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The spCauchy family has heavy-tailed global behavior and admits an exact differentiable reparameterization by applying a M\\\"obius transformation to uniform samples on the sphere. We show that, in the high-concentration limit, spCauchy recovers the local tangent-space geometry of the von Mises-Fisher (vMF) distribution under an explicit concentration parameter mapping, while avoiding the high-order Bessel-function evaluations required by vMF implementations. For training, the Kullback-Leibler divergence to a uniform spherical prior admits rapidly convergent series, stable quadrature, and high-concentration asymptotic forms. We further establish monotonicity of the concentration-dependent KL core and derive analytic brackets with closed-form surrogates and error control, supporting stable approximation in extreme ","title":"Hyperspherical Variational Autoencoders Using Efficient Spherical Cauchy Distribution","url":"https://arxiv.org/abs/2506.21278","vendor":"arxiv_cs_ai"},"summary":"arXiv:2506.21278v3 Announce Type: replace-cross \nAbstract: We propose spherical Cauchy (spCauchy) latent variables for variational autoencoders on hyperspherical latent spaces. The spCauchy family has heavy-tailed global behavior and admits an exact differentiable reparameterization by applying a M\\\"obius transformation to uniform samples on the sphere. We show that, in the high-concentration limit, spCauchy recovers the local tangent-space geometry of the von Mises-Fisher (vMF) distribution under an explicit concentration parameter mapping, while avoiding the high-order Bessel-function evaluations required by vMF implementations. For training, the Kullback-Leibler divergence to a uniform spherical prior admits rapidly convergent series, stable quadrature, and high-concentration asymptotic forms. We further establish monotonicity of the concentration-dependent KL core and derive analytic brackets with closed-form surrogates and error control, supporting stable approximation in extreme ","title":"Hyperspherical Variational Autoencoders Using Efficient Spherical Cauchy Distribution","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-02T04:43:38Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2506.21278"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:1549b6d9a3b9ca919c64ef1d1883b190199bccc3af97c10e048e9c1a7bb7c2693f9d3ba2ac963c72e03504e835511716c6bbab24aab71c58a185467e25f6ad05","signer":"crovia.substrate","subject":{"observed_at":"2026-06-02T04:43:38Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2506.21278"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"47c399e8f42cda53146ab18a846355ba39ca005e70a95b097a646a41b4036d88","leaf_index":205861,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"53658aad84e106dc1cbc82976f814da1ee06ef05a6f1f991b62acabc6f029ecd","side":"left"},{"sibling":"29e3848d06c1174f0966f90287c35f6b494f13bd500622d77f2c7782f9a5d43f","side":"right"},{"sibling":"091e90a987f6c8b02632aa618b4b755b492a71ccb3c5f1ede24c1430f08106a4","side":"left"},{"sibling":"18884630a27b75dad1f94a40c66bb14dadd20cece9750307bb94e0415ae7416f","side":"right"},{"sibling":"2e8ab506ec416eb20413e6783c7b86ce17c861c5306e40c42ddf6fc03afb6216","side":"right"},{"sibling":"4f16de82ab0db0ac5454af010b59885c3266df92e72c858a67542f343f45793c","side":"left"},{"sibling":"c67e085a85c0f23aa2cb50fd322074122571e52743812cc3860e76bbffd3a91b","side":"right"},{"sibling":"a5c0411da65d36a27f4e797deeace23f77314552708425e4e91c3ebf671bc23b","side":"right"},{"sibling":"6ac554ede1f78dc3a28ebe5e1155c2b9c258b71805fdd7ad2ec992697f3ccd0c","side":"right"},{"sibling":"5e1949edfad76bc6a73d008dc8be8a0c6fe4a7fb64c8beaf70e5023ca11d35e0","side":"right"},{"sibling":"e4bd1aaaf3f336d9b072b4d1fc234246fc3cf2874ca873b7741c03eaf97911f2","side":"left"},{"sibling":"e6adead8216db4cae92f0a036d53baebf30eed95a99c0d10758aa75bb7780f2f","side":"right"},{"sibling":"1acc2b7ff453ffd8c97b80ae4db5358780f0c6796874fd75403791dbe99f8cd7","side":"right"},{"sibling":"24d1bb4b13e0e46131b27b70a48e65fcf4e2e14b95e3bb83ade821e9df530f6b","side":"left"},{"sibling":"5f86f58c28b1a86ae06dfff4666bb9fba8866021a81fd4f1d200aa9af4722dfb","side":"right"},{"sibling":"f6cc6f94f6944ae21390afc65ac9e91dc31f84ee6e060681bba5ae08058294bd","side":"right"},{"sibling":"c300cf0154c136afc09b1702a0be98f4ba5b6dc5cf57e8cc714ec1eaf4196eff","side":"left"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":206226,"merkle_root":"d2a6d32b13cbf343fb143b21a756d0533864ae6577a376ee84ba867b949207ec","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260602T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-02T05:37:46Z","sig_algorithm":"ed25519","signature":"abd9956cfb19dd1fb8142c46a220bac2514848c6abb0e79b8b0940206cc3ebb00894d4daaf9f786427f82a7cc12482e7fda79054ebb06bceaa9b4b97e23fb30e","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_d472d04cfbe40825608a55a7b8ebdeb48b6a3b21c23aa01457e77ae204d2f57d"}}