{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:3OC3MVNVPTYIC7TMYLGQ4OJ4TY","short_pith_number":"pith:3OC3MVNV","canonical_record":{"source":{"id":"2501.13031","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-01-22T17:25:47Z","cross_cats_sorted":[],"title_canon_sha256":"04fd1aa65c284c03362dbf41559843816ba004c8c93eb6242eba5fe6bf2c1bda","abstract_canon_sha256":"1c9b7f98dc9339f5d80f6d5e47179ddd10935f6ee8cacfa269d9e8c216833efe"},"schema_version":"1.0"},"canonical_sha256":"db85b655b57cf0817e6cc2cd0e393c9e11606de6d433de07adec519140bfcc50","source":{"kind":"arxiv","id":"2501.13031","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.13031","created_at":"2026-07-05T11:09:44Z"},{"alias_kind":"arxiv_version","alias_value":"2501.13031v2","created_at":"2026-07-05T11:09:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.13031","created_at":"2026-07-05T11:09:44Z"},{"alias_kind":"pith_short_12","alias_value":"3OC3MVNVPTYI","created_at":"2026-07-05T11:09:44Z"},{"alias_kind":"pith_short_16","alias_value":"3OC3MVNVPTYIC7TM","created_at":"2026-07-05T11:09:44Z"},{"alias_kind":"pith_short_8","alias_value":"3OC3MVNV","created_at":"2026-07-05T11:09:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:3OC3MVNVPTYIC7TMYLGQ4OJ4TY","target":"record","payload":{"canonical_record":{"source":{"id":"2501.13031","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-01-22T17:25:47Z","cross_cats_sorted":[],"title_canon_sha256":"04fd1aa65c284c03362dbf41559843816ba004c8c93eb6242eba5fe6bf2c1bda","abstract_canon_sha256":"1c9b7f98dc9339f5d80f6d5e47179ddd10935f6ee8cacfa269d9e8c216833efe"},"schema_version":"1.0"},"canonical_sha256":"db85b655b57cf0817e6cc2cd0e393c9e11606de6d433de07adec519140bfcc50","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:09:44.675636Z","signature_b64":"4KVcRjqYwwudjUoCArKgJyvsNWmcWULWSDdRhSY7lGM+lAK+DjaQxtwo/eosI41GmC7MKGGGqzdSgauRiek7Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db85b655b57cf0817e6cc2cd0e393c9e11606de6d433de07adec519140bfcc50","last_reissued_at":"2026-07-05T11:09:44.675134Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:09:44.675134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.13031","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":"2026-07-05T11:09:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5nVKluTtAfDYEVxiCl96pkRhWjVQfMmta84zDDHKqeal8qlseImWombvL2RUKRhePBecsA1VCIwY6NoGAaWJAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T04:36:07.184441Z"},"content_sha256":"c817222f0fb6645d9b75ecc22cc28c7f56266b5d444b259b51622236cf30c1c8","schema_version":"1.0","event_id":"sha256:c817222f0fb6645d9b75ecc22cc28c7f56266b5d444b259b51622236cf30c1c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:3OC3MVNVPTYIC7TMYLGQ4OJ4TY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Probabilistic Model for Non-Contrastive Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Debarghya Ghoshdastidar, Maximilian Fleissner, Pascal Esser","submitted_at":"2025-01-22T17:25:47Z","abstract_excerpt":"Self-supervised learning (SSL) aims to find meaningful representations from unlabeled data by encoding semantic similarities through data augmentations. Despite its current popularity, theoretical insights about SSL are still scarce. For example, it is not yet known whether commonly used SSL loss functions can be related to a statistical model, much in the same as OLS, generalized linear models or PCA naturally emerge as maximum likelihood estimates of an underlying generative process. In this short paper, we consider a latent variable statistical model for SSL that exhibits an interesting pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.13031","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/2501.13031/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":"2026-07-05T11:09:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qzoki7cbwdj/rXEmGgiJqZgg6+n11a2VyDaIxpQdeP5vHldNX2OelMbcpL53LI8EKrc6mr/NCxvWLy4jQS6nBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T04:36:07.185342Z"},"content_sha256":"667a8e3339bd1a0da127c1db03e6454c8c929df98552d93f5f7a9e6843703dde","schema_version":"1.0","event_id":"sha256:667a8e3339bd1a0da127c1db03e6454c8c929df98552d93f5f7a9e6843703dde"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3OC3MVNVPTYIC7TMYLGQ4OJ4TY/bundle.json","state_url":"https://pith.science/pith/3OC3MVNVPTYIC7TMYLGQ4OJ4TY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3OC3MVNVPTYIC7TMYLGQ4OJ4TY/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":"2026-08-18T04:36:07Z","links":{"resolver":"https://pith.science/pith/3OC3MVNVPTYIC7TMYLGQ4OJ4TY","bundle":"https://pith.science/pith/3OC3MVNVPTYIC7TMYLGQ4OJ4TY/bundle.json","state":"https://pith.science/pith/3OC3MVNVPTYIC7TMYLGQ4OJ4TY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3OC3MVNVPTYIC7TMYLGQ4OJ4TY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3OC3MVNVPTYIC7TMYLGQ4OJ4TY","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":"1c9b7f98dc9339f5d80f6d5e47179ddd10935f6ee8cacfa269d9e8c216833efe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-01-22T17:25:47Z","title_canon_sha256":"04fd1aa65c284c03362dbf41559843816ba004c8c93eb6242eba5fe6bf2c1bda"},"schema_version":"1.0","source":{"id":"2501.13031","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.13031","created_at":"2026-07-05T11:09:44Z"},{"alias_kind":"arxiv_version","alias_value":"2501.13031v2","created_at":"2026-07-05T11:09:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.13031","created_at":"2026-07-05T11:09:44Z"},{"alias_kind":"pith_short_12","alias_value":"3OC3MVNVPTYI","created_at":"2026-07-05T11:09:44Z"},{"alias_kind":"pith_short_16","alias_value":"3OC3MVNVPTYIC7TM","created_at":"2026-07-05T11:09:44Z"},{"alias_kind":"pith_short_8","alias_value":"3OC3MVNV","created_at":"2026-07-05T11:09:44Z"}],"graph_snapshots":[{"event_id":"sha256:667a8e3339bd1a0da127c1db03e6454c8c929df98552d93f5f7a9e6843703dde","target":"graph","created_at":"2026-07-05T11:09:44Z","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/2501.13031/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Self-supervised learning (SSL) aims to find meaningful representations from unlabeled data by encoding semantic similarities through data augmentations. Despite its current popularity, theoretical insights about SSL are still scarce. For example, it is not yet known whether commonly used SSL loss functions can be related to a statistical model, much in the same as OLS, generalized linear models or PCA naturally emerge as maximum likelihood estimates of an underlying generative process. In this short paper, we consider a latent variable statistical model for SSL that exhibits an interesting pro","authors_text":"Debarghya Ghoshdastidar, Maximilian Fleissner, Pascal Esser","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-01-22T17:25:47Z","title":"A Probabilistic Model for Non-Contrastive Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.13031","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:c817222f0fb6645d9b75ecc22cc28c7f56266b5d444b259b51622236cf30c1c8","target":"record","created_at":"2026-07-05T11:09:44Z","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":"1c9b7f98dc9339f5d80f6d5e47179ddd10935f6ee8cacfa269d9e8c216833efe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-01-22T17:25:47Z","title_canon_sha256":"04fd1aa65c284c03362dbf41559843816ba004c8c93eb6242eba5fe6bf2c1bda"},"schema_version":"1.0","source":{"id":"2501.13031","kind":"arxiv","version":2}},"canonical_sha256":"db85b655b57cf0817e6cc2cd0e393c9e11606de6d433de07adec519140bfcc50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db85b655b57cf0817e6cc2cd0e393c9e11606de6d433de07adec519140bfcc50","first_computed_at":"2026-07-05T11:09:44.675134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:09:44.675134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4KVcRjqYwwudjUoCArKgJyvsNWmcWULWSDdRhSY7lGM+lAK+DjaQxtwo/eosI41GmC7MKGGGqzdSgauRiek7Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:09:44.675636Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.13031","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c817222f0fb6645d9b75ecc22cc28c7f56266b5d444b259b51622236cf30c1c8","sha256:667a8e3339bd1a0da127c1db03e6454c8c929df98552d93f5f7a9e6843703dde"],"state_sha256":"03fdb6c9bf30943724782df5bb1166dbaa4ff50d6a1145456dc1475060e4df7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1//86E2e/iHLP05b00pb1inqKmqjZ76brlJPezH7J6Upb+8bDwcSBpCT0BeCn5I5GT+DO4Cq9Dabd2QbnNqaDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T04:36:07.192542Z","bundle_sha256":"bb54871f26769b973ec54291aa5e63fc3a497f8dd952e079c8ad77420133a50c"}}