{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZAPW76G2NNAP7MFZRKPZJIUG3T","short_pith_number":"pith:ZAPW76G2","canonical_record":{"source":{"id":"1807.06399","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-07-17T13:08:21Z","cross_cats_sorted":["cs.NE","stat.ML"],"title_canon_sha256":"c7c87800e95d116225b2c709a1d0871d697f40dc1dc62065cd70cbe1dfd7fb7d","abstract_canon_sha256":"e3a15207ea921c3420e657e098d6588c0b077095328f627c909cc3030a74432f"},"schema_version":"1.0"},"canonical_sha256":"c81f6ff8da6b40ffb0b98a9f94a286dcfa0e3a2b939a68b863bac18b2643a94e","source":{"kind":"arxiv","id":"1807.06399","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.06399","created_at":"2026-05-18T00:10:33Z"},{"alias_kind":"arxiv_version","alias_value":"1807.06399v1","created_at":"2026-05-18T00:10:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06399","created_at":"2026-05-18T00:10:33Z"},{"alias_kind":"pith_short_12","alias_value":"ZAPW76G2NNAP","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"ZAPW76G2NNAP7MFZ","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"ZAPW76G2","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZAPW76G2NNAP7MFZRKPZJIUG3T","target":"record","payload":{"canonical_record":{"source":{"id":"1807.06399","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-07-17T13:08:21Z","cross_cats_sorted":["cs.NE","stat.ML"],"title_canon_sha256":"c7c87800e95d116225b2c709a1d0871d697f40dc1dc62065cd70cbe1dfd7fb7d","abstract_canon_sha256":"e3a15207ea921c3420e657e098d6588c0b077095328f627c909cc3030a74432f"},"schema_version":"1.0"},"canonical_sha256":"c81f6ff8da6b40ffb0b98a9f94a286dcfa0e3a2b939a68b863bac18b2643a94e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:33.165136Z","signature_b64":"Ef2ajTwZ2VxaSS8WaRXv4wc9gI4MQeET1PxWLyqI9aenAgOg83kv0J8yOsbYE/spWXJf+a3d6xDIYdJJb87GDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c81f6ff8da6b40ffb0b98a9f94a286dcfa0e3a2b939a68b863bac18b2643a94e","last_reissued_at":"2026-05-18T00:10:33.164332Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:33.164332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.06399","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":"2026-05-18T00:10:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/wSAOx0rDn/zEZ5iD2Aus9RoZ1DQVTBcxxSqK7z8uBoKJuG0RICVaNwMqV/ZNlDSgAECBy/vp1ZJsPj5ReuFDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T12:42:55.965458Z"},"content_sha256":"aaf08d824ff2e72904cb2b9a74b94e0023ce7b5ab31079c60942044c4ca28e42","schema_version":"1.0","event_id":"sha256:aaf08d824ff2e72904cb2b9a74b94e0023ce7b5ab31079c60942044c4ca28e42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZAPW76G2NNAP7MFZRKPZJIUG3T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Are Efficient Deep Representations Learnable?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NE","stat.ML"],"primary_cat":"cs.LG","authors_text":"Andrew Saxe, Maxwell Nye","submitted_at":"2018-07-17T13:08:21Z","abstract_excerpt":"Many theories of deep learning have shown that a deep network can require dramatically fewer resources to represent a given function compared to a shallow network. But a question remains: can these efficient representations be learned using current deep learning techniques? In this work, we test whether standard deep learning methods can in fact find the efficient representations posited by several theories of deep representation. Specifically, we train deep neural networks to learn two simple functions with known efficient solutions: the parity function and the fast Fourier transform. We find"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06399","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":"2026-05-18T00:10:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h1AifqBiA6RjfVp33V23Y3amtZ0Pqt44joQ1/jXvqU8I/6/tsbDOH26LoaTDiQqLckP3hUEyu2cU9OfrVfbmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T12:42:55.966169Z"},"content_sha256":"ece8dab67a59466a81481055ff581f8264abb7aa67ade6bb7ab61b2bb7ff2956","schema_version":"1.0","event_id":"sha256:ece8dab67a59466a81481055ff581f8264abb7aa67ade6bb7ab61b2bb7ff2956"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZAPW76G2NNAP7MFZRKPZJIUG3T/bundle.json","state_url":"https://pith.science/pith/ZAPW76G2NNAP7MFZRKPZJIUG3T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZAPW76G2NNAP7MFZRKPZJIUG3T/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":"2026-06-07T12:42:55Z","links":{"resolver":"https://pith.science/pith/ZAPW76G2NNAP7MFZRKPZJIUG3T","bundle":"https://pith.science/pith/ZAPW76G2NNAP7MFZRKPZJIUG3T/bundle.json","state":"https://pith.science/pith/ZAPW76G2NNAP7MFZRKPZJIUG3T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZAPW76G2NNAP7MFZRKPZJIUG3T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZAPW76G2NNAP7MFZRKPZJIUG3T","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":"e3a15207ea921c3420e657e098d6588c0b077095328f627c909cc3030a74432f","cross_cats_sorted":["cs.NE","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-07-17T13:08:21Z","title_canon_sha256":"c7c87800e95d116225b2c709a1d0871d697f40dc1dc62065cd70cbe1dfd7fb7d"},"schema_version":"1.0","source":{"id":"1807.06399","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.06399","created_at":"2026-05-18T00:10:33Z"},{"alias_kind":"arxiv_version","alias_value":"1807.06399v1","created_at":"2026-05-18T00:10:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06399","created_at":"2026-05-18T00:10:33Z"},{"alias_kind":"pith_short_12","alias_value":"ZAPW76G2NNAP","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"ZAPW76G2NNAP7MFZ","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"ZAPW76G2","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:ece8dab67a59466a81481055ff581f8264abb7aa67ade6bb7ab61b2bb7ff2956","target":"graph","created_at":"2026-05-18T00:10:33Z","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":"Many theories of deep learning have shown that a deep network can require dramatically fewer resources to represent a given function compared to a shallow network. But a question remains: can these efficient representations be learned using current deep learning techniques? In this work, we test whether standard deep learning methods can in fact find the efficient representations posited by several theories of deep representation. Specifically, we train deep neural networks to learn two simple functions with known efficient solutions: the parity function and the fast Fourier transform. We find","authors_text":"Andrew Saxe, Maxwell Nye","cross_cats":["cs.NE","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-07-17T13:08:21Z","title":"Are Efficient Deep Representations Learnable?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06399","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:aaf08d824ff2e72904cb2b9a74b94e0023ce7b5ab31079c60942044c4ca28e42","target":"record","created_at":"2026-05-18T00:10:33Z","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":"e3a15207ea921c3420e657e098d6588c0b077095328f627c909cc3030a74432f","cross_cats_sorted":["cs.NE","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-07-17T13:08:21Z","title_canon_sha256":"c7c87800e95d116225b2c709a1d0871d697f40dc1dc62065cd70cbe1dfd7fb7d"},"schema_version":"1.0","source":{"id":"1807.06399","kind":"arxiv","version":1}},"canonical_sha256":"c81f6ff8da6b40ffb0b98a9f94a286dcfa0e3a2b939a68b863bac18b2643a94e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c81f6ff8da6b40ffb0b98a9f94a286dcfa0e3a2b939a68b863bac18b2643a94e","first_computed_at":"2026-05-18T00:10:33.164332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:33.164332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ef2ajTwZ2VxaSS8WaRXv4wc9gI4MQeET1PxWLyqI9aenAgOg83kv0J8yOsbYE/spWXJf+a3d6xDIYdJJb87GDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:33.165136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.06399","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aaf08d824ff2e72904cb2b9a74b94e0023ce7b5ab31079c60942044c4ca28e42","sha256:ece8dab67a59466a81481055ff581f8264abb7aa67ade6bb7ab61b2bb7ff2956"],"state_sha256":"aae4e770388270ba77c20ed187444865daa522595cd943d509c6a711e90eeee5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aKIS+KLpk5+evUmYskluHJ/oMxhGUqEzuxHLM/Z5s3Yxfsdwv44ymATy1I1BbbHHNF1c/pcu+f9M5UNvdkYvDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T12:42:55.969638Z","bundle_sha256":"28f0cc3748e14928e36d75ed2f85cb6ccb6151eb4f4b4b8a2947a3bc13606b8d"}}