{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NMEC27BJN6I67YRTHIXKYBCQLA","short_pith_number":"pith:NMEC27BJ","canonical_record":{"source":{"id":"1810.08578","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2018-10-19T16:43:26Z","cross_cats_sorted":[],"title_canon_sha256":"69ba315ae59e2596747e9fc458b8d7012995bf3d15f81768d381c86dc9daa3f0","abstract_canon_sha256":"8a9d32d4a858ac4419f61702ad1199a288c2e0221ccafc59647439a80b5137f2"},"schema_version":"1.0"},"canonical_sha256":"6b082d7c296f91efe2333a2eac0450582bc971510c2e579e631c3b1d7b1f1ea0","source":{"kind":"arxiv","id":"1810.08578","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08578","created_at":"2026-05-18T00:02:46Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08578v1","created_at":"2026-05-18T00:02:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08578","created_at":"2026-05-18T00:02:46Z"},{"alias_kind":"pith_short_12","alias_value":"NMEC27BJN6I6","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NMEC27BJN6I67YRT","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NMEC27BJ","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NMEC27BJN6I67YRTHIXKYBCQLA","target":"record","payload":{"canonical_record":{"source":{"id":"1810.08578","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2018-10-19T16:43:26Z","cross_cats_sorted":[],"title_canon_sha256":"69ba315ae59e2596747e9fc458b8d7012995bf3d15f81768d381c86dc9daa3f0","abstract_canon_sha256":"8a9d32d4a858ac4419f61702ad1199a288c2e0221ccafc59647439a80b5137f2"},"schema_version":"1.0"},"canonical_sha256":"6b082d7c296f91efe2333a2eac0450582bc971510c2e579e631c3b1d7b1f1ea0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:46.265768Z","signature_b64":"5JAWp1dU1ZpSwF7BM8pk4mHDBseWgtbTd+TOlJwRYQx7Bs3lhrgOXTTjyIZD50yUaugTSS62n1tovglDgXNFAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b082d7c296f91efe2333a2eac0450582bc971510c2e579e631c3b1d7b1f1ea0","last_reissued_at":"2026-05-18T00:02:46.265374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:46.265374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.08578","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":"2026-05-18T00:02:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a3BswvBwUChD8WqAr6UiZToLGtMqQGHSlj0mdY4UFH8YrX83ttJ9yRG+kt0jAw+oiqavrl4RIv2hZlvb/wZFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T09:40:19.420259Z"},"content_sha256":"cc5ede7997d2a96e906bab9f98b40d778a1f320808b6c4f3a22d4d8e78eea6e6","schema_version":"1.0","event_id":"sha256:cc5ede7997d2a96e906bab9f98b40d778a1f320808b6c4f3a22d4d8e78eea6e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NMEC27BJN6I67YRTHIXKYBCQLA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Leveraging Product as an Activation Function in Deep Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.NE","authors_text":"Luke B. Godfrey, Michael S. Gashler","submitted_at":"2018-10-19T16:43:26Z","abstract_excerpt":"Product unit neural networks (PUNNs) are powerful representational models with a strong theoretical basis, but have proven to be difficult to train with gradient-based optimizers. We present windowed product unit neural networks (WPUNNs), a simple method of leveraging product as a nonlinearity in a neural network. Windowing the product tames the complex gradient surface and enables WPUNNs to learn effectively, solving the problems faced by PUNNs. WPUNNs use product layers between traditional sum layers, capturing the representational power of product units and using the product itself as a non"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08578","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":"2026-05-18T00:02:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"53RKdw/ZC2qmuMVQ/iyZbwPARf9DuH2reBTZxvK3K71+E42wHvOQnwL94dWzW+/volH89kEG7TyyohjA8G3EDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T09:40:19.420845Z"},"content_sha256":"8a6aa52d2e064d4efbecc9c3ec799c99eeaf4526af0eb1fe378a4048e72b950b","schema_version":"1.0","event_id":"sha256:8a6aa52d2e064d4efbecc9c3ec799c99eeaf4526af0eb1fe378a4048e72b950b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NMEC27BJN6I67YRTHIXKYBCQLA/bundle.json","state_url":"https://pith.science/pith/NMEC27BJN6I67YRTHIXKYBCQLA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NMEC27BJN6I67YRTHIXKYBCQLA/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":"2026-07-01T09:40:19Z","links":{"resolver":"https://pith.science/pith/NMEC27BJN6I67YRTHIXKYBCQLA","bundle":"https://pith.science/pith/NMEC27BJN6I67YRTHIXKYBCQLA/bundle.json","state":"https://pith.science/pith/NMEC27BJN6I67YRTHIXKYBCQLA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NMEC27BJN6I67YRTHIXKYBCQLA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NMEC27BJN6I67YRTHIXKYBCQLA","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":"8a9d32d4a858ac4419f61702ad1199a288c2e0221ccafc59647439a80b5137f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2018-10-19T16:43:26Z","title_canon_sha256":"69ba315ae59e2596747e9fc458b8d7012995bf3d15f81768d381c86dc9daa3f0"},"schema_version":"1.0","source":{"id":"1810.08578","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08578","created_at":"2026-05-18T00:02:46Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08578v1","created_at":"2026-05-18T00:02:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08578","created_at":"2026-05-18T00:02:46Z"},{"alias_kind":"pith_short_12","alias_value":"NMEC27BJN6I6","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NMEC27BJN6I67YRT","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NMEC27BJ","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:8a6aa52d2e064d4efbecc9c3ec799c99eeaf4526af0eb1fe378a4048e72b950b","target":"graph","created_at":"2026-05-18T00:02:46Z","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":"Product unit neural networks (PUNNs) are powerful representational models with a strong theoretical basis, but have proven to be difficult to train with gradient-based optimizers. We present windowed product unit neural networks (WPUNNs), a simple method of leveraging product as a nonlinearity in a neural network. Windowing the product tames the complex gradient surface and enables WPUNNs to learn effectively, solving the problems faced by PUNNs. WPUNNs use product layers between traditional sum layers, capturing the representational power of product units and using the product itself as a non","authors_text":"Luke B. Godfrey, Michael S. Gashler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2018-10-19T16:43:26Z","title":"Leveraging Product as an Activation Function in Deep Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08578","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:cc5ede7997d2a96e906bab9f98b40d778a1f320808b6c4f3a22d4d8e78eea6e6","target":"record","created_at":"2026-05-18T00:02:46Z","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":"8a9d32d4a858ac4419f61702ad1199a288c2e0221ccafc59647439a80b5137f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2018-10-19T16:43:26Z","title_canon_sha256":"69ba315ae59e2596747e9fc458b8d7012995bf3d15f81768d381c86dc9daa3f0"},"schema_version":"1.0","source":{"id":"1810.08578","kind":"arxiv","version":1}},"canonical_sha256":"6b082d7c296f91efe2333a2eac0450582bc971510c2e579e631c3b1d7b1f1ea0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b082d7c296f91efe2333a2eac0450582bc971510c2e579e631c3b1d7b1f1ea0","first_computed_at":"2026-05-18T00:02:46.265374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:46.265374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5JAWp1dU1ZpSwF7BM8pk4mHDBseWgtbTd+TOlJwRYQx7Bs3lhrgOXTTjyIZD50yUaugTSS62n1tovglDgXNFAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:46.265768Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.08578","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc5ede7997d2a96e906bab9f98b40d778a1f320808b6c4f3a22d4d8e78eea6e6","sha256:8a6aa52d2e064d4efbecc9c3ec799c99eeaf4526af0eb1fe378a4048e72b950b"],"state_sha256":"dc90e7cd91986e6d9c8e4901a90b567aeb3213347284c8417192edd97de29630"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1XHknxt+PtOBmlC0oxxcHxk4LzxDu4eYeIRRWw2rDSIQLTjQdEG+QBL/em9kw+AwV1e2qpJ7gAIsQLVbyPXyBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T09:40:19.423903Z","bundle_sha256":"af7c7c9df5488e1d0cd03d33457ec1caa85d859be1dab64e2c7696d4e3b02d4c"}}