{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:TIL3VDWIMWWPPBHROTTU4QXMNO","short_pith_number":"pith:TIL3VDWI","canonical_record":{"source":{"id":"2203.09255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-03-17T11:23:18Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"ecc74d17cf943e5dd76a9cfde87be425bd21ec4c49f8f9be027c2d1e288b0da5","abstract_canon_sha256":"5d619b231d0576f6f8c24c6d27840c8c732eba10944b356837cda26e7313f5a0"},"schema_version":"1.0"},"canonical_sha256":"9a17ba8ec865acf784f174e74e42ec6ba58193fb1c12551e438360b4b933412b","source":{"kind":"arxiv","id":"2203.09255","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.09255","created_at":"2026-07-05T04:06:09Z"},{"alias_kind":"arxiv_version","alias_value":"2203.09255v1","created_at":"2026-07-05T04:06:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.09255","created_at":"2026-07-05T04:06:09Z"},{"alias_kind":"pith_short_12","alias_value":"TIL3VDWIMWWP","created_at":"2026-07-05T04:06:09Z"},{"alias_kind":"pith_short_16","alias_value":"TIL3VDWIMWWPPBHR","created_at":"2026-07-05T04:06:09Z"},{"alias_kind":"pith_short_8","alias_value":"TIL3VDWI","created_at":"2026-07-05T04:06:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:TIL3VDWIMWWPPBHROTTU4QXMNO","target":"record","payload":{"canonical_record":{"source":{"id":"2203.09255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-03-17T11:23:18Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"ecc74d17cf943e5dd76a9cfde87be425bd21ec4c49f8f9be027c2d1e288b0da5","abstract_canon_sha256":"5d619b231d0576f6f8c24c6d27840c8c732eba10944b356837cda26e7313f5a0"},"schema_version":"1.0"},"canonical_sha256":"9a17ba8ec865acf784f174e74e42ec6ba58193fb1c12551e438360b4b933412b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:06:09.348075Z","signature_b64":"N+91JQmHLWmxSYQL06S4jwGNpE1HdYRe1Lero5XCWbt279Psbzwt6Ga6XAeJJshOdeg5zqhNV4gBFQ2emCSlAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a17ba8ec865acf784f174e74e42ec6ba58193fb1c12551e438360b4b933412b","last_reissued_at":"2026-07-05T04:06:09.347584Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:06:09.347584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2203.09255","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":"2026-07-05T04:06:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5i59NbYzk2UzD+F/TPUuFaZ2/BpA+SPkrc/+nUaSYuBYQ7VWiBKhRawZPHXWTeWY/4+rXHAhru7VnnpBoCFMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T19:30:45.033523Z"},"content_sha256":"bdbc4771c001e33f67724875007a54efae7767180f42218479a8a8e4381d5eb0","schema_version":"1.0","event_id":"sha256:bdbc4771c001e33f67724875007a54efae7767180f42218479a8a8e4381d5eb0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:TIL3VDWIMWWPPBHROTTU4QXMNO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Spectral Bias of Convolutional Neural Tangent and Gaussian Process Kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Amnon Geifman, David Jacobs, Meirav Galun, Ronen Basri","submitted_at":"2022-03-17T11:23:18Z","abstract_excerpt":"We study the properties of various over-parametrized convolutional neural architectures through their respective Gaussian process and neural tangent kernels. We prove that, with normalized multi-channel input and ReLU activation, the eigenfunctions of these kernels with the uniform measure are formed by products of spherical harmonics, defined over the channels of the different pixels. We next use hierarchical factorizable kernels to bound their respective eigenvalues. We show that the eigenvalues decay polynomially, quantify the rate of decay, and derive measures that reflect the composition "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.09255","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.09255/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:06:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SPxsw5jcZftaUSVF+HLZ1QD+RIuafYBq5bX23os2Fhxu+StSejwYsm8VjSfBNWyjVf4ezDEDrkvO+AG+lZEGCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T19:30:45.033897Z"},"content_sha256":"aab06b491db2ee1f1ad88c740d1698c79b87fa2f3b0b9650815f2e852ef94287","schema_version":"1.0","event_id":"sha256:aab06b491db2ee1f1ad88c740d1698c79b87fa2f3b0b9650815f2e852ef94287"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TIL3VDWIMWWPPBHROTTU4QXMNO/bundle.json","state_url":"https://pith.science/pith/TIL3VDWIMWWPPBHROTTU4QXMNO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TIL3VDWIMWWPPBHROTTU4QXMNO/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":"2026-07-06T19:30:45Z","links":{"resolver":"https://pith.science/pith/TIL3VDWIMWWPPBHROTTU4QXMNO","bundle":"https://pith.science/pith/TIL3VDWIMWWPPBHROTTU4QXMNO/bundle.json","state":"https://pith.science/pith/TIL3VDWIMWWPPBHROTTU4QXMNO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TIL3VDWIMWWPPBHROTTU4QXMNO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:TIL3VDWIMWWPPBHROTTU4QXMNO","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":"5d619b231d0576f6f8c24c6d27840c8c732eba10944b356837cda26e7313f5a0","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-03-17T11:23:18Z","title_canon_sha256":"ecc74d17cf943e5dd76a9cfde87be425bd21ec4c49f8f9be027c2d1e288b0da5"},"schema_version":"1.0","source":{"id":"2203.09255","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.09255","created_at":"2026-07-05T04:06:09Z"},{"alias_kind":"arxiv_version","alias_value":"2203.09255v1","created_at":"2026-07-05T04:06:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.09255","created_at":"2026-07-05T04:06:09Z"},{"alias_kind":"pith_short_12","alias_value":"TIL3VDWIMWWP","created_at":"2026-07-05T04:06:09Z"},{"alias_kind":"pith_short_16","alias_value":"TIL3VDWIMWWPPBHR","created_at":"2026-07-05T04:06:09Z"},{"alias_kind":"pith_short_8","alias_value":"TIL3VDWI","created_at":"2026-07-05T04:06:09Z"}],"graph_snapshots":[{"event_id":"sha256:aab06b491db2ee1f1ad88c740d1698c79b87fa2f3b0b9650815f2e852ef94287","target":"graph","created_at":"2026-07-05T04:06:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2203.09255/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the properties of various over-parametrized convolutional neural architectures through their respective Gaussian process and neural tangent kernels. We prove that, with normalized multi-channel input and ReLU activation, the eigenfunctions of these kernels with the uniform measure are formed by products of spherical harmonics, defined over the channels of the different pixels. We next use hierarchical factorizable kernels to bound their respective eigenvalues. We show that the eigenvalues decay polynomially, quantify the rate of decay, and derive measures that reflect the composition ","authors_text":"Amnon Geifman, David Jacobs, Meirav Galun, Ronen Basri","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-03-17T11:23:18Z","title":"On the Spectral Bias of Convolutional Neural Tangent and Gaussian Process Kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.09255","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:bdbc4771c001e33f67724875007a54efae7767180f42218479a8a8e4381d5eb0","target":"record","created_at":"2026-07-05T04:06:09Z","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":"5d619b231d0576f6f8c24c6d27840c8c732eba10944b356837cda26e7313f5a0","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-03-17T11:23:18Z","title_canon_sha256":"ecc74d17cf943e5dd76a9cfde87be425bd21ec4c49f8f9be027c2d1e288b0da5"},"schema_version":"1.0","source":{"id":"2203.09255","kind":"arxiv","version":1}},"canonical_sha256":"9a17ba8ec865acf784f174e74e42ec6ba58193fb1c12551e438360b4b933412b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a17ba8ec865acf784f174e74e42ec6ba58193fb1c12551e438360b4b933412b","first_computed_at":"2026-07-05T04:06:09.347584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:06:09.347584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N+91JQmHLWmxSYQL06S4jwGNpE1HdYRe1Lero5XCWbt279Psbzwt6Ga6XAeJJshOdeg5zqhNV4gBFQ2emCSlAw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:06:09.348075Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.09255","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdbc4771c001e33f67724875007a54efae7767180f42218479a8a8e4381d5eb0","sha256:aab06b491db2ee1f1ad88c740d1698c79b87fa2f3b0b9650815f2e852ef94287"],"state_sha256":"d411494a3239b11b040590f538d1f3c4e055276ff147369c02aeb8a3f3b601f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4WvKfuifJC+OXdd58JwXRLstTBAGybu/sqGnkt1ZL7ykLgAQpSgqEyJ2PPhC/bte22r7ZBEuZA8dS4EbqxbsDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T19:30:45.035849Z","bundle_sha256":"f151333eb52f05a2248bfb39dd6f3434f66d901cb93ad71ae50fd2c7a60feb84"}}