{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:TYZ2MHBPDFHQ3ISS2CNFEXGJ2Y","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":"a3931903e0f72a8e4763791cb45da06ed698c45da154750793ad03fb07ef75ab","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-06-12T17:51:20Z","title_canon_sha256":"8c203122d0de6bbab3578a7ecd900f02bd5cde43e0621d291504b3b033b837f1"},"schema_version":"1.0","source":{"id":"2006.07360","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.07360","created_at":"2026-07-05T01:10:41Z"},{"alias_kind":"arxiv_version","alias_value":"2006.07360v2","created_at":"2026-07-05T01:10:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.07360","created_at":"2026-07-05T01:10:41Z"},{"alias_kind":"pith_short_12","alias_value":"TYZ2MHBPDFHQ","created_at":"2026-07-05T01:10:41Z"},{"alias_kind":"pith_short_16","alias_value":"TYZ2MHBPDFHQ3ISS","created_at":"2026-07-05T01:10:41Z"},{"alias_kind":"pith_short_8","alias_value":"TYZ2MHBP","created_at":"2026-07-05T01:10:41Z"}],"graph_snapshots":[{"event_id":"sha256:7e4e47de4faa7952f85f37ecf89b441a459dad5cdf46fd4e73999d72b057303d","target":"graph","created_at":"2026-07-05T01:10:41Z","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/2006.07360/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Neural networks have historically been built layerwise from the set of functions in ${f: \\mathbb{R}^n \\to \\mathbb{R}^m }$, i.e. with activations and weights/parameters represented by real numbers, $\\mathbb{R}$. Our work considers a richer set of objects for activations and weights, and undertakes a comprehensive study of alternative algebras as number representations by studying their performance on two challenging problems: large-scale image classification using the ImageNet dataset and language modeling using the enwiki8 and WikiText-103 datasets. We denote this broader class of models as Al","authors_text":"Erich Elsen, Jordan Hoffmann, Karen Simonyan, Simon Osindero, Simon Schmitt","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-06-12T17:51:20Z","title":"AlgebraNets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.07360","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":"sha256:274614bc09c575c773074f66fba7afaefa77b8c58907dd4fe41456b80ab9574b","target":"record","created_at":"2026-07-05T01:10:41Z","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":"a3931903e0f72a8e4763791cb45da06ed698c45da154750793ad03fb07ef75ab","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-06-12T17:51:20Z","title_canon_sha256":"8c203122d0de6bbab3578a7ecd900f02bd5cde43e0621d291504b3b033b837f1"},"schema_version":"1.0","source":{"id":"2006.07360","kind":"arxiv","version":2}},"canonical_sha256":"9e33a61c2f194f0da252d09a525cc9d62f45b76b4239fda7ce25fef845d5d9a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e33a61c2f194f0da252d09a525cc9d62f45b76b4239fda7ce25fef845d5d9a5","first_computed_at":"2026-07-05T01:10:41.002663Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:10:41.002663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BbFH1Q/cttzETjvtiMn48/lzfya6lYNGho+dEZRQCdVyEq2LGEFl1pqaSfUl6Y4F2ItCP1DYKDXF+FPpzxfZAg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:10:41.003203Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.07360","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:274614bc09c575c773074f66fba7afaefa77b8c58907dd4fe41456b80ab9574b","sha256:7e4e47de4faa7952f85f37ecf89b441a459dad5cdf46fd4e73999d72b057303d"],"state_sha256":"41678fa1824419c685c52492dea8a7fb37c4b3c16c7fdbb7ffb1de8721f50dcc"}