{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GU4KLHIQ43NURRP5ZCXE4MZQZQ","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":"a31aa834b89642a91c9290c12552a8a469e5c5672d4bdcdd3a6621c736408618","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-11-08T06:07:25Z","title_canon_sha256":"0e18c0b940c732eaf512136d1103e9a13ee6cf9b1fab9ef684e5e10e4a4997f2"},"schema_version":"1.0","source":{"id":"1611.02401","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02401","created_at":"2026-05-18T00:03:25Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02401v7","created_at":"2026-05-18T00:03:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02401","created_at":"2026-05-18T00:03:25Z"},{"alias_kind":"pith_short_12","alias_value":"GU4KLHIQ43NU","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GU4KLHIQ43NURRP5","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GU4KLHIQ","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:4a90076a621794a7d16a8ea748a862637ed735bfb043a6b096275986f00ef3e0","target":"graph","created_at":"2026-05-18T00:03:25Z","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":"We consider the learning of algorithmic tasks by mere observation of input-output pairs. Rather than studying this as a black-box discrete regression problem with no assumption whatsoever on the input-output mapping, we concentrate on tasks that are amenable to the principle of divide and conquer, and study what are its implications in terms of learning. This principle creates a powerful inductive bias that we leverage with neural architectures that are defined recursively and dynamically, by learning two scale-invariant atomic operations: how to split a given input into smaller sets, and how ","authors_text":"Alex Nowak-Vila, David Folqu\\'e, Joan Bruna","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-11-08T06:07:25Z","title":"Divide and Conquer Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02401","kind":"arxiv","version":7},"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":"sha256:46f4e6bdc92b3f7cde8269ffc009335f656733dac2f9eb6190955b184cfc8b9c","target":"record","created_at":"2026-05-18T00:03:25Z","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":"a31aa834b89642a91c9290c12552a8a469e5c5672d4bdcdd3a6621c736408618","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-11-08T06:07:25Z","title_canon_sha256":"0e18c0b940c732eaf512136d1103e9a13ee6cf9b1fab9ef684e5e10e4a4997f2"},"schema_version":"1.0","source":{"id":"1611.02401","kind":"arxiv","version":7}},"canonical_sha256":"3538a59d10e6db48c5fdc8ae4e3330cc1827d670489ee4e8bee3bc7f806505b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3538a59d10e6db48c5fdc8ae4e3330cc1827d670489ee4e8bee3bc7f806505b1","first_computed_at":"2026-05-18T00:03:25.264994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:25.264994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jE3Vi8D4XodKt2LQOOsRjo3Enul4l1avo0wZebjNEu3+jRYBGq9c+BEytX3u4fkf0EXVbJLoOORt3mevdkTVDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:25.265518Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.02401","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46f4e6bdc92b3f7cde8269ffc009335f656733dac2f9eb6190955b184cfc8b9c","sha256:4a90076a621794a7d16a8ea748a862637ed735bfb043a6b096275986f00ef3e0"],"state_sha256":"2cd53a45fbce7a39fc8cc9018a51d79a03ab85977ce072f991cf096ed9bbd178"}