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Predominant methods aggregate unimodal inference distributions using either a product of experts (PoE), a mixture of experts (MoE), or their combinations to approximate the joint posterior. In this work, we revisit multimodal inference through the lens of probabilistic opinion pooling, an optimization-based approach. We start from H\\\"older pooling with $\\alpha=0.5$, which corresponds to the unique symmetric member of the $\\alpha\\text{-divergence}$ family, and derive a moment-matching approximation, termed Hellinger. 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We then leverage such an approximation to propose HELVAE, a multimodal VAE that avoids sub-sampling, yielding an efficient yet effective model that: (i) learns more expressive latent representations as additional modalities are observed; and (ii) empirically achieves better trade-offs betwee","title":"Hellinger Multimodal Variational Autoencoders","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-12T04:43:44Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2601.06572"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:c78b6daf7b7e39dd9218af88525c7a10a6558ddac19036a860722834c42f77a705da4f4eca6d2b628d982c9f0b7995b5a54228f2e2066411af39f16913380700","signer":"crovia.substrate","subject":{"observed_at":"2026-06-12T04:43:44Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2601.06572"},"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":"5ff5ea5b433f451e058e18155953678bb024bf9dfad5343ebbd2929691ba7d14","leaf_index":229862,"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":"2402d9897f6aaf374c5738ea503274b49fdcb0ae49b3e80e8452c189c54a203d","side":"right"},{"sibling":"a28bbc9fddb3a91af70c0f4aa81288ac9289b814bc63012da2b335c87cd6fc5e","side":"left"},{"sibling":"6eeeea48b35be327ac947ad289d2591dfabcf032bc001c83f375996ce31355b0","side":"left"},{"sibling":"8864de611b135b909e97bdf444c834e698fc4ada5f33e457307329c53360c8c9","side":"right"},{"sibling":"0c9dccebd38fdcb0409a63b7a697e9f24cc9bd0e4349ce6e7f09c4ae9a4d97cd","side":"right"},{"sibling":"17e2e769c49a0f0412de9a8660ec966b27ca94aab000943b74557ef687255c70","side":"left"},{"sibling":"f816461bcfd19ac42215605cc2844a30588d3ec7755490de2c1e82f01f0ff5de","side":"left"},{"sibling":"ae0aa292f48289283e26aa363532f22206cc7cea51771c75c6c011c898bec69c","side":"left"},{"sibling":"99d288e6cd43a807fba958865176bb1c08b82471afe942f6e4989eaeeb7275aa","side":"left"},{"sibling":"d385017d38a86f6abc492026a7cd60ceb3b3ff2486142dc49e5acb179f4b7d11","side":"right"},{"sibling":"bde25d7e94e64717e426a97f6fcb4907e92b5c61fc89d92d7e0947a2249c3f6b","side":"right"},{"sibling":"d10d772a4984cae00e65ab24af21d1d260e475bbaae3f17871859eb705bd3999","side":"right"},{"sibling":"e79159853f2f35ddae8e3247d515e433c534277b287d65bbd77ae989aa4992fa","side":"right"},{"sibling":"3054319f1840cce0eaaf0bc4b1ae38e5bf8b6210927d924a750775cc7d77cca6","side":"right"},{"sibling":"0fd8b5059f279c4a4a6688de2472fdbc25543fee183df19b21dacca880354cff","side":"right"},{"sibling":"a04392fb9f2a3a620840e3b3fecd93d12e6d224e481c162389d8ae64e7194599","side":"left"},{"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":232015,"merkle_root":"62bfb7809bb55667ad7eeebdb48267b9b2c1ee89bb808ea1e6d3a814a15aa402","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260617T133701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-17T13:39:59Z","sig_algorithm":"ed25519","signature":"930a3563c643cc7518d048b12a1f5392a96a5edce49533ba0a56f11b6cc69319bb1c800aacc46b52a6941c4d05dae255a45cac757d6093c971b96852c24f140e","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_bcee866e0099962419bd758fff166505e573534393523694f39c86fdb5c119ea"}}