{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2BBSZDWS3HR4XA3OITAHLFKVC6","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":"30c6fb05ce8316db2ae00fca8e2ac65414b9b546882d809bceed1ceef95b4afd","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2016-01-25T21:29:11Z","title_canon_sha256":"9f6a587f9db608d3e3c091b6cc36f26b444cd6c36de4178a0d28e567d4ac5e08"},"schema_version":"1.0","source":{"id":"1601.06815","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.06815","created_at":"2026-05-18T01:21:59Z"},{"alias_kind":"arxiv_version","alias_value":"1601.06815v1","created_at":"2026-05-18T01:21:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06815","created_at":"2026-05-18T01:21:59Z"},{"alias_kind":"pith_short_12","alias_value":"2BBSZDWS3HR4","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"2BBSZDWS3HR4XA3O","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"2BBSZDWS","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:7852de829bb2e4aa355f5e473693de4444f81cf8a30b8e9e71fca1a7cf92df99","target":"graph","created_at":"2026-05-18T01:21:59Z","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":"Convolutional neural networks (CNNs) are currently state-of-the-art for various classification tasks, but are computationally expensive. Propagating through the convolutional layers is very slow, as each kernel in each layer must sequentially calculate many dot products for a single forward and backward propagation which equates to $\\mathcal{O}(N^{2}n^{2})$ per kernel per layer where the inputs are $N \\times N$ arrays and the kernels are $n \\times n$ arrays. Convolution can be efficiently performed as a Hadamard product in the frequency domain. The bottleneck is the transformation which has a ","authors_text":"Andres Rodriguez, Tyler Highlander","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2016-01-25T21:29:11Z","title":"Very Efficient Training of Convolutional Neural Networks using Fast Fourier Transform and Overlap-and-Add"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06815","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:d8ff20c5af0d9885218fc935c75ddcfaa3846d7a40eb1d6dcc166ad6d2f55567","target":"record","created_at":"2026-05-18T01:21:59Z","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":"30c6fb05ce8316db2ae00fca8e2ac65414b9b546882d809bceed1ceef95b4afd","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2016-01-25T21:29:11Z","title_canon_sha256":"9f6a587f9db608d3e3c091b6cc36f26b444cd6c36de4178a0d28e567d4ac5e08"},"schema_version":"1.0","source":{"id":"1601.06815","kind":"arxiv","version":1}},"canonical_sha256":"d0432c8ed2d9e3cb836e44c0759555179a4a240f9017d72df16bd78aa93cf87d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0432c8ed2d9e3cb836e44c0759555179a4a240f9017d72df16bd78aa93cf87d","first_computed_at":"2026-05-18T01:21:59.743765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:59.743765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ja9pbpZJ6IgC0SM2+QiHqWgA+pqq3gbB1GX+ZuVfkLW8kWbjcze69S4I3V+hyj8dDp7TzHAInnpLyUxvi3kRBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:59.744307Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.06815","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8ff20c5af0d9885218fc935c75ddcfaa3846d7a40eb1d6dcc166ad6d2f55567","sha256:7852de829bb2e4aa355f5e473693de4444f81cf8a30b8e9e71fca1a7cf92df99"],"state_sha256":"d61a0bfe44856c3bbf01420386012fb3a1b491e9eb4b38271e4c6c0dcdd78c89"}