{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:BIPAZBEK3XUPOTVUJZXVTOC6CG","short_pith_number":"pith:BIPAZBEK","canonical_record":{"source":{"id":"2506.13984","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2025-06-08T17:48:44Z","cross_cats_sorted":["cs.AI","cs.LG"],"title_canon_sha256":"3f394795b55ead1aef4922baf73aa8de016ac5aceb9303664b37bae66bfe79f2","abstract_canon_sha256":"fbd30f412eb7c1c62310e68578dc10bd1cdccd474358829c35a99cf7d0d9e9d6"},"schema_version":"1.0"},"canonical_sha256":"0a1e0c848adde8f74eb44e6f59b85e11bc54261252ebca275754f87dde891257","source":{"kind":"arxiv","id":"2506.13984","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.13984","created_at":"2026-07-05T11:22:46Z"},{"alias_kind":"arxiv_version","alias_value":"2506.13984v1","created_at":"2026-07-05T11:22:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.13984","created_at":"2026-07-05T11:22:46Z"},{"alias_kind":"pith_short_12","alias_value":"BIPAZBEK3XUP","created_at":"2026-07-05T11:22:46Z"},{"alias_kind":"pith_short_16","alias_value":"BIPAZBEK3XUPOTVU","created_at":"2026-07-05T11:22:46Z"},{"alias_kind":"pith_short_8","alias_value":"BIPAZBEK","created_at":"2026-07-05T11:22:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:BIPAZBEK3XUPOTVUJZXVTOC6CG","target":"record","payload":{"canonical_record":{"source":{"id":"2506.13984","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2025-06-08T17:48:44Z","cross_cats_sorted":["cs.AI","cs.LG"],"title_canon_sha256":"3f394795b55ead1aef4922baf73aa8de016ac5aceb9303664b37bae66bfe79f2","abstract_canon_sha256":"fbd30f412eb7c1c62310e68578dc10bd1cdccd474358829c35a99cf7d0d9e9d6"},"schema_version":"1.0"},"canonical_sha256":"0a1e0c848adde8f74eb44e6f59b85e11bc54261252ebca275754f87dde891257","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:22:46.784072Z","signature_b64":"4PwY3u4sYHGIL9k3H4/RykAduNcZkHltrwJ/el5KP/bOLREdbcCITndFVEOLYh/jjX0VTNjTZufbuyEzCnmcDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a1e0c848adde8f74eb44e6f59b85e11bc54261252ebca275754f87dde891257","last_reissued_at":"2026-07-05T11:22:46.783591Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:22:46.783591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.13984","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:22:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W+IPrTbywVOB/vBNMUGJ0XKShChpnEQQkIepa3taFscIOoqybBynhKc7fWw9td0xtS/LLVhDDVHvqfyFlysnBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T06:58:03.406459Z"},"content_sha256":"bb25c12c8b6cca0958173279d6868d05d0e52fcf5cda07bcf5c497691fa82ec4","schema_version":"1.0","event_id":"sha256:bb25c12c8b6cca0958173279d6868d05d0e52fcf5cda07bcf5c497691fa82ec4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:BIPAZBEK3XUPOTVUJZXVTOC6CG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mirror Descent Using the Tempesta Generalized Multi-parametric Logarithms","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.AI","cs.LG"],"primary_cat":"stat.ML","authors_text":"Andrzej Cichocki","submitted_at":"2025-06-08T17:48:44Z","abstract_excerpt":"In this paper, we develop a wide class Mirror Descent (MD) algorithms, which play a key role in machine learning. For this purpose we formulated the constrained optimization problem, in which we exploits the Bregman divergence with the Tempesta multi-parametric deformation logarithm as a link function. This link function called also mirror function defines the mapping between the primal and dual spaces and is associated with a very-wide (in fact, theoretically infinite) class of generalized trace-form entropies. In order to derive novel MD updates, we estimate generalized exponential function,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.13984","kind":"arxiv","version":1},"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/2506.13984/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":"2026-07-05T11:22:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/vUNb2mhybbSAIM6A4vO1k+dUniVBTcZIxaF19w19r4ujRYmA00qTTQV4AkUo/OgUBxp7ekd1DECBI7ytku9Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T06:58:03.407103Z"},"content_sha256":"ed2153ed9b6a1f3867c8f0f014f34e2ed8c852ccca9f3162b619ab05799f8c95","schema_version":"1.0","event_id":"sha256:ed2153ed9b6a1f3867c8f0f014f34e2ed8c852ccca9f3162b619ab05799f8c95"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BIPAZBEK3XUPOTVUJZXVTOC6CG/bundle.json","state_url":"https://pith.science/pith/BIPAZBEK3XUPOTVUJZXVTOC6CG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BIPAZBEK3XUPOTVUJZXVTOC6CG/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":"2026-08-08T06:58:03Z","links":{"resolver":"https://pith.science/pith/BIPAZBEK3XUPOTVUJZXVTOC6CG","bundle":"https://pith.science/pith/BIPAZBEK3XUPOTVUJZXVTOC6CG/bundle.json","state":"https://pith.science/pith/BIPAZBEK3XUPOTVUJZXVTOC6CG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BIPAZBEK3XUPOTVUJZXVTOC6CG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BIPAZBEK3XUPOTVUJZXVTOC6CG","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":"fbd30f412eb7c1c62310e68578dc10bd1cdccd474358829c35a99cf7d0d9e9d6","cross_cats_sorted":["cs.AI","cs.LG"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2025-06-08T17:48:44Z","title_canon_sha256":"3f394795b55ead1aef4922baf73aa8de016ac5aceb9303664b37bae66bfe79f2"},"schema_version":"1.0","source":{"id":"2506.13984","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.13984","created_at":"2026-07-05T11:22:46Z"},{"alias_kind":"arxiv_version","alias_value":"2506.13984v1","created_at":"2026-07-05T11:22:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.13984","created_at":"2026-07-05T11:22:46Z"},{"alias_kind":"pith_short_12","alias_value":"BIPAZBEK3XUP","created_at":"2026-07-05T11:22:46Z"},{"alias_kind":"pith_short_16","alias_value":"BIPAZBEK3XUPOTVU","created_at":"2026-07-05T11:22:46Z"},{"alias_kind":"pith_short_8","alias_value":"BIPAZBEK","created_at":"2026-07-05T11:22:46Z"}],"graph_snapshots":[{"event_id":"sha256:ed2153ed9b6a1f3867c8f0f014f34e2ed8c852ccca9f3162b619ab05799f8c95","target":"graph","created_at":"2026-07-05T11:22:46Z","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/2506.13984/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we develop a wide class Mirror Descent (MD) algorithms, which play a key role in machine learning. For this purpose we formulated the constrained optimization problem, in which we exploits the Bregman divergence with the Tempesta multi-parametric deformation logarithm as a link function. This link function called also mirror function defines the mapping between the primal and dual spaces and is associated with a very-wide (in fact, theoretically infinite) class of generalized trace-form entropies. In order to derive novel MD updates, we estimate generalized exponential function,","authors_text":"Andrzej Cichocki","cross_cats":["cs.AI","cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2025-06-08T17:48:44Z","title":"Mirror Descent Using the Tempesta Generalized Multi-parametric Logarithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.13984","kind":"arxiv","version":1},"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:bb25c12c8b6cca0958173279d6868d05d0e52fcf5cda07bcf5c497691fa82ec4","target":"record","created_at":"2026-07-05T11:22:46Z","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":"fbd30f412eb7c1c62310e68578dc10bd1cdccd474358829c35a99cf7d0d9e9d6","cross_cats_sorted":["cs.AI","cs.LG"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2025-06-08T17:48:44Z","title_canon_sha256":"3f394795b55ead1aef4922baf73aa8de016ac5aceb9303664b37bae66bfe79f2"},"schema_version":"1.0","source":{"id":"2506.13984","kind":"arxiv","version":1}},"canonical_sha256":"0a1e0c848adde8f74eb44e6f59b85e11bc54261252ebca275754f87dde891257","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a1e0c848adde8f74eb44e6f59b85e11bc54261252ebca275754f87dde891257","first_computed_at":"2026-07-05T11:22:46.783591Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:22:46.783591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4PwY3u4sYHGIL9k3H4/RykAduNcZkHltrwJ/el5KP/bOLREdbcCITndFVEOLYh/jjX0VTNjTZufbuyEzCnmcDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:22:46.784072Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.13984","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb25c12c8b6cca0958173279d6868d05d0e52fcf5cda07bcf5c497691fa82ec4","sha256:ed2153ed9b6a1f3867c8f0f014f34e2ed8c852ccca9f3162b619ab05799f8c95"],"state_sha256":"85604808e3ba73d6260bce52cd4d81a63d89338a6ce4236e8a934c403c7c8d82"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"btW4PNXcrHzKAev7rord0Q5P5SxrlH2FmiskY//85B6aYSciKFkJOl1xBhlzdw5b9EtEAhJmuzzUkJKSba13BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T06:58:03.412560Z","bundle_sha256":"144e638018ada94777eefab4c515537f28cf63f8fb2ba3b3b2f690db3f6b5b42"}}