{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2X2GCH5DNSJVCXNLO5GRZOKLP4","short_pith_number":"pith:2X2GCH5D","canonical_record":{"source":{"id":"1604.07356","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-04-25T18:33:59Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"8274cbc3e729077b1a10735db6b645e499e76d5c1f66b4a481890a550ad57c0b","abstract_canon_sha256":"551f51f51f4a4805ea9d18dace353f17e14955bf47cfd701dc8531f7d3a1b768"},"schema_version":"1.0"},"canonical_sha256":"d5f4611fa36c93515dab774d1cb94b7f2e158c38c366bf36f4ea816e7f8d8b99","source":{"kind":"arxiv","id":"1604.07356","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.07356","created_at":"2026-05-18T01:16:22Z"},{"alias_kind":"arxiv_version","alias_value":"1604.07356v1","created_at":"2026-05-18T01:16:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.07356","created_at":"2026-05-18T01:16:22Z"},{"alias_kind":"pith_short_12","alias_value":"2X2GCH5DNSJV","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2X2GCH5DNSJVCXNL","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2X2GCH5D","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2X2GCH5DNSJVCXNLO5GRZOKLP4","target":"record","payload":{"canonical_record":{"source":{"id":"1604.07356","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-04-25T18:33:59Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"8274cbc3e729077b1a10735db6b645e499e76d5c1f66b4a481890a550ad57c0b","abstract_canon_sha256":"551f51f51f4a4805ea9d18dace353f17e14955bf47cfd701dc8531f7d3a1b768"},"schema_version":"1.0"},"canonical_sha256":"d5f4611fa36c93515dab774d1cb94b7f2e158c38c366bf36f4ea816e7f8d8b99","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:22.340767Z","signature_b64":"DS0r9rBJxKtpuK3rDFQehrlTT3BKCZsGbCHJBleBHdu2NBQJGthu3nMZGUW2FR9q4hnfDqDc2JxSkWGSmGXBAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5f4611fa36c93515dab774d1cb94b7f2e158c38c366bf36f4ea816e7f8d8b99","last_reissued_at":"2026-05-18T01:16:22.340108Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:22.340108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.07356","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:16:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0FCviQPWYwLl8vppIsfVV/4JmIW22fks4wKNJKjmhADnK6xnhXD4BJGzBmOU10Tul36UZYFaqa9aragdwTm9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:46:15.715162Z"},"content_sha256":"c5118fcb6b8cd3496b060776edd1f5a100a03fe87470c1e5e3c344eb48e3da9e","schema_version":"1.0","event_id":"sha256:c5118fcb6b8cd3496b060776edd1f5a100a03fe87470c1e5e3c344eb48e3da9e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2X2GCH5DNSJVCXNLO5GRZOKLP4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast nonlinear embeddings via structured matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Francois Fagan, Krzysztof Choromanski","submitted_at":"2016-04-25T18:33:59Z","abstract_excerpt":"We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above that, the presented framework covers multivariate randomized functions. As a byproduct, we propose an algorithmic approach that also leads to a significant reduction of space complexity. Our method is based on careful recycling of Gaussian vectors into structured matrices that share properties of fully random matrices. The quality of the proposed structured a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07356","kind":"arxiv","version":1},"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":"2026-05-18T01:16:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+F6FGbTYBcdb4s6pa6OOD9kHxmD6Y0EFLuIf/TFIY5T4hUHNG30J+eU5I7I5idZIwYBVI3vo+j2CLUnppcLzCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T09:46:15.715761Z"},"content_sha256":"b207840b0fd78907fdaa915048d839277b421d00c6a349385f97c064a17aa611","schema_version":"1.0","event_id":"sha256:b207840b0fd78907fdaa915048d839277b421d00c6a349385f97c064a17aa611"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2X2GCH5DNSJVCXNLO5GRZOKLP4/bundle.json","state_url":"https://pith.science/pith/2X2GCH5DNSJVCXNLO5GRZOKLP4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2X2GCH5DNSJVCXNLO5GRZOKLP4/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":"2026-06-12T09:46:15Z","links":{"resolver":"https://pith.science/pith/2X2GCH5DNSJVCXNLO5GRZOKLP4","bundle":"https://pith.science/pith/2X2GCH5DNSJVCXNLO5GRZOKLP4/bundle.json","state":"https://pith.science/pith/2X2GCH5DNSJVCXNLO5GRZOKLP4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2X2GCH5DNSJVCXNLO5GRZOKLP4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2X2GCH5DNSJVCXNLO5GRZOKLP4","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":"551f51f51f4a4805ea9d18dace353f17e14955bf47cfd701dc8531f7d3a1b768","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-04-25T18:33:59Z","title_canon_sha256":"8274cbc3e729077b1a10735db6b645e499e76d5c1f66b4a481890a550ad57c0b"},"schema_version":"1.0","source":{"id":"1604.07356","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.07356","created_at":"2026-05-18T01:16:22Z"},{"alias_kind":"arxiv_version","alias_value":"1604.07356v1","created_at":"2026-05-18T01:16:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.07356","created_at":"2026-05-18T01:16:22Z"},{"alias_kind":"pith_short_12","alias_value":"2X2GCH5DNSJV","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2X2GCH5DNSJVCXNL","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2X2GCH5D","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:b207840b0fd78907fdaa915048d839277b421d00c6a349385f97c064a17aa611","target":"graph","created_at":"2026-05-18T01:16:22Z","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":"We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above that, the presented framework covers multivariate randomized functions. As a byproduct, we propose an algorithmic approach that also leads to a significant reduction of space complexity. Our method is based on careful recycling of Gaussian vectors into structured matrices that share properties of fully random matrices. The quality of the proposed structured a","authors_text":"Francois Fagan, Krzysztof Choromanski","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-04-25T18:33:59Z","title":"Fast nonlinear embeddings via structured matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07356","kind":"arxiv","version":1},"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:c5118fcb6b8cd3496b060776edd1f5a100a03fe87470c1e5e3c344eb48e3da9e","target":"record","created_at":"2026-05-18T01:16:22Z","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":"551f51f51f4a4805ea9d18dace353f17e14955bf47cfd701dc8531f7d3a1b768","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-04-25T18:33:59Z","title_canon_sha256":"8274cbc3e729077b1a10735db6b645e499e76d5c1f66b4a481890a550ad57c0b"},"schema_version":"1.0","source":{"id":"1604.07356","kind":"arxiv","version":1}},"canonical_sha256":"d5f4611fa36c93515dab774d1cb94b7f2e158c38c366bf36f4ea816e7f8d8b99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5f4611fa36c93515dab774d1cb94b7f2e158c38c366bf36f4ea816e7f8d8b99","first_computed_at":"2026-05-18T01:16:22.340108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:22.340108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DS0r9rBJxKtpuK3rDFQehrlTT3BKCZsGbCHJBleBHdu2NBQJGthu3nMZGUW2FR9q4hnfDqDc2JxSkWGSmGXBAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:22.340767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.07356","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5118fcb6b8cd3496b060776edd1f5a100a03fe87470c1e5e3c344eb48e3da9e","sha256:b207840b0fd78907fdaa915048d839277b421d00c6a349385f97c064a17aa611"],"state_sha256":"85507dac3eb8a79460436bf1ae03460741b220bdfd6d11eb3da854651be84728"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tHbOkhyaKeq5oO2oKK7pDlKdZO0+eWBIuURo/2fypEQRl2pvaEyc2BaarSzitni5+s6I1LbZA94x0mgtTYjHDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T09:46:15.718425Z","bundle_sha256":"09686735c3bc62b06a7c61a2a2ecf4d9b4ca7d53a6f741a28bef4b929fc658cf"}}