{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:2DKG2C4EZK4WRCGN6KG2U3RUTR","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":"8337f4746eddbcef74faa8edad03441cabd2117f78240efab35e250ff5c5d972","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-07-05T18:48:20Z","title_canon_sha256":"9a9210db2c6275a6a5b85596f621f7d5b1a7b4d6f3fa6b5af8282a33a4632a18"},"schema_version":"1.0","source":{"id":"2307.02598","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.02598","created_at":"2026-07-05T07:08:09Z"},{"alias_kind":"arxiv_version","alias_value":"2307.02598v2","created_at":"2026-07-05T07:08:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.02598","created_at":"2026-07-05T07:08:09Z"},{"alias_kind":"pith_short_12","alias_value":"2DKG2C4EZK4W","created_at":"2026-07-05T07:08:09Z"},{"alias_kind":"pith_short_16","alias_value":"2DKG2C4EZK4WRCGN","created_at":"2026-07-05T07:08:09Z"},{"alias_kind":"pith_short_8","alias_value":"2DKG2C4E","created_at":"2026-07-05T07:08:09Z"}],"graph_snapshots":[{"event_id":"sha256:e9f3f1330ba14b9c9c14b375f3e2d3bbf0f2b810b5587c38c20af43d1fe52624","target":"graph","created_at":"2026-07-05T07:08:09Z","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/2307.02598/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We tackle the problems of latent variables identification and ``out-of-support'' image generation in representation learning. We show that both are possible for a class of decoders that we call additive, which are reminiscent of decoders used for object-centric representation learning (OCRL) and well suited for images that can be decomposed as a sum of object-specific images. We provide conditions under which exactly solving the reconstruction problem using an additive decoder is guaranteed to identify the blocks of latent variables up to permutation and block-wise invertible transformations. ","authors_text":"Divyat Mahajan, Ioannis Mitliagkas, S\\'ebastien Lachapelle, Simon Lacoste-Julien","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-07-05T18:48:20Z","title":"Additive Decoders for Latent Variables Identification and Cartesian-Product Extrapolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.02598","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:e3ca87fa46100f7f4857b306bac8c7150c7773c02dd13a082ad7f0387b6a7ceb","target":"record","created_at":"2026-07-05T07:08:09Z","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":"8337f4746eddbcef74faa8edad03441cabd2117f78240efab35e250ff5c5d972","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-07-05T18:48:20Z","title_canon_sha256":"9a9210db2c6275a6a5b85596f621f7d5b1a7b4d6f3fa6b5af8282a33a4632a18"},"schema_version":"1.0","source":{"id":"2307.02598","kind":"arxiv","version":2}},"canonical_sha256":"d0d46d0b84cab96888cdf28daa6e349c666c822d00c662b2228ecf80e8a70d88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0d46d0b84cab96888cdf28daa6e349c666c822d00c662b2228ecf80e8a70d88","first_computed_at":"2026-07-05T07:08:09.117061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:08:09.117061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UQqEZuUaNDOB2THyPWXTks7zAe28jIXXjxE7nS6X3p2xTCorWt39hO0iubMB184s+GHcoYcRs1TADqk8HeY6Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T07:08:09.117540Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.02598","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3ca87fa46100f7f4857b306bac8c7150c7773c02dd13a082ad7f0387b6a7ceb","sha256:e9f3f1330ba14b9c9c14b375f3e2d3bbf0f2b810b5587c38c20af43d1fe52624"],"state_sha256":"296caa95b7e23ad48232fd0a8db1999ae60a3415b43b3d127bd21d4d542cb68f"}