{"as_of":"2026-08-16T14:50:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:b70a84bf44ea223b79d080aa9001192094ca896b988a4ba52e194ae2dd0215fd","coverage":[{"denominator":25,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":25,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T05:23:01.032626Z","state":"measured"},{"denominator":25,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":25,"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/2412.00659/citation-record","integrity":"/paper/2412.00659/integrity","json":"/paper/2412.00659/citation-record.json","paper":"/paper/2412.00659"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2111.14580","last_updated":"2022-07-11T14:05:08Z","snapshot_observed_at":"2026-08-14T10:35:18.069849Z","submitted_at":"2021-11-29T15:10:09Z","title":"Amortized Implicit Differentiation for Stochastic Bilevel Optimization","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2111.14580","snapshot_observed_at":"2026-08-12T05:23:00.935397Z","title":"Amortized implicit differentiation for stochastic bilevel optimization","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:00.935397Z"},"links":{"cited_paper":"/paper/2111.14580","citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:545a4787ab2794c3a3d6fea034b048f7f3184c310ad0b9fd647e3870cd7e2479","observation_id":"93901944-9265-4be5-953a-ac3294388f15","resolution":{"observed_at":"2026-08-12T05:23:00.935397Z","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":"2026-08-12T05:23:01.324014Z","title":"Exponential convergence bounds using integral quadratic constraints","venue":null,"work_id":"2da5a597-61bc-479a-9df3-70463599bbf5","year":2015},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:00.940457Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:0d6d7e3f7bc7b6d69222aa3279936db68f154bd7384ae2609e234a4a6ac6f54c","observation_id":"1e5c2a99-0115-483d-86b7-300f166804f2","resolution":{"observed_at":"2026-08-12T05:23:01.328354Z","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":"2026-08-12T05:23:00.944845Z","title":"Closing the gap: Tighter analysis of alternating stochastic gradient methods for bilevel problems","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:00.944845Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:206fa9401a6ba81f7a4be3dd29707ea5f436aa13222929cfb52eb7daa839c34a","observation_id":"af9c1fe8-447a-4d8a-998c-1a3f39959182","resolution":{"observed_at":"2026-08-12T05:23:00.944845Z","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":"2026-08-12T05:23:00.948634Z","title":"A single-timescale method for stochastic bilevel optimization","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:00.948634Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:428aae43c2e62adeedf34d97a8f95481644dea8f0e053db2211351689581d43e","observation_id":"80be432e-b9f1-456e-b506-1ee3bcba43f1","resolution":{"observed_at":"2026-08-12T05:23:00.948634Z","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":"2026-08-12T05:23:01.297371Z","title":"Feedback systems: input-output properties","venue":null,"work_id":"15198d32-218d-4cc6-8e14-bbd3457589e4","year":2009},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:00.952844Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:4c9140fca8b890b1ef32607382346738fac5266546e1b9495bb5600a9a35b741","observation_id":"ff8317f3-bfee-4182-a976-17eecae6b1e6","resolution":{"observed_at":"2026-08-12T05:23:01.301425Z","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":"2026-08-12T05:23:01.284950Z","title":"A course in robust control theory: a convex approach, volume 36","venue":null,"work_id":"7ca19fd1-7d33-48b0-bb8e-e241ef88271f","year":2013},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:00.957214Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:cef339111a38c9e1d36f469e7c1d775fb98c283a1b6f0021f7b38aba9bb6b7da","observation_id":"c0bbcf94-21c4-4032-8fac-91432d3fe801","resolution":{"observed_at":"2026-08-12T05:23:01.289157Z","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":"2026-08-12T05:23:00.961778Z","title":"Forward and reverse gradient-based hyperparameter optimization","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:00.961778Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:d517703bd4876b9ee281b49226ce886be6c96542721f4607232ee4ab4bb89101","observation_id":"f582e691-b981-4cab-9013-4f1e967db832","resolution":{"observed_at":"2026-08-12T05:23:00.961778Z","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":"2026-08-12T05:23:00.965428Z","title":"Bilevel programming for hyperparameter optimization and meta-learning","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:00.965428Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:f6b7d796477c510db2c68bf391fa2ce7f7989b7c1f61045abd3f3b094581ab55","observation_id":"20bedd64-4b02-4ab6-b52c-85b41f8c8292","resolution":{"observed_at":"2026-08-12T05:23:00.965428Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1802.02246","last_updated":"2018-02-06T22:10:14Z","snapshot_observed_at":"2026-08-14T19:48:10.374742Z","submitted_at":"2018-02-06T22:10:14Z","title":"Approximation Methods for Bilevel Programming","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1802.02246","snapshot_observed_at":"2026-08-12T05:23:00.969258Z","title":"Approximation methods for bilevel programming","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:00.969258Z"},"links":{"cited_paper":"/paper/1802.02246","citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:2964955a421e7c5b868ed2335acd8bb1d2765458caef72cc368c5d90e8237461","observation_id":"a2ac3841-d3ed-4d65-8064-eb48d7fcf43d","resolution":{"observed_at":"2026-08-12T05:23:00.969258Z","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":"2026-08-12T05:23:00.974097Z","title":"A two-timescale stochastic algorithm framework for bilevel optimization: Complexity analysis and application to actor-critic","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:00.974097Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:d3d1167622a3c4f6f390d0f3b89d237632c85637b5bdbb67fafaba377d59901c","observation_id":"04e5a3d2-7cc8-4b80-be57-6a1aa2748c13","resolution":{"observed_at":"2026-08-12T05:23:00.974097Z","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":"2026-08-12T05:23:01.251146Z","title":"Control interpretations for first-order optimization methods","venue":null,"work_id":"00567441-b860-4fdd-b56e-a04c6318dc8e","year":2017},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:00.977871Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:1d8f534ea652fa17ba9c1ba0e2c49417ef4ac1fb72a26e600e8ffa77d459fb56","observation_id":"60d43e23-af05-48f3-8892-31e5c9ff6e15","resolution":{"observed_at":"2026-08-12T05:23:01.255325Z","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":"2026-08-12T05:23:01.237565Z","title":"Dissipativity theory for nesterov’s accelerated method","venue":null,"work_id":"59c40410-7dd3-445b-9fa8-251ceba281c4","year":2017},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:00.982040Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:7970d21d6d5e6f3e412d5f149217b336539308a26e80304072bb6b7212455ee6","observation_id":"b6e079d4-da48-4f39-9035-8e2ddf5d0f4f","resolution":{"observed_at":"2026-08-12T05:23:01.242134Z","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":"2026-08-12T05:23:01.224720Z","title":"Metapoison: Practical general-purpose clean-label data poisoning","venue":null,"work_id":"33bbde3d-3cd6-4853-8cc5-51bc2b22460f","year":2020},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:00.985863Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:8f6d879334d43a1b86432134649e1a33a2e0504d9f6ab65977e2706a28cc67ba","observation_id":"d2c36172-b171-4435-bad2-722c9ced63c9","resolution":{"observed_at":"2026-08-12T05:23:01.229083Z","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":"2026-08-12T05:23:01.212186Z","title":"Lower bounds and accelerated algorithms for bilevel optimization","venue":null,"work_id":"a9814505-4852-43bd-9bdd-557b2563448b","year":2023},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:00.989798Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:2430673b50682f5a5f99bcdfa3e802a81ec30cfd6010546d8717e0ed3bab8871","observation_id":"da0a09f8-53bc-4a1c-aedb-c00aeba88f9b","resolution":{"observed_at":"2026-08-12T05:23:01.216471Z","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":"2026-08-12T05:23:00.993513Z","title":"Bilevel optimization: Convergence analysis and enhanced design","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:00.993513Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:3035b3b633c45e1663e35321f87d65c5b9201ef25c4c644716ea02ac6f0db075","observation_id":"77e4f8f9-9c43-41ea-bc5c-1d68da79f02a","resolution":{"observed_at":"2026-08-12T05:23:00.993513Z","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":"2026-08-12T05:23:00.997209Z","title":"A near-optimal algorithm for stochastic bilevel optimization via double-momentum","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:00.997209Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:8238c22545e39c2d21cea9c45d47a7f32c76e601098763b85b09d91f338b80ba","observation_id":"effdb644-8c21-4e5b-bc2d-06e5cd3750b7","resolution":{"observed_at":"2026-08-12T05:23:00.997209Z","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":"2026-08-12T05:23:01.000950Z","title":"Analysis and design of optimization algorithms via integral quadratic constraints","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:01.000950Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:9c6c87d02d9b847f09cabb2bae84371e52afd0d2f0f5c3ef9e12ca605242555a","observation_id":"c4466d0b-3936-455e-a7de-5f192e9b5532","resolution":{"observed_at":"2026-08-12T05:23:01.000950Z","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":"2026-08-12T05:23:01.175932Z","title":"A fully single loop algorithm for bilevel optimization without hessian inverse","venue":null,"work_id":"c0a6cfd0-01c2-4eb4-82cb-64cba42efc07","year":2022},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:01.005376Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:7415bab346253c65c2eba108265f0c84c56b4f48394f31921e2be3a579b38eb1","observation_id":"7b9ddbd2-c629-45af-9776-37346beaf3a0","resolution":{"observed_at":"2026-08-12T05:23:01.181200Z","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":"2026-08-12T05:23:01.163224Z","title":"Inducing equilibria via incentives: Simultaneous design-and-play ensures global convergence","venue":null,"work_id":"43b5101c-e0e3-40ef-9f4c-baaef4778b41","year":2022},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:01.008990Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:f5bb3e682339f79f8664d8aac4281bb901fa456cee6f58ca62a0e952a22d2d86","observation_id":"7a855a81-ea1c-499f-95e2-c5bc546987a3","resolution":{"observed_at":"2026-08-12T05:23:01.167375Z","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":"2026-08-12T05:23:01.150502Z","title":"On lp-hyperparameter learning via bilevel nonsmooth optimization","venue":null,"work_id":"39e4f10e-6428-4172-9375-49e6868ff367","year":2021},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:01.012732Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:bd68ab6f2eb1169a4f253e6733790b5adf50636ed74692ba05c411535e53c4e8","observation_id":"f86a3099-090a-4ede-9f1f-daf162497a86","resolution":{"observed_at":"2026-08-12T05:23:01.154987Z","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":"2306.11035","last_updated":"2024-03-18T18:55:44Z","snapshot_observed_at":"2026-08-15T10:25:46.036582Z","submitted_at":"2023-06-19T16:00:48Z","title":"Adversarial Training Should Be Cast as a Non-Zero-Sum Game","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2306.11035","snapshot_observed_at":"2026-08-12T05:23:01.016654Z","title":"Adversarial training should be cast as a non-zero-sum game","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:01.016654Z"},"links":{"cited_paper":"/paper/2306.11035","citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:0340aa5d85fd7fe2acdf900036a922e390e89b776876fb02578037ed177fba92","observation_id":"b5f77084-c586-4ef0-a523-90c3ebcc1c0d","resolution":{"observed_at":"2026-08-12T05:23:01.016654Z","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":"2026-08-12T05:23:01.138775Z","title":"Hydra: Pruning adversarially robust neural networks","venue":null,"work_id":"5ab86b6f-e01c-4fa8-b312-ec5c7f502eb9","year":2020},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:01.020613Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:4230b83785563618dfd05da0cd6bd26e2cf81e4dae01f095eb0a60a870063aca","observation_id":"684e6851-c877-4d77-8381-8fc88c1b772b","resolution":{"observed_at":"2026-08-12T05:23:01.142788Z","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":"2026-08-12T05:23:01.126483Z","title":"Reward design for driver repositioning using multi-agent reinforcement learning","venue":null,"work_id":"edaa2889-878a-42f6-a02a-5612da068fd0","year":2020},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:01.024755Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:dc53589d24dd2cb06f699d49ea3622770381ec331df15e149bdde97964c2ea39","observation_id":"410be691-5f44-4f87-90e0-cf40d1532f9c","resolution":{"observed_at":"2026-08-12T05:23:01.130647Z","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":"2007.11022","last_updated":"2020-07-21T18:15:08Z","snapshot_observed_at":"2026-08-15T19:32:42.802112Z","submitted_at":"2020-07-21T18:15:08Z","title":"A Gradient-based Bilevel Optimization Approach for Tuning Hyperparameters in Machine Learning","version":1},"cited_work":{"arxiv_id":"2007.11022","doi":null,"metadata_source":"pith","pith_arxiv_id":"2007.11022","snapshot_observed_at":"2026-08-12T05:23:01.064214Z","title":"A Gradient-based Bilevel Optimization Approach for Tuning Hyperparameters in Machine Learning","venue":"cs.LG","work_id":"6986bd34-f6e8-4428-a846-f9125c890694","year":2020},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:01.028552Z"},"links":{"cited_paper":"/paper/2007.11022","citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:488617d2d93f5329642a567fdecba727491f9378728341cc18d04d431e757a7b","observation_id":"0b8ccdd7-18f9-46c5-8a73-c0046fc213d3","resolution":{"observed_at":"2026-08-12T05:23:01.071119Z","resolver_source":"local_arxiv","status":"verified_exact"},"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":"2026-08-12T05:23:01.114445Z","title":"Advancing model pruning via bi-level optimization","venue":null,"work_id":"676fecbd-9b54-4290-8b8e-65b76e2d87e9","year":2022},"citing_paper":{"arxiv_id":"2412.00659","last_updated":"2024-12-01T03:42:17Z","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-12T05:23:01.032626Z"},"links":{"citing_paper":"/paper/2412.00659"},"observation_digest":"sha256:7c555a25d89f271b5b7eab9a0d9e809325a4f5e826e88bafa8181293113580b7","observation_id":"2361136e-5563-4855-bfcc-67822d9fb63a","resolution":{"observed_at":"2026-08-12T05:23:01.118453Z","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":"2412.00659","last_updated":"2024-12-01T03:42:17Z","latest_version":1,"primary_category":"math.OC","snapshot_observed_at":"2026-08-12T05:06:25.422190Z","submitted_at":"2024-12-01T03:42:17Z","title":"Linear Convergence Analysis of Single-loop Algorithm for Bilevel Optimization via Small-gain Theorem"},"reference_resolution":{"displayed":25,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":11,"verified_exact":1,"verified_fuzzy":13},"total_outbound_references":25},"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 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2412.00659."}