{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ATCYYAFIVLDY6DDXJNHQXSQKZI","short_pith_number":"pith:ATCYYAFI","canonical_record":{"source":{"id":"1812.03928","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-12-10T17:26:25Z","cross_cats_sorted":["cs.CV","stat.ML"],"title_canon_sha256":"c6388105f8ffcfb690dfc74d0cba31bead8704cfd69910dfdf8bab405ad5ca26","abstract_canon_sha256":"063514ade1ba94c01c95a0195b9690e204d9fb9d73c96cd6919c73ae1a9f3655"},"schema_version":"1.0"},"canonical_sha256":"04c58c00a8aac78f0c774b4f0bca0aca29583c6adf46c8a3cce5b4df1a549b92","source":{"kind":"arxiv","id":"1812.03928","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.03928","created_at":"2026-05-17T23:56:22Z"},{"alias_kind":"arxiv_version","alias_value":"1812.03928v3","created_at":"2026-05-17T23:56:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03928","created_at":"2026-05-17T23:56:22Z"},{"alias_kind":"pith_short_12","alias_value":"ATCYYAFIVLDY","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"ATCYYAFIVLDY6DDX","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"ATCYYAFI","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ATCYYAFIVLDY6DDXJNHQXSQKZI","target":"record","payload":{"canonical_record":{"source":{"id":"1812.03928","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-12-10T17:26:25Z","cross_cats_sorted":["cs.CV","stat.ML"],"title_canon_sha256":"c6388105f8ffcfb690dfc74d0cba31bead8704cfd69910dfdf8bab405ad5ca26","abstract_canon_sha256":"063514ade1ba94c01c95a0195b9690e204d9fb9d73c96cd6919c73ae1a9f3655"},"schema_version":"1.0"},"canonical_sha256":"04c58c00a8aac78f0c774b4f0bca0aca29583c6adf46c8a3cce5b4df1a549b92","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:22.877968Z","signature_b64":"x4MwxtOznJjEoYcLrCsYDhIZBFaU/0qLUCj8gPhIlIa+BZ6RjQuOe0OP+ZhnhR9BE0jBT3tbgIPVtFTijEneCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04c58c00a8aac78f0c774b4f0bca0aca29583c6adf46c8a3cce5b4df1a549b92","last_reissued_at":"2026-05-17T23:56:22.877267Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:22.877267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.03928","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pq0wEGN6HSeCkfe/tMkV6Z4rG9Yj4FhNDEg/S7WGlnTaQhVRn3pFozZHqc6eCODzo9s4fZ0CAKt52+iRHmePBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T20:06:17.532092Z"},"content_sha256":"2d730052ae752d2024b7497047d3c8eb786959266b3c42d0f9a96bb601e7479f","schema_version":"1.0","event_id":"sha256:2d730052ae752d2024b7497047d3c8eb786959266b3c42d0f9a96bb601e7479f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ATCYYAFIVLDY6DDXJNHQXSQKZI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning Representations of Sets through Optimized Permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","stat.ML"],"primary_cat":"cs.LG","authors_text":"Adam Pr\\\"ugel-Bennett, Jonathon Hare, Yan Zhang","submitted_at":"2018-12-10T17:26:25Z","abstract_excerpt":"Representations of sets are challenging to learn because operations on sets should be permutation-invariant. To this end, we propose a Permutation-Optimisation module that learns how to permute a set end-to-end. The permuted set can be further processed to learn a permutation-invariant representation of that set, avoiding a bottleneck in traditional set models. We demonstrate our model's ability to learn permutations and set representations with either explicit or implicit supervision on four datasets, on which we achieve state-of-the-art results: number sorting, image mosaics, classification "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03928","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-17T23:56:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r7kBH/+kN1GMP6236dScdQmCi+8wwCNvPyAP2Kbbw735Z7WGCJ7RPrTkQgEZprmsHQYMDauNFY3sOyDvATKfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T20:06:17.532498Z"},"content_sha256":"4a294ba0bef1c291515dc81ac98906ca087e8ebace27d4f0ae854b6b14cfb25c","schema_version":"1.0","event_id":"sha256:4a294ba0bef1c291515dc81ac98906ca087e8ebace27d4f0ae854b6b14cfb25c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ATCYYAFIVLDY6DDXJNHQXSQKZI/bundle.json","state_url":"https://pith.science/pith/ATCYYAFIVLDY6DDXJNHQXSQKZI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ATCYYAFIVLDY6DDXJNHQXSQKZI/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":"2026-05-21T20:06:17Z","links":{"resolver":"https://pith.science/pith/ATCYYAFIVLDY6DDXJNHQXSQKZI","bundle":"https://pith.science/pith/ATCYYAFIVLDY6DDXJNHQXSQKZI/bundle.json","state":"https://pith.science/pith/ATCYYAFIVLDY6DDXJNHQXSQKZI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ATCYYAFIVLDY6DDXJNHQXSQKZI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ATCYYAFIVLDY6DDXJNHQXSQKZI","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":"063514ade1ba94c01c95a0195b9690e204d9fb9d73c96cd6919c73ae1a9f3655","cross_cats_sorted":["cs.CV","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-12-10T17:26:25Z","title_canon_sha256":"c6388105f8ffcfb690dfc74d0cba31bead8704cfd69910dfdf8bab405ad5ca26"},"schema_version":"1.0","source":{"id":"1812.03928","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.03928","created_at":"2026-05-17T23:56:22Z"},{"alias_kind":"arxiv_version","alias_value":"1812.03928v3","created_at":"2026-05-17T23:56:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03928","created_at":"2026-05-17T23:56:22Z"},{"alias_kind":"pith_short_12","alias_value":"ATCYYAFIVLDY","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"ATCYYAFIVLDY6DDX","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"ATCYYAFI","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:4a294ba0bef1c291515dc81ac98906ca087e8ebace27d4f0ae854b6b14cfb25c","target":"graph","created_at":"2026-05-17T23:56:22Z","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"},"paper":{"abstract_excerpt":"Representations of sets are challenging to learn because operations on sets should be permutation-invariant. To this end, we propose a Permutation-Optimisation module that learns how to permute a set end-to-end. The permuted set can be further processed to learn a permutation-invariant representation of that set, avoiding a bottleneck in traditional set models. We demonstrate our model's ability to learn permutations and set representations with either explicit or implicit supervision on four datasets, on which we achieve state-of-the-art results: number sorting, image mosaics, classification ","authors_text":"Adam Pr\\\"ugel-Bennett, Jonathon Hare, Yan Zhang","cross_cats":["cs.CV","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-12-10T17:26:25Z","title":"Learning Representations of Sets through Optimized Permutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03928","kind":"arxiv","version":3},"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":"sha256:2d730052ae752d2024b7497047d3c8eb786959266b3c42d0f9a96bb601e7479f","target":"record","created_at":"2026-05-17T23:56:22Z","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":"063514ade1ba94c01c95a0195b9690e204d9fb9d73c96cd6919c73ae1a9f3655","cross_cats_sorted":["cs.CV","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-12-10T17:26:25Z","title_canon_sha256":"c6388105f8ffcfb690dfc74d0cba31bead8704cfd69910dfdf8bab405ad5ca26"},"schema_version":"1.0","source":{"id":"1812.03928","kind":"arxiv","version":3}},"canonical_sha256":"04c58c00a8aac78f0c774b4f0bca0aca29583c6adf46c8a3cce5b4df1a549b92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04c58c00a8aac78f0c774b4f0bca0aca29583c6adf46c8a3cce5b4df1a549b92","first_computed_at":"2026-05-17T23:56:22.877267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:22.877267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x4MwxtOznJjEoYcLrCsYDhIZBFaU/0qLUCj8gPhIlIa+BZ6RjQuOe0OP+ZhnhR9BE0jBT3tbgIPVtFTijEneCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:22.877968Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.03928","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d730052ae752d2024b7497047d3c8eb786959266b3c42d0f9a96bb601e7479f","sha256:4a294ba0bef1c291515dc81ac98906ca087e8ebace27d4f0ae854b6b14cfb25c"],"state_sha256":"a5ae2f87a6eff6262349e8e42e321d45def09ac102aca6db266b33ebce775eac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wd27ETRUiebjrJmWt9IxC2Uvwim0HJzw5NmZu3uNDCq8DawzsJUN9e/G9nyplR4YfLs74NtXMNPBDO/dYN4CDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T20:06:17.534710Z","bundle_sha256":"06cd4a82736989a24ef3d2d8d2f150954b23c3f689d839400a8638e68fc62d7e"}}