{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:J5TAESLZ5W5BI2J3XU65KOMKIY","short_pith_number":"pith:J5TAESLZ","canonical_record":{"source":{"id":"2210.06671","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-10-13T01:58:02Z","cross_cats_sorted":[],"title_canon_sha256":"f0a467c9abe26d53f963c3c6b94bf3e7f289c2d31ca0e58699caa8abeaffabb4","abstract_canon_sha256":"83cc64a11178a9cccd655e5e21a601f59990b41005fc6716b2bd06f39069cdec"},"schema_version":"1.0"},"canonical_sha256":"4f66024979edba14693bbd3dd5398a4634206504adb8452d17dc32cc1c34486d","source":{"kind":"arxiv","id":"2210.06671","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.06671","created_at":"2026-07-05T05:06:18Z"},{"alias_kind":"arxiv_version","alias_value":"2210.06671v1","created_at":"2026-07-05T05:06:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.06671","created_at":"2026-07-05T05:06:18Z"},{"alias_kind":"pith_short_12","alias_value":"J5TAESLZ5W5B","created_at":"2026-07-05T05:06:18Z"},{"alias_kind":"pith_short_16","alias_value":"J5TAESLZ5W5BI2J3","created_at":"2026-07-05T05:06:18Z"},{"alias_kind":"pith_short_8","alias_value":"J5TAESLZ","created_at":"2026-07-05T05:06:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:J5TAESLZ5W5BI2J3XU65KOMKIY","target":"record","payload":{"canonical_record":{"source":{"id":"2210.06671","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-10-13T01:58:02Z","cross_cats_sorted":[],"title_canon_sha256":"f0a467c9abe26d53f963c3c6b94bf3e7f289c2d31ca0e58699caa8abeaffabb4","abstract_canon_sha256":"83cc64a11178a9cccd655e5e21a601f59990b41005fc6716b2bd06f39069cdec"},"schema_version":"1.0"},"canonical_sha256":"4f66024979edba14693bbd3dd5398a4634206504adb8452d17dc32cc1c34486d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:06:18.553599Z","signature_b64":"BLhEDNRdzhU89HX9O4Ef+YyMovQrALOB7NdS7lYrVzPyIgwkm6ugPaZWtg+Pma9p6dwYM8Q83xZgikXs9vYNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f66024979edba14693bbd3dd5398a4634206504adb8452d17dc32cc1c34486d","last_reissued_at":"2026-07-05T05:06:18.553071Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:06:18.553071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2210.06671","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":"2026-07-05T05:06:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TFbZdsss605X+J0koMzdaNRij9BHeImboAlRO/keiIATttM2LrR1Yjocl6KIIfvBoQbTI67eP6dG4WxQveU1Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T06:32:14.123846Z"},"content_sha256":"8da889ea7ddb10bff53ff841a6cf931a249839ee5e1d34833d27aff3ec26b905","schema_version":"1.0","event_id":"sha256:8da889ea7ddb10bff53ff841a6cf931a249839ee5e1d34833d27aff3ec26b905"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:J5TAESLZ5W5BI2J3XU65KOMKIY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wasserstein Barycenter-based Model Fusion and Linear Mode Connectivity of Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Aditya Kumar Akash, Nicol\\'as Garc\\'ia Trillos, Sixu Li","submitted_at":"2022-10-13T01:58:02Z","abstract_excerpt":"Based on the concepts of Wasserstein barycenter (WB) and Gromov-Wasserstein barycenter (GWB), we propose a unified mathematical framework for neural network (NN) model fusion and utilize it to reveal new insights about the linear mode connectivity of SGD solutions. In our framework, the fusion occurs in a layer-wise manner and builds on an interpretation of a node in a network as a function of the layer preceding it. The versatility of our mathematical framework allows us to talk about model fusion and linear mode connectivity for a broad class of NNs, including fully connected NN, CNN, ResNet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.06671","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/2210.06671/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":"2026-07-05T05:06:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jfD7nIm+qc0NuaPaj+bvobt4xmpF/qBXrLLs4tYSj/pMSlNCSEj9y9ZkEi+tcnB67MRwZBlGBIr21THaLwe5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T06:32:14.125521Z"},"content_sha256":"514899ffb08f10b699ccd7594bc24a65a10be67906f8a2103037459399842241","schema_version":"1.0","event_id":"sha256:514899ffb08f10b699ccd7594bc24a65a10be67906f8a2103037459399842241"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J5TAESLZ5W5BI2J3XU65KOMKIY/bundle.json","state_url":"https://pith.science/pith/J5TAESLZ5W5BI2J3XU65KOMKIY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J5TAESLZ5W5BI2J3XU65KOMKIY/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":"2026-08-10T06:32:14Z","links":{"resolver":"https://pith.science/pith/J5TAESLZ5W5BI2J3XU65KOMKIY","bundle":"https://pith.science/pith/J5TAESLZ5W5BI2J3XU65KOMKIY/bundle.json","state":"https://pith.science/pith/J5TAESLZ5W5BI2J3XU65KOMKIY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J5TAESLZ5W5BI2J3XU65KOMKIY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:J5TAESLZ5W5BI2J3XU65KOMKIY","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":"83cc64a11178a9cccd655e5e21a601f59990b41005fc6716b2bd06f39069cdec","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-10-13T01:58:02Z","title_canon_sha256":"f0a467c9abe26d53f963c3c6b94bf3e7f289c2d31ca0e58699caa8abeaffabb4"},"schema_version":"1.0","source":{"id":"2210.06671","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.06671","created_at":"2026-07-05T05:06:18Z"},{"alias_kind":"arxiv_version","alias_value":"2210.06671v1","created_at":"2026-07-05T05:06:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.06671","created_at":"2026-07-05T05:06:18Z"},{"alias_kind":"pith_short_12","alias_value":"J5TAESLZ5W5B","created_at":"2026-07-05T05:06:18Z"},{"alias_kind":"pith_short_16","alias_value":"J5TAESLZ5W5BI2J3","created_at":"2026-07-05T05:06:18Z"},{"alias_kind":"pith_short_8","alias_value":"J5TAESLZ","created_at":"2026-07-05T05:06:18Z"}],"graph_snapshots":[{"event_id":"sha256:514899ffb08f10b699ccd7594bc24a65a10be67906f8a2103037459399842241","target":"graph","created_at":"2026-07-05T05:06:18Z","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/2210.06671/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Based on the concepts of Wasserstein barycenter (WB) and Gromov-Wasserstein barycenter (GWB), we propose a unified mathematical framework for neural network (NN) model fusion and utilize it to reveal new insights about the linear mode connectivity of SGD solutions. In our framework, the fusion occurs in a layer-wise manner and builds on an interpretation of a node in a network as a function of the layer preceding it. The versatility of our mathematical framework allows us to talk about model fusion and linear mode connectivity for a broad class of NNs, including fully connected NN, CNN, ResNet","authors_text":"Aditya Kumar Akash, Nicol\\'as Garc\\'ia Trillos, Sixu Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-10-13T01:58:02Z","title":"Wasserstein Barycenter-based Model Fusion and Linear Mode Connectivity of Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.06671","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":"sha256:8da889ea7ddb10bff53ff841a6cf931a249839ee5e1d34833d27aff3ec26b905","target":"record","created_at":"2026-07-05T05:06:18Z","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":"83cc64a11178a9cccd655e5e21a601f59990b41005fc6716b2bd06f39069cdec","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2022-10-13T01:58:02Z","title_canon_sha256":"f0a467c9abe26d53f963c3c6b94bf3e7f289c2d31ca0e58699caa8abeaffabb4"},"schema_version":"1.0","source":{"id":"2210.06671","kind":"arxiv","version":1}},"canonical_sha256":"4f66024979edba14693bbd3dd5398a4634206504adb8452d17dc32cc1c34486d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f66024979edba14693bbd3dd5398a4634206504adb8452d17dc32cc1c34486d","first_computed_at":"2026-07-05T05:06:18.553071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:06:18.553071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BLhEDNRdzhU89HX9O4Ef+YyMovQrALOB7NdS7lYrVzPyIgwkm6ugPaZWtg+Pma9p6dwYM8Q83xZgikXs9vYNCA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:06:18.553599Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.06671","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8da889ea7ddb10bff53ff841a6cf931a249839ee5e1d34833d27aff3ec26b905","sha256:514899ffb08f10b699ccd7594bc24a65a10be67906f8a2103037459399842241"],"state_sha256":"b4bec0f1cb930e0aef799404e09ea21d6c2d1e92826bef2bf36c7870c622b7b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8r7o4OpNJsfKtUAJjZEiFJ77S10UDV8ubuTAEO2QGHa+Fi2F4Jqw4LUuAOgOznSQMPbG9fETQ3XRoNkg7PjZBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T06:32:14.134341Z","bundle_sha256":"661c095133c3d24784be3ac2c8d9b870d49b8c8bf7ced38122829934b1081c9f"}}