{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:ZUXAG63J6STUG7YKEA7TC435M7","short_pith_number":"pith:ZUXAG63J","schema_version":"1.0","canonical_sha256":"cd2e037b69f4a7437f0a203f31737d67fa1a88cca6f3888f77f0860e83b47abb","source":{"kind":"arxiv","id":"2106.09526","version":3},"attestation_state":"computed","paper":{"title":"Exploring the Properties and Evolution of Neural Network Eigenspaces during Training","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Anne-Kathrin Patricia Windler, Leila Malihi, Mats L. Richter, Ulf Krumnack","submitted_at":"2021-06-17T14:18:12Z","abstract_excerpt":"In this work we explore the information processing inside neural networks using logistic regression probes \\cite{probes} and the saturation metric \\cite{featurespace_saturation}. We show that problem difficulty and neural network capacity affect the predictive performance in an antagonistic manner, opening the possibility of detecting over- and under-parameterization of neural networks for a given task. We further show that the observed effects are independent from previously reported pathological patterns like the ``tail pattern'' described in \\cite{featurespace_saturation}. Finally we are ab"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2106.09526","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-06-17T14:18:12Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"05ce8a22085346ee4e059ff9bce4922d5cc762c6ce5cab9592590340fca0663d","abstract_canon_sha256":"4816e021da159a237a854b4f804923259e43e388f5e623db3f3b1f7a1e3c448f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:26:18.483101Z","signature_b64":"mHlXKmfcQpZVSYo31rW4XCYGlA1o9kSOf115bNz3XYXyoj0xZYiBORUsAQXr2mWs31zt8Kbb2RdgQctQjdnPCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd2e037b69f4a7437f0a203f31737d67fa1a88cca6f3888f77f0860e83b47abb","last_reissued_at":"2026-07-05T03:26:18.482657Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:26:18.482657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exploring the Properties and Evolution of Neural Network Eigenspaces during Training","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Anne-Kathrin Patricia Windler, Leila Malihi, Mats L. Richter, Ulf Krumnack","submitted_at":"2021-06-17T14:18:12Z","abstract_excerpt":"In this work we explore the information processing inside neural networks using logistic regression probes \\cite{probes} and the saturation metric \\cite{featurespace_saturation}. We show that problem difficulty and neural network capacity affect the predictive performance in an antagonistic manner, opening the possibility of detecting over- and under-parameterization of neural networks for a given task. We further show that the observed effects are independent from previously reported pathological patterns like the ``tail pattern'' described in \\cite{featurespace_saturation}. Finally we are ab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.09526","kind":"arxiv","version":3},"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/2106.09526/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2106.09526","created_at":"2026-07-05T03:26:18.482715+00:00"},{"alias_kind":"arxiv_version","alias_value":"2106.09526v3","created_at":"2026-07-05T03:26:18.482715+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.09526","created_at":"2026-07-05T03:26:18.482715+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZUXAG63J6STU","created_at":"2026-07-05T03:26:18.482715+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZUXAG63J6STUG7YK","created_at":"2026-07-05T03:26:18.482715+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZUXAG63J","created_at":"2026-07-05T03:26:18.482715+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZUXAG63J6STUG7YKEA7TC435M7","json":"https://pith.science/pith/ZUXAG63J6STUG7YKEA7TC435M7.json","graph_json":"https://pith.science/api/pith-number/ZUXAG63J6STUG7YKEA7TC435M7/graph.json","events_json":"https://pith.science/api/pith-number/ZUXAG63J6STUG7YKEA7TC435M7/events.json","paper":"https://pith.science/paper/ZUXAG63J"},"agent_actions":{"view_html":"https://pith.science/pith/ZUXAG63J6STUG7YKEA7TC435M7","download_json":"https://pith.science/pith/ZUXAG63J6STUG7YKEA7TC435M7.json","view_paper":"https://pith.science/paper/ZUXAG63J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2106.09526&json=true","fetch_graph":"https://pith.science/api/pith-number/ZUXAG63J6STUG7YKEA7TC435M7/graph.json","fetch_events":"https://pith.science/api/pith-number/ZUXAG63J6STUG7YKEA7TC435M7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZUXAG63J6STUG7YKEA7TC435M7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZUXAG63J6STUG7YKEA7TC435M7/action/storage_attestation","attest_author":"https://pith.science/pith/ZUXAG63J6STUG7YKEA7TC435M7/action/author_attestation","sign_citation":"https://pith.science/pith/ZUXAG63J6STUG7YKEA7TC435M7/action/citation_signature","submit_replication":"https://pith.science/pith/ZUXAG63J6STUG7YKEA7TC435M7/action/replication_record"}},"created_at":"2026-07-05T03:26:18.482715+00:00","updated_at":"2026-07-05T03:26:18.482715+00:00"}