{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:BZMMVRF4YT5TOYIJCSDFFMXRAD","short_pith_number":"pith:BZMMVRF4","schema_version":"1.0","canonical_sha256":"0e58cac4bcc4fb376109148652b2f100e5446b0da99cf8ae69c6d9d8a0a9fd82","source":{"kind":"arxiv","id":"2605.14413","version":1},"attestation_state":"computed","paper":{"title":"MahaVar: OOD Detection via Class-wise Mahalanobis Distance Variance under Neural Collapse","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Class-wise Mahalanobis distance variance distinguishes in-distribution from out-of-distribution samples under Neural Collapse geometry.","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Donghwan Kim, Hyunsoo Yoon","submitted_at":"2026-05-14T05:58:19Z","abstract_excerpt":"Out-of-distribution (OOD) detection is a critical component for ensuring the reliability of deep neural networks in safety-critical applications. In this work, we present a key empirical observation: for in-distribution (ID) samples, class-wise Mahalanobis distances exhibit a pronounced sharp minimum structure, where the distance to the nearest class is small while distances to all other classes remain large, resulting in high variance across classes. In contrast, OOD samples tend to exhibit a less pronounced sharp minimum structure, producing comparatively lower variance across classes. We fu"},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.14413","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-14T05:58:19Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"f3822713da12a3622a8b7784d24a32d9d96184005ac759827cee2cd5a6dc43e1","abstract_canon_sha256":"278f8490cab73b8d676a5fa087764f7f15c41047d3f8689c9d9b034f3d931324"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:07.339573Z","signature_b64":"5wkCtA4VVra/Xi4ISo4Xu4aCpG8nG7hVvcqUNUv405M/XGDE8w1p+97XDPe8s41kU/bDBfh88YdQVQarZJxEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e58cac4bcc4fb376109148652b2f100e5446b0da99cf8ae69c6d9d8a0a9fd82","last_reissued_at":"2026-05-17T23:39:07.339041Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:07.339041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"MahaVar: OOD Detection via Class-wise Mahalanobis Distance Variance under Neural Collapse","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Class-wise Mahalanobis distance variance distinguishes in-distribution from out-of-distribution samples under Neural Collapse geometry.","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Donghwan Kim, Hyunsoo Yoon","submitted_at":"2026-05-14T05:58:19Z","abstract_excerpt":"Out-of-distribution (OOD) detection is a critical component for ensuring the reliability of deep neural networks in safety-critical applications. In this work, we present a key empirical observation: for in-distribution (ID) samples, class-wise Mahalanobis distances exhibit a pronounced sharp minimum structure, where the distance to the nearest class is small while distances to all other classes remain large, resulting in high variance across classes. In contrast, OOD samples tend to exhibit a less pronounced sharp minimum structure, producing comparatively lower variance across classes. We fu"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"MahaVar achieves state-of-the-art performance on CIFAR-100 and ImageNet, with consistent improvements in both AUROC and FPR@95 over existing Mahalanobis-based methods across all benchmarks.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The theoretical analysis relies on relaxed Neural Collapse assumptions on within-class compactness and inter-class separation to establish that ID samples structurally exhibit high class-wise distance variance.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"MahaVar augments the Mahalanobis OOD score with class-wise distance variance, which is theoretically higher for in-distribution samples under relaxed Neural Collapse geometry.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Class-wise Mahalanobis distance variance distinguishes in-distribution from out-of-distribution samples under Neural Collapse geometry.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d3359c8335d105794d1950ecd084ecadc20780d0094beb94a37150a36232cf07"},"source":{"id":"2605.14413","kind":"arxiv","version":1},"verdict":{"id":"cb715e4e-01d8-40a7-b0be-cee8eb5adde0","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:14:03.966574Z","strongest_claim":"MahaVar achieves state-of-the-art performance on CIFAR-100 and ImageNet, with consistent improvements in both AUROC and FPR@95 over existing Mahalanobis-based methods across all benchmarks.","one_line_summary":"MahaVar augments the Mahalanobis OOD score with class-wise distance variance, which is theoretically higher for in-distribution samples under relaxed Neural Collapse geometry.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The theoretical analysis relies on relaxed Neural Collapse assumptions on within-class compactness and inter-class separation to establish that ID samples structurally exhibit high class-wise distance variance.","pith_extraction_headline":"Class-wise Mahalanobis distance variance distinguishes in-distribution from out-of-distribution samples under Neural Collapse geometry."},"references":{"count":40,"sample":[{"doi":"","year":2024,"title":"NECO: NEural collapse based out-of-distribution detection","work_id":"da4988e7-8795-4a41-bdd6-4dc4ed9473a4","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"In or out? fixing imagenet out-of- distribution detection evaluation","work_id":"10e1041e-c563-4f30-a880-29fb50e87354","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2014,"title":"Describing textures in the wild","work_id":"177d7e6f-6d89-41e0-9ef5-2181a523583c","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2009,"title":"Imagenet: A large- scale hierarchical image database","work_id":"6ee29c54-0013-4f3e-8bcb-5c870412e0cb","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2012,"title":"The mnist database of handwritten digit images for machine learning research [best of the web].IEEE signal processing magazine, 29(6):141–142","work_id":"cbfd4ad1-6390-4562-a243-80a69e09024a","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":40,"snapshot_sha256":"be93e79618ce647363858ebf9514d1c3c259f2447680c74a79888bb305a5ea94","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"7a525b10c7ee14b74822fd655cab5ddf759705043a8cee62bc949a2179c5343e"},"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":"2605.14413","created_at":"2026-05-17T23:39:07.339127+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.14413v1","created_at":"2026-05-17T23:39:07.339127+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.14413","created_at":"2026-05-17T23:39:07.339127+00:00"},{"alias_kind":"pith_short_12","alias_value":"BZMMVRF4YT5T","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"BZMMVRF4YT5TOYIJ","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"BZMMVRF4","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BZMMVRF4YT5TOYIJCSDFFMXRAD","json":"https://pith.science/pith/BZMMVRF4YT5TOYIJCSDFFMXRAD.json","graph_json":"https://pith.science/api/pith-number/BZMMVRF4YT5TOYIJCSDFFMXRAD/graph.json","events_json":"https://pith.science/api/pith-number/BZMMVRF4YT5TOYIJCSDFFMXRAD/events.json","paper":"https://pith.science/paper/BZMMVRF4"},"agent_actions":{"view_html":"https://pith.science/pith/BZMMVRF4YT5TOYIJCSDFFMXRAD","download_json":"https://pith.science/pith/BZMMVRF4YT5TOYIJCSDFFMXRAD.json","view_paper":"https://pith.science/paper/BZMMVRF4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.14413&json=true","fetch_graph":"https://pith.science/api/pith-number/BZMMVRF4YT5TOYIJCSDFFMXRAD/graph.json","fetch_events":"https://pith.science/api/pith-number/BZMMVRF4YT5TOYIJCSDFFMXRAD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BZMMVRF4YT5TOYIJCSDFFMXRAD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BZMMVRF4YT5TOYIJCSDFFMXRAD/action/storage_attestation","attest_author":"https://pith.science/pith/BZMMVRF4YT5TOYIJCSDFFMXRAD/action/author_attestation","sign_citation":"https://pith.science/pith/BZMMVRF4YT5TOYIJCSDFFMXRAD/action/citation_signature","submit_replication":"https://pith.science/pith/BZMMVRF4YT5TOYIJCSDFFMXRAD/action/replication_record"}},"created_at":"2026-05-17T23:39:07.339127+00:00","updated_at":"2026-05-17T23:39:07.339127+00:00"}