{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:WVUTI2QMS5Q3UMKYTUMSGGZ4PD","short_pith_number":"pith:WVUTI2QM","canonical_record":{"source":{"id":"1907.06800","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-07-16T00:28:19Z","cross_cats_sorted":["cs.NA","math.NA","stat.ML"],"title_canon_sha256":"df7163d2f448f745a0a3399862f4ea0c2a26969c4e81db1f4b0a7acb5c4406d0","abstract_canon_sha256":"49f3b97070d3196f6c3797fbbcba0d53facdbba526fb2e1322e841572799f49c"},"schema_version":"1.0"},"canonical_sha256":"b569346a0c9761ba31589d19231b3c78e92345fe8c498b691c62dda00f17f849","source":{"kind":"arxiv","id":"1907.06800","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.06800","created_at":"2026-05-17T23:40:29Z"},{"alias_kind":"arxiv_version","alias_value":"1907.06800v1","created_at":"2026-05-17T23:40:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.06800","created_at":"2026-05-17T23:40:29Z"},{"alias_kind":"pith_short_12","alias_value":"WVUTI2QMS5Q3","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"WVUTI2QMS5Q3UMKY","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"WVUTI2QM","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:WVUTI2QMS5Q3UMKYTUMSGGZ4PD","target":"record","payload":{"canonical_record":{"source":{"id":"1907.06800","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-07-16T00:28:19Z","cross_cats_sorted":["cs.NA","math.NA","stat.ML"],"title_canon_sha256":"df7163d2f448f745a0a3399862f4ea0c2a26969c4e81db1f4b0a7acb5c4406d0","abstract_canon_sha256":"49f3b97070d3196f6c3797fbbcba0d53facdbba526fb2e1322e841572799f49c"},"schema_version":"1.0"},"canonical_sha256":"b569346a0c9761ba31589d19231b3c78e92345fe8c498b691c62dda00f17f849","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:29.096051Z","signature_b64":"b8k8ZGtNW2eZWQQG6rofhfzsttbdiiFOqSMXQcCi1d7fNCOWQVZC52d4fJqOyfedAeA/LUNoI52+2pywQS1IBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b569346a0c9761ba31589d19231b3c78e92345fe8c498b691c62dda00f17f849","last_reissued_at":"2026-05-17T23:40:29.095201Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:29.095201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.06800","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":"2026-05-17T23:40:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gxaawFsM3oOiDObXSLOXJFjamS+9O4JmSgCDoQ9f0sO16asrtiwtKNqpxxb94k4cHwwkObrUIYrVuHfzyU2iBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:28:29.692408Z"},"content_sha256":"701c4996fa96e26c2b535b8b1d530981573981ebb3737b0ea8ab63db524430ee","schema_version":"1.0","event_id":"sha256:701c4996fa96e26c2b535b8b1d530981573981ebb3737b0ea8ab63db524430ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:WVUTI2QMS5Q3UMKYTUMSGGZ4PD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graph Interpolating Activation Improves Both Natural and Robust Accuracies in Data-Efficient Deep Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","stat.ML"],"primary_cat":"cs.LG","authors_text":"Bao Wang, Stanley J. Osher","submitted_at":"2019-07-16T00:28:19Z","abstract_excerpt":"Improving the accuracy and robustness of deep neural nets (DNNs) and adapting them to small training data are primary tasks in deep learning research. In this paper, we replace the output activation function of DNNs, typically the data-agnostic softmax function, with a graph Laplacian-based high dimensional interpolating function which, in the continuum limit, converges to the solution of a Laplace-Beltrami equation on a high dimensional manifold. Furthermore, we propose end-to-end training and testing algorithms for this new architecture. The proposed DNN with graph interpolating activation i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06800","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":"2026-05-17T23:40:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FfmeHbqYUzZnlGLAFeW7+D0FGI8mvGBWxr4iA2escarFWwAirh40oBlWEJ5sxKz4LOVYtFKZ3bnqhbBamK7jBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:28:29.693101Z"},"content_sha256":"4e6649d5c0a3d00d7e9e52a887592afac489dc4b89379961cc4d79abe3365910","schema_version":"1.0","event_id":"sha256:4e6649d5c0a3d00d7e9e52a887592afac489dc4b89379961cc4d79abe3365910"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WVUTI2QMS5Q3UMKYTUMSGGZ4PD/bundle.json","state_url":"https://pith.science/pith/WVUTI2QMS5Q3UMKYTUMSGGZ4PD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WVUTI2QMS5Q3UMKYTUMSGGZ4PD/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":"2026-05-25T20:28:29Z","links":{"resolver":"https://pith.science/pith/WVUTI2QMS5Q3UMKYTUMSGGZ4PD","bundle":"https://pith.science/pith/WVUTI2QMS5Q3UMKYTUMSGGZ4PD/bundle.json","state":"https://pith.science/pith/WVUTI2QMS5Q3UMKYTUMSGGZ4PD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WVUTI2QMS5Q3UMKYTUMSGGZ4PD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WVUTI2QMS5Q3UMKYTUMSGGZ4PD","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":"49f3b97070d3196f6c3797fbbcba0d53facdbba526fb2e1322e841572799f49c","cross_cats_sorted":["cs.NA","math.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-07-16T00:28:19Z","title_canon_sha256":"df7163d2f448f745a0a3399862f4ea0c2a26969c4e81db1f4b0a7acb5c4406d0"},"schema_version":"1.0","source":{"id":"1907.06800","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.06800","created_at":"2026-05-17T23:40:29Z"},{"alias_kind":"arxiv_version","alias_value":"1907.06800v1","created_at":"2026-05-17T23:40:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.06800","created_at":"2026-05-17T23:40:29Z"},{"alias_kind":"pith_short_12","alias_value":"WVUTI2QMS5Q3","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"WVUTI2QMS5Q3UMKY","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"WVUTI2QM","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:4e6649d5c0a3d00d7e9e52a887592afac489dc4b89379961cc4d79abe3365910","target":"graph","created_at":"2026-05-17T23:40:29Z","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":"Improving the accuracy and robustness of deep neural nets (DNNs) and adapting them to small training data are primary tasks in deep learning research. In this paper, we replace the output activation function of DNNs, typically the data-agnostic softmax function, with a graph Laplacian-based high dimensional interpolating function which, in the continuum limit, converges to the solution of a Laplace-Beltrami equation on a high dimensional manifold. Furthermore, we propose end-to-end training and testing algorithms for this new architecture. The proposed DNN with graph interpolating activation i","authors_text":"Bao Wang, Stanley J. Osher","cross_cats":["cs.NA","math.NA","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-07-16T00:28:19Z","title":"Graph Interpolating Activation Improves Both Natural and Robust Accuracies in Data-Efficient Deep Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06800","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":"sha256:701c4996fa96e26c2b535b8b1d530981573981ebb3737b0ea8ab63db524430ee","target":"record","created_at":"2026-05-17T23:40:29Z","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":"49f3b97070d3196f6c3797fbbcba0d53facdbba526fb2e1322e841572799f49c","cross_cats_sorted":["cs.NA","math.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-07-16T00:28:19Z","title_canon_sha256":"df7163d2f448f745a0a3399862f4ea0c2a26969c4e81db1f4b0a7acb5c4406d0"},"schema_version":"1.0","source":{"id":"1907.06800","kind":"arxiv","version":1}},"canonical_sha256":"b569346a0c9761ba31589d19231b3c78e92345fe8c498b691c62dda00f17f849","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b569346a0c9761ba31589d19231b3c78e92345fe8c498b691c62dda00f17f849","first_computed_at":"2026-05-17T23:40:29.095201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:29.095201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b8k8ZGtNW2eZWQQG6rofhfzsttbdiiFOqSMXQcCi1d7fNCOWQVZC52d4fJqOyfedAeA/LUNoI52+2pywQS1IBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:29.096051Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.06800","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:701c4996fa96e26c2b535b8b1d530981573981ebb3737b0ea8ab63db524430ee","sha256:4e6649d5c0a3d00d7e9e52a887592afac489dc4b89379961cc4d79abe3365910"],"state_sha256":"4e14dd17490684decb91736c619c163278fb0354a94d22ea9ffb455032a1eb36"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PSQRvSrkv0pWfT35mAWcPpH0zSSNJQFJQ5YEw/ABqn+J2JihvFk+wgv3KdfXuH6keadhNs/GINyQvJl/6WMCDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T20:28:29.696807Z","bundle_sha256":"fa6a850b9f3b1f7abaa56545e15527103754fc3814b89db700f6f28e7988b27a"}}