{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:5JRYYR6WOTLL4VWXU6GGW5F4DE","short_pith_number":"pith:5JRYYR6W","canonical_record":{"source":{"id":"2305.12568","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-05-21T21:09:53Z","cross_cats_sorted":[],"title_canon_sha256":"12e5f64c8a160dd225918099615dd24c5f4ca70954ccdb9ce143616cecaa0496","abstract_canon_sha256":"6520641ed77e426bf21020a24a5493c49488a9bf9b308b345d104b54b310d832"},"schema_version":"1.0"},"canonical_sha256":"ea638c47d674d6be56d7a78c6b74bc1931fd044cf0f7628392d899564ef82d53","source":{"kind":"arxiv","id":"2305.12568","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.12568","created_at":"2026-07-05T08:10:13Z"},{"alias_kind":"arxiv_version","alias_value":"2305.12568v2","created_at":"2026-07-05T08:10:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.12568","created_at":"2026-07-05T08:10:13Z"},{"alias_kind":"pith_short_12","alias_value":"5JRYYR6WOTLL","created_at":"2026-07-05T08:10:13Z"},{"alias_kind":"pith_short_16","alias_value":"5JRYYR6WOTLL4VWX","created_at":"2026-07-05T08:10:13Z"},{"alias_kind":"pith_short_8","alias_value":"5JRYYR6W","created_at":"2026-07-05T08:10:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:5JRYYR6WOTLL4VWXU6GGW5F4DE","target":"record","payload":{"canonical_record":{"source":{"id":"2305.12568","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-05-21T21:09:53Z","cross_cats_sorted":[],"title_canon_sha256":"12e5f64c8a160dd225918099615dd24c5f4ca70954ccdb9ce143616cecaa0496","abstract_canon_sha256":"6520641ed77e426bf21020a24a5493c49488a9bf9b308b345d104b54b310d832"},"schema_version":"1.0"},"canonical_sha256":"ea638c47d674d6be56d7a78c6b74bc1931fd044cf0f7628392d899564ef82d53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:10:13.921001Z","signature_b64":"Qkfqo9NVzrG0awHL+6Rhg587tvpnYORidqlmCN3dT9mwUy+hwtO1KVO+8SJpZC+IF+yOLZmMIvm6Ak9GCkilBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea638c47d674d6be56d7a78c6b74bc1931fd044cf0f7628392d899564ef82d53","last_reissued_at":"2026-07-05T08:10:13.920572Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:10:13.920572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2305.12568","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:10:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/TDfnKaM0VWQFJjO4QoVAqAw9mkvNv+ahhayCvzSyCk9PPjlHqUIUgjQ24T4aQaUa8vIzi2npil4dATnwkAeAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T02:16:02.490492Z"},"content_sha256":"6b3b80c038d0369491a55ffc93636324fa6b2db60a24c61c44807bfaa3bd163e","schema_version":"1.0","event_id":"sha256:6b3b80c038d0369491a55ffc93636324fa6b2db60a24c61c44807bfaa3bd163e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:5JRYYR6WOTLL4VWXU6GGW5F4DE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Det-CGD: Compressed Gradient Descent with Matrix Stepsizes for Non-Convex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Avetik Karagulyan, Hanmin Li, Peter Richt\\'arik","submitted_at":"2023-05-21T21:09:53Z","abstract_excerpt":"This paper introduces a new method for minimizing matrix-smooth non-convex objectives through the use of novel Compressed Gradient Descent (CGD) algorithms enhanced with a matrix-valued stepsize. The proposed algorithms are theoretically analyzed first in the single-node and subsequently in the distributed settings. Our theoretical results reveal that the matrix stepsize in CGD can capture the objective's structure and lead to faster convergence compared to a scalar stepsize. As a byproduct of our general results, we emphasize the importance of selecting the compression mechanism and the matri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.12568","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.12568/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:10:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"50NEQZyAisue+THKmqrTjdaXLgA5bvGlH9QTavJsgWKdTTR9LLp2+EVVwBAuH/2vo0C8cgcC/mqyIDdd9/8nBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T02:16:02.491097Z"},"content_sha256":"9134e781343aa83a925547e33fbdf4ff713f363e04b6b202cb0b7ea8697a2840","schema_version":"1.0","event_id":"sha256:9134e781343aa83a925547e33fbdf4ff713f363e04b6b202cb0b7ea8697a2840"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5JRYYR6WOTLL4VWXU6GGW5F4DE/bundle.json","state_url":"https://pith.science/pith/5JRYYR6WOTLL4VWXU6GGW5F4DE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5JRYYR6WOTLL4VWXU6GGW5F4DE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-05T02:16:02Z","links":{"resolver":"https://pith.science/pith/5JRYYR6WOTLL4VWXU6GGW5F4DE","bundle":"https://pith.science/pith/5JRYYR6WOTLL4VWXU6GGW5F4DE/bundle.json","state":"https://pith.science/pith/5JRYYR6WOTLL4VWXU6GGW5F4DE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5JRYYR6WOTLL4VWXU6GGW5F4DE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:5JRYYR6WOTLL4VWXU6GGW5F4DE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6520641ed77e426bf21020a24a5493c49488a9bf9b308b345d104b54b310d832","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-05-21T21:09:53Z","title_canon_sha256":"12e5f64c8a160dd225918099615dd24c5f4ca70954ccdb9ce143616cecaa0496"},"schema_version":"1.0","source":{"id":"2305.12568","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.12568","created_at":"2026-07-05T08:10:13Z"},{"alias_kind":"arxiv_version","alias_value":"2305.12568v2","created_at":"2026-07-05T08:10:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.12568","created_at":"2026-07-05T08:10:13Z"},{"alias_kind":"pith_short_12","alias_value":"5JRYYR6WOTLL","created_at":"2026-07-05T08:10:13Z"},{"alias_kind":"pith_short_16","alias_value":"5JRYYR6WOTLL4VWX","created_at":"2026-07-05T08:10:13Z"},{"alias_kind":"pith_short_8","alias_value":"5JRYYR6W","created_at":"2026-07-05T08:10:13Z"}],"graph_snapshots":[{"event_id":"sha256:9134e781343aa83a925547e33fbdf4ff713f363e04b6b202cb0b7ea8697a2840","target":"graph","created_at":"2026-07-05T08:10:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2305.12568/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper introduces a new method for minimizing matrix-smooth non-convex objectives through the use of novel Compressed Gradient Descent (CGD) algorithms enhanced with a matrix-valued stepsize. The proposed algorithms are theoretically analyzed first in the single-node and subsequently in the distributed settings. Our theoretical results reveal that the matrix stepsize in CGD can capture the objective's structure and lead to faster convergence compared to a scalar stepsize. As a byproduct of our general results, we emphasize the importance of selecting the compression mechanism and the matri","authors_text":"Avetik Karagulyan, Hanmin Li, Peter Richt\\'arik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-05-21T21:09:53Z","title":"Det-CGD: Compressed Gradient Descent with Matrix Stepsizes for Non-Convex Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.12568","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6b3b80c038d0369491a55ffc93636324fa6b2db60a24c61c44807bfaa3bd163e","target":"record","created_at":"2026-07-05T08:10:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6520641ed77e426bf21020a24a5493c49488a9bf9b308b345d104b54b310d832","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-05-21T21:09:53Z","title_canon_sha256":"12e5f64c8a160dd225918099615dd24c5f4ca70954ccdb9ce143616cecaa0496"},"schema_version":"1.0","source":{"id":"2305.12568","kind":"arxiv","version":2}},"canonical_sha256":"ea638c47d674d6be56d7a78c6b74bc1931fd044cf0f7628392d899564ef82d53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea638c47d674d6be56d7a78c6b74bc1931fd044cf0f7628392d899564ef82d53","first_computed_at":"2026-07-05T08:10:13.920572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:10:13.920572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qkfqo9NVzrG0awHL+6Rhg587tvpnYORidqlmCN3dT9mwUy+hwtO1KVO+8SJpZC+IF+yOLZmMIvm6Ak9GCkilBw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:10:13.921001Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.12568","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b3b80c038d0369491a55ffc93636324fa6b2db60a24c61c44807bfaa3bd163e","sha256:9134e781343aa83a925547e33fbdf4ff713f363e04b6b202cb0b7ea8697a2840"],"state_sha256":"d99a6f3c0175c0d52c0efa7ed44c42cf3af85e34323fa6f839b290501e585b24"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BZMuyso5UwHhvcfKC0aq+DfiiZfG+3PEU5jcnKFsi5CAOInVNWrKYxoHrn2/0anMJ/t22Q6hshDowUdQLy0TBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T02:16:02.496763Z","bundle_sha256":"e879e2c558e426d18b7d850d95f37f609bba403096998cdc8e4880d52b7d7c7a"}}