f5bbc148","observation_id":"a5bbd946-bdfe-4194-9047-748ced98c066","resolution":{"observed_at":"2026-08-14T14:46:14.627430Z","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":"2026-08-14T14:46:14.869227Z","title":"Stochastic appr oximations and differential inclusions,","venue":null,"work_id":"5c136a25-9a7e-4419-8ddc-4e227875fc6b","year":2005},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.640388Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:ca01deda30dec2e2b95bc196dcb38f661f6185703696230ec8ace7a8045312d9","observation_id":"cc2f4a46-4ceb-406a-a53d-65464e2d8a40","resolution":{"observed_at":"2026-08-14T14:46:14.875461Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:46:14.836210Z","title":"Lakshmikantham and S","venue":null,"work_id":"2b21eb15-c3d4-4456-b202-94b14435104f","year":1969},"citing_paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-14T14:46:14.645227Z"},"links":{"citing_paper":"/paper/1908.02747"},"observation_digest":"sha256:bda0e6fc034447541f336fb462ff97b9d53f52ba882b7d2f099cf5a2c2eae18a","observation_id":"b5fc412e-6e35-4058-ad75-120e2322303c","resolution":{"observed_at":"2026-08-14T14:46:14.844825Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.02747","last_updated":"2019-10-23T17:46:35Z","latest_version":2,"primary_category":"math.OC","snapshot_observed_at":"2026-08-16T13:08:04.023131Z","submitted_at":"2019-08-07T17:57:59Z","title":"Distributed Gradient Descent: Nonconvergence to Saddle Points and the Stable-Manifold Theorem"},"reference_resolution":{"displayed":28,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":0,"verified_fuzzy":23},"total_outbound_references":28},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:1908.02747."}