{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:RYGSZEOHGLZWYUABKIYTMDCL4E","short_pith_number":"pith:RYGSZEOH","canonical_record":{"source":{"id":"2202.03348","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-02-07T16:48:14Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"d890731d239c7f13c780546244de65a6dad04d49da90544a2e3060709cf4d880","abstract_canon_sha256":"726d27ce95ff2478fa8a61cb1351dc18aadbc431880743edcd41fb51d822aab0"},"schema_version":"1.0"},"canonical_sha256":"8e0d2c91c732f36c50015231360c4be132a63b336c1a06843177c17a2a9c849e","source":{"kind":"arxiv","id":"2202.03348","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.03348","created_at":"2026-07-05T03:57:31Z"},{"alias_kind":"arxiv_version","alias_value":"2202.03348v2","created_at":"2026-07-05T03:57:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.03348","created_at":"2026-07-05T03:57:31Z"},{"alias_kind":"pith_short_12","alias_value":"RYGSZEOHGLZW","created_at":"2026-07-05T03:57:31Z"},{"alias_kind":"pith_short_16","alias_value":"RYGSZEOHGLZWYUAB","created_at":"2026-07-05T03:57:31Z"},{"alias_kind":"pith_short_8","alias_value":"RYGSZEOH","created_at":"2026-07-05T03:57:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:RYGSZEOHGLZWYUABKIYTMDCL4E","target":"record","payload":{"canonical_record":{"source":{"id":"2202.03348","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-02-07T16:48:14Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"d890731d239c7f13c780546244de65a6dad04d49da90544a2e3060709cf4d880","abstract_canon_sha256":"726d27ce95ff2478fa8a61cb1351dc18aadbc431880743edcd41fb51d822aab0"},"schema_version":"1.0"},"canonical_sha256":"8e0d2c91c732f36c50015231360c4be132a63b336c1a06843177c17a2a9c849e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:57:31.794605Z","signature_b64":"qG1g0d7Q3Li6dG4iCe1wYOm8VLZBBTsFZ7xH7pInCeIvxwrN2TIc6DDgolAeLKAWE07FrMEZiGBEIPoMxDIaAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e0d2c91c732f36c50015231360c4be132a63b336c1a06843177c17a2a9c849e","last_reissued_at":"2026-07-05T03:57:31.794174Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:57:31.794174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2202.03348","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:57:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gy2XTjRUdyaA1m/ZLeUcShCLIP4G+240j8nru6nVCl4XCImDirzHr2zKPyj2LozUxnR5IFU0lnE6b7Sl/zUpDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T17:29:39.739637Z"},"content_sha256":"c47c3dde4b997470d0cc6fbdfc9e2e06bdc429c08b24fda06173aa7393988569","schema_version":"1.0","event_id":"sha256:c47c3dde4b997470d0cc6fbdfc9e2e06bdc429c08b24fda06173aa7393988569"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:RYGSZEOHGLZWYUABKIYTMDCL4E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Failure and success of the spectral bias prediction for Kernel Ridge Regression: the case of low-dimensional data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cs.LG","authors_text":"Antonio Sclocchi, Matthieu Wyart, Umberto M. Tomasini","submitted_at":"2022-02-07T16:48:14Z","abstract_excerpt":"Recently, several theories including the replica method made predictions for the generalization error of Kernel Ridge Regression. In some regimes, they predict that the method has a `spectral bias': decomposing the true function $f^*$ on the eigenbasis of the kernel, it fits well the coefficients associated with the O(P) largest eigenvalues, where $P$ is the size of the training set. This prediction works very well on benchmark data sets such as images, yet the assumptions these approaches make on the data are never satisfied in practice. To clarify when the spectral bias prediction holds, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.03348","kind":"arxiv","version":2},"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/2202.03348/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":"2026-07-05T03:57:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oQW0/d8zGFqyccHRyPUKCn16rxCYoR20yAmRfjq8xBEXqOSSxXaF7xiuZYO1Wy4E26qNTUv1RUCvV4GOFALGDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T17:29:39.740007Z"},"content_sha256":"1ec4a7fbfc0afcbc3fb058c70a5688f3a8d351b969de7996bfc0160f76e2d7fa","schema_version":"1.0","event_id":"sha256:1ec4a7fbfc0afcbc3fb058c70a5688f3a8d351b969de7996bfc0160f76e2d7fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RYGSZEOHGLZWYUABKIYTMDCL4E/bundle.json","state_url":"https://pith.science/pith/RYGSZEOHGLZWYUABKIYTMDCL4E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RYGSZEOHGLZWYUABKIYTMDCL4E/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":"2026-07-08T17:29:39Z","links":{"resolver":"https://pith.science/pith/RYGSZEOHGLZWYUABKIYTMDCL4E","bundle":"https://pith.science/pith/RYGSZEOHGLZWYUABKIYTMDCL4E/bundle.json","state":"https://pith.science/pith/RYGSZEOHGLZWYUABKIYTMDCL4E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RYGSZEOHGLZWYUABKIYTMDCL4E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:RYGSZEOHGLZWYUABKIYTMDCL4E","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":"726d27ce95ff2478fa8a61cb1351dc18aadbc431880743edcd41fb51d822aab0","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-02-07T16:48:14Z","title_canon_sha256":"d890731d239c7f13c780546244de65a6dad04d49da90544a2e3060709cf4d880"},"schema_version":"1.0","source":{"id":"2202.03348","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.03348","created_at":"2026-07-05T03:57:31Z"},{"alias_kind":"arxiv_version","alias_value":"2202.03348v2","created_at":"2026-07-05T03:57:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.03348","created_at":"2026-07-05T03:57:31Z"},{"alias_kind":"pith_short_12","alias_value":"RYGSZEOHGLZW","created_at":"2026-07-05T03:57:31Z"},{"alias_kind":"pith_short_16","alias_value":"RYGSZEOHGLZWYUAB","created_at":"2026-07-05T03:57:31Z"},{"alias_kind":"pith_short_8","alias_value":"RYGSZEOH","created_at":"2026-07-05T03:57:31Z"}],"graph_snapshots":[{"event_id":"sha256:1ec4a7fbfc0afcbc3fb058c70a5688f3a8d351b969de7996bfc0160f76e2d7fa","target":"graph","created_at":"2026-07-05T03:57:31Z","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/2202.03348/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recently, several theories including the replica method made predictions for the generalization error of Kernel Ridge Regression. In some regimes, they predict that the method has a `spectral bias': decomposing the true function $f^*$ on the eigenbasis of the kernel, it fits well the coefficients associated with the O(P) largest eigenvalues, where $P$ is the size of the training set. This prediction works very well on benchmark data sets such as images, yet the assumptions these approaches make on the data are never satisfied in practice. To clarify when the spectral bias prediction holds, we ","authors_text":"Antonio Sclocchi, Matthieu Wyart, Umberto M. Tomasini","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-02-07T16:48:14Z","title":"Failure and success of the spectral bias prediction for Kernel Ridge Regression: the case of low-dimensional data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.03348","kind":"arxiv","version":2},"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:c47c3dde4b997470d0cc6fbdfc9e2e06bdc429c08b24fda06173aa7393988569","target":"record","created_at":"2026-07-05T03:57:31Z","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":"726d27ce95ff2478fa8a61cb1351dc18aadbc431880743edcd41fb51d822aab0","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-02-07T16:48:14Z","title_canon_sha256":"d890731d239c7f13c780546244de65a6dad04d49da90544a2e3060709cf4d880"},"schema_version":"1.0","source":{"id":"2202.03348","kind":"arxiv","version":2}},"canonical_sha256":"8e0d2c91c732f36c50015231360c4be132a63b336c1a06843177c17a2a9c849e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e0d2c91c732f36c50015231360c4be132a63b336c1a06843177c17a2a9c849e","first_computed_at":"2026-07-05T03:57:31.794174Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:57:31.794174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qG1g0d7Q3Li6dG4iCe1wYOm8VLZBBTsFZ7xH7pInCeIvxwrN2TIc6DDgolAeLKAWE07FrMEZiGBEIPoMxDIaAg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:57:31.794605Z","signed_message":"canonical_sha256_bytes"},"source_id":"2202.03348","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c47c3dde4b997470d0cc6fbdfc9e2e06bdc429c08b24fda06173aa7393988569","sha256:1ec4a7fbfc0afcbc3fb058c70a5688f3a8d351b969de7996bfc0160f76e2d7fa"],"state_sha256":"4c1d28a39b0f3d8ef29e13e97b9b7eb677b38365ec8403708f220a0ca4600ad0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CAPe14AnutVkFsdG36mfVO5Qhs4q7cg1X8OG8P85RDMl+5xoeTbJKmtNC0goM6VDZqzYXj/FGa3iOjDquMiBBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T17:29:39.741884Z","bundle_sha256":"aabae0d2b5d26deecc045fd2cc11da7d0da0f39bc29c25945ac07d46463be850"}}