{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:Q2B65K6M6BEXK3DDKDFYJRZ452","short_pith_number":"pith:Q2B65K6M","schema_version":"1.0","canonical_sha256":"8683eeabccf049756c6350cb84c73ceeb26d874ee4c51d52999bb6bd5d8028d4","source":{"kind":"arxiv","id":"2006.04437","version":2},"attestation_state":"computed","paper":{"title":"The Power Spherical distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Nicola De Cao, Wilker Aziz","submitted_at":"2020-06-08T09:51:43Z","abstract_excerpt":"There is a growing interest in probabilistic models defined in hyper-spherical spaces, be it to accommodate observed data or latent structure. The von Mises-Fisher (vMF) distribution, often regarded as the Normal distribution on the hyper-sphere, is a standard modeling choice: it is an exponential family and thus enjoys important statistical results, for example, known Kullback-Leibler (KL) divergence from other vMF distributions. Sampling from a vMF distribution, however, requires a rejection sampling procedure which besides being slow poses difficulties in the context of stochastic backpropa"},"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":"2006.04437","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-06-08T09:51:43Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"cf76aa138b57d4fd51f01f232d07dfb39bf7fab6b9f25835a2d1117253bac7f6","abstract_canon_sha256":"69ebeed1481ba1c85620d277cee6737bc2b9e44021e1de7dbdf5b5cbf119bc9e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:10:16.217230Z","signature_b64":"AgL7zlL9ueoYvdxIima2P8ci+CefqpB6h7Cqs+Y6uwlH2XZRql4pgUCuaUc6xnwuRmJaTturkDr8ytlNnLGeCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8683eeabccf049756c6350cb84c73ceeb26d874ee4c51d52999bb6bd5d8028d4","last_reissued_at":"2026-07-05T01:10:16.216764Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:10:16.216764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Power Spherical distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Nicola De Cao, Wilker Aziz","submitted_at":"2020-06-08T09:51:43Z","abstract_excerpt":"There is a growing interest in probabilistic models defined in hyper-spherical spaces, be it to accommodate observed data or latent structure. The von Mises-Fisher (vMF) distribution, often regarded as the Normal distribution on the hyper-sphere, is a standard modeling choice: it is an exponential family and thus enjoys important statistical results, for example, known Kullback-Leibler (KL) divergence from other vMF distributions. Sampling from a vMF distribution, however, requires a rejection sampling procedure which besides being slow poses difficulties in the context of stochastic backpropa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.04437","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/2006.04437/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":"2006.04437","created_at":"2026-07-05T01:10:16.216819+00:00"},{"alias_kind":"arxiv_version","alias_value":"2006.04437v2","created_at":"2026-07-05T01:10:16.216819+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.04437","created_at":"2026-07-05T01:10:16.216819+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q2B65K6M6BEX","created_at":"2026-07-05T01:10:16.216819+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q2B65K6M6BEXK3DD","created_at":"2026-07-05T01:10:16.216819+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q2B65K6M","created_at":"2026-07-05T01:10:16.216819+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.30366","citing_title":"Escaping the Linearity Trap: Manifold Detours for Black-Box Adversarial Attacks on Singing Audio Deepfake Detection","ref_index":43,"is_internal_anchor":false},{"citing_arxiv_id":"2604.28122","citing_title":"Beyond Gaussian Bottlenecks: Topologically Aligned Encoding of Vision-Transformer Feature Spaces","ref_index":4,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Q2B65K6M6BEXK3DDKDFYJRZ452","json":"https://pith.science/pith/Q2B65K6M6BEXK3DDKDFYJRZ452.json","graph_json":"https://pith.science/api/pith-number/Q2B65K6M6BEXK3DDKDFYJRZ452/graph.json","events_json":"https://pith.science/api/pith-number/Q2B65K6M6BEXK3DDKDFYJRZ452/events.json","paper":"https://pith.science/paper/Q2B65K6M"},"agent_actions":{"view_html":"https://pith.science/pith/Q2B65K6M6BEXK3DDKDFYJRZ452","download_json":"https://pith.science/pith/Q2B65K6M6BEXK3DDKDFYJRZ452.json","view_paper":"https://pith.science/paper/Q2B65K6M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2006.04437&json=true","fetch_graph":"https://pith.science/api/pith-number/Q2B65K6M6BEXK3DDKDFYJRZ452/graph.json","fetch_events":"https://pith.science/api/pith-number/Q2B65K6M6BEXK3DDKDFYJRZ452/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q2B65K6M6BEXK3DDKDFYJRZ452/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q2B65K6M6BEXK3DDKDFYJRZ452/action/storage_attestation","attest_author":"https://pith.science/pith/Q2B65K6M6BEXK3DDKDFYJRZ452/action/author_attestation","sign_citation":"https://pith.science/pith/Q2B65K6M6BEXK3DDKDFYJRZ452/action/citation_signature","submit_replication":"https://pith.science/pith/Q2B65K6M6BEXK3DDKDFYJRZ452/action/replication_record"}},"created_at":"2026-07-05T01:10:16.216819+00:00","updated_at":"2026-07-05T01:10:16.216819+00:00"}