{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:N4RSSRTTO4XY7WGM2TYHBDI32A","short_pith_number":"pith:N4RSSRTT","canonical_record":{"source":{"id":"1710.03263","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2017-10-09T18:52:42Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"3c700ee73209257f54e233cb7e98e988bb0c4a10953c400e1f999eb7214cf21b","abstract_canon_sha256":"ae9998471644b041f7895c99a6419c0846c86c47b139981009cba49ababd27c7"},"schema_version":"1.0"},"canonical_sha256":"6f23294673772f8fd8ccd4f0708d1bd01768b55a899d9fae6cd0b7ac8e020924","source":{"kind":"arxiv","id":"1710.03263","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.03263","created_at":"2026-05-18T00:33:12Z"},{"alias_kind":"arxiv_version","alias_value":"1710.03263v1","created_at":"2026-05-18T00:33:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03263","created_at":"2026-05-18T00:33:12Z"},{"alias_kind":"pith_short_12","alias_value":"N4RSSRTTO4XY","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"N4RSSRTTO4XY7WGM","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"N4RSSRTT","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:N4RSSRTTO4XY7WGM2TYHBDI32A","target":"record","payload":{"canonical_record":{"source":{"id":"1710.03263","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2017-10-09T18:52:42Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"3c700ee73209257f54e233cb7e98e988bb0c4a10953c400e1f999eb7214cf21b","abstract_canon_sha256":"ae9998471644b041f7895c99a6419c0846c86c47b139981009cba49ababd27c7"},"schema_version":"1.0"},"canonical_sha256":"6f23294673772f8fd8ccd4f0708d1bd01768b55a899d9fae6cd0b7ac8e020924","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:12.558144Z","signature_b64":"StyCgBjTFXIUuJGtokFUFzx3NkNmzSnBT1jp80wA/fWhlToOaV21cqjLgzBXqEjBlbBaNhpCsMos9EGGQD/EAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f23294673772f8fd8ccd4f0708d1bd01768b55a899d9fae6cd0b7ac8e020924","last_reissued_at":"2026-05-18T00:33:12.557520Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:12.557520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.03263","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":"2026-05-18T00:33:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3oRuulfc/9B1ptr3KE9Y/FYK+DPhTMT6i1ODMNe21MspdA+9f4z9QLfnI6lu4/0dVZ5Z5VTYWHDsmlc+gjV6Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:37:12.783855Z"},"content_sha256":"d7c5989632b7671760c273b3031865589615bc0d01c8c14799539b293d05382f","schema_version":"1.0","event_id":"sha256:d7c5989632b7671760c273b3031865589615bc0d01c8c14799539b293d05382f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:N4RSSRTTO4XY7WGM2TYHBDI32A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Function space analysis of deep learning representation layers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.AI","authors_text":"Oren Elisha, Shai Dekel","submitted_at":"2017-10-09T18:52:42Z","abstract_excerpt":"In this paper we propose a function space approach to Representation Learning and the analysis of the representation layers in deep learning architectures. We show how to compute a weak-type Besov smoothness index that quantifies the geometry of the clustering in the feature space. This approach was already applied successfully to improve the performance of machine learning algorithms such as the Random Forest and tree-based Gradient Boosting. Our experiments demonstrate that in well-known and well-performing trained networks, the Besov smoothness of the training set, measured in the correspon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03263","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":"2026-05-18T00:33:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YvhB0417WL3ALho8tw9E6IJ9lokJJQyW340MGp3dvOJby/toUSeTWRARIfAS50rvtnX5labFRWMMxIfgwC9+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:37:12.784363Z"},"content_sha256":"0ff85efd06c99709ced60e91faabd68eced907b555fbacd8724d5eb129a6a106","schema_version":"1.0","event_id":"sha256:0ff85efd06c99709ced60e91faabd68eced907b555fbacd8724d5eb129a6a106"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N4RSSRTTO4XY7WGM2TYHBDI32A/bundle.json","state_url":"https://pith.science/pith/N4RSSRTTO4XY7WGM2TYHBDI32A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N4RSSRTTO4XY7WGM2TYHBDI32A/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":"2026-05-30T02:37:12Z","links":{"resolver":"https://pith.science/pith/N4RSSRTTO4XY7WGM2TYHBDI32A","bundle":"https://pith.science/pith/N4RSSRTTO4XY7WGM2TYHBDI32A/bundle.json","state":"https://pith.science/pith/N4RSSRTTO4XY7WGM2TYHBDI32A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N4RSSRTTO4XY7WGM2TYHBDI32A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:N4RSSRTTO4XY7WGM2TYHBDI32A","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":"ae9998471644b041f7895c99a6419c0846c86c47b139981009cba49ababd27c7","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2017-10-09T18:52:42Z","title_canon_sha256":"3c700ee73209257f54e233cb7e98e988bb0c4a10953c400e1f999eb7214cf21b"},"schema_version":"1.0","source":{"id":"1710.03263","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.03263","created_at":"2026-05-18T00:33:12Z"},{"alias_kind":"arxiv_version","alias_value":"1710.03263v1","created_at":"2026-05-18T00:33:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03263","created_at":"2026-05-18T00:33:12Z"},{"alias_kind":"pith_short_12","alias_value":"N4RSSRTTO4XY","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"N4RSSRTTO4XY7WGM","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"N4RSSRTT","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:0ff85efd06c99709ced60e91faabd68eced907b555fbacd8724d5eb129a6a106","target":"graph","created_at":"2026-05-18T00:33:12Z","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":"In this paper we propose a function space approach to Representation Learning and the analysis of the representation layers in deep learning architectures. We show how to compute a weak-type Besov smoothness index that quantifies the geometry of the clustering in the feature space. This approach was already applied successfully to improve the performance of machine learning algorithms such as the Random Forest and tree-based Gradient Boosting. Our experiments demonstrate that in well-known and well-performing trained networks, the Besov smoothness of the training set, measured in the correspon","authors_text":"Oren Elisha, Shai Dekel","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2017-10-09T18:52:42Z","title":"Function space analysis of deep learning representation layers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03263","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:d7c5989632b7671760c273b3031865589615bc0d01c8c14799539b293d05382f","target":"record","created_at":"2026-05-18T00:33:12Z","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":"ae9998471644b041f7895c99a6419c0846c86c47b139981009cba49ababd27c7","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2017-10-09T18:52:42Z","title_canon_sha256":"3c700ee73209257f54e233cb7e98e988bb0c4a10953c400e1f999eb7214cf21b"},"schema_version":"1.0","source":{"id":"1710.03263","kind":"arxiv","version":1}},"canonical_sha256":"6f23294673772f8fd8ccd4f0708d1bd01768b55a899d9fae6cd0b7ac8e020924","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f23294673772f8fd8ccd4f0708d1bd01768b55a899d9fae6cd0b7ac8e020924","first_computed_at":"2026-05-18T00:33:12.557520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:12.557520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"StyCgBjTFXIUuJGtokFUFzx3NkNmzSnBT1jp80wA/fWhlToOaV21cqjLgzBXqEjBlbBaNhpCsMos9EGGQD/EAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:12.558144Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.03263","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7c5989632b7671760c273b3031865589615bc0d01c8c14799539b293d05382f","sha256:0ff85efd06c99709ced60e91faabd68eced907b555fbacd8724d5eb129a6a106"],"state_sha256":"23be1b4492f05e5d28211eb36d6651baa36275c1913628619a140ea96bcce163"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JYzQeEGthKVuxnHIYjNlE4qAy/a6DPe5D2npj39blY6N4NjFuuovR2yOhACXxMlXkcIncS3DWwGFtFmuSN4ADw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T02:37:12.787783Z","bundle_sha256":"1bf80db8bd3a887938fd805aec88ecb609680591419f08b00aa7b0a0acf26e72"}}