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We show that this is not merely a benign default. For a known structured downstream geometry $H\\succ0$, the minimax and maximum-entropy covariance under a Hamiltonian energy budget is $(c/d)H^{-1}$, and Euclidean isotropy incurs a closed-form price of isotropy. More importantly, when the downstream geometry is unknown, no geometry-independent fixed marginal target is canonical: every fixed covariance shape can be maximally misaligned for some structured geometry. We further show that even oracle one-view marginals do not identify the JEPA view-to-view predictive coupling. These results suggest that the structural bias in JEPAs should enter the cross-view coupling rather than a fixed encoder marginal. We instantiate this principle with \\textbf{HamJEPA}, which encodes each view as a phase-space state $(q,","title":"Beyond Isotropy in JEPAs: Hamiltonian Geometry and Symplectic Prediction","url":"https://arxiv.org/abs/2605.20107","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.20107v1 Announce Type: cross \nAbstract: JEPAs often regularize one-view embeddings toward an isotropic Gaussian, implicitly baking Euclidean symmetry into the representation. We show that this is not merely a benign default. For a known structured downstream geometry $H\\succ0$, the minimax and maximum-entropy covariance under a Hamiltonian energy budget is $(c/d)H^{-1}$, and Euclidean isotropy incurs a closed-form price of isotropy. More importantly, when the downstream geometry is unknown, no geometry-independent fixed marginal target is canonical: every fixed covariance shape can be maximally misaligned for some structured geometry. We further show that even oracle one-view marginals do not identify the JEPA view-to-view predictive coupling. These results suggest that the structural bias in JEPAs should enter the cross-view coupling rather than a fixed encoder marginal. We instantiate this principle with \\textbf{HamJEPA}, which encodes each view as a phase-space state $(q,","title":"Beyond Isotropy in JEPAs: Hamiltonian Geometry and Symplectic Prediction","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-20T04:43:44Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.20107"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:b35dc9bc0094456eeda55834ac44b2c67a9b36fe6adf2a23c03723f1f46638220c4ab87e60ba1cbff44a7c89498afa3dad970de50c7f705bdfefee8ffbc0680b","signer":"crovia.substrate","subject":{"observed_at":"2026-05-20T04:43:44Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.20107"},"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":"8ded12edc63d02bc3e9411652cc644da05323930adf14c9221c8d34858bd5759","leaf_index":145199,"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":"6ebe3b5c3609edb080a6eb3f80d06a928262548f2aef83e50aa2b227cc3e2531","side":"left"},{"sibling":"025f1507b111f872c0df384bfef8b2fe8d80d44251a369cb7291f4790679fa8e","side":"left"},{"sibling":"aa19bfde8ac82289a02c5e53391cdc4735e915dda7bb957cba519d129f4af973","side":"left"},{"sibling":"53912bb3ba99e4973b3b9c9e2b184761aec3f282907c2456342db6f3635a4916","side":"left"},{"sibling":"8a6468c7e8e39173e294d7a873f5e6b8457f9706ac8044ba4d224ac6b862e834","side":"right"},{"sibling":"c317c2a6056894749be42405fa1830e73e03e187230c1f4ddb7d8e32279cc63a","side":"left"},{"sibling":"d77ffc4da30d9a4e8a195ba75c70a311b679833ea9892b2b0316f75590747950","side":"right"},{"sibling":"79fb6d27e8a49dd15a97fca96f52d62ff5ee7213d44a5526459d33f42a050928","side":"right"},{"sibling":"f073aa7be27ee7e1d9eb0de5f129f7e9bae0c584fb959378c395b65831dc1d1d","side":"left"},{"sibling":"1526885f19d1fadf6955cf519dbc4e62d593a4bba99d741e8c301740a7068233","side":"left"},{"sibling":"e3a7d5c07f161682d61bd453ffc02ecdf87cfeda70f986d6650017f9d2d6b265","side":"left"},{"sibling":"edbc49f08e5b92291934c05c9e6efd270a6b0698d8d2fa474006366027dfe098","side":"right"},{"sibling":"3e4df6e7457cecbf36f350375e72dcab336a3984422e4c406ef809e4e2944e96","side":"left"},{"sibling":"8f4c0fbe56b6c010fbb8c782ebcd478079bb3f991d8704e2534209a075d9163c","side":"left"},{"sibling":"be08fedc4e72a6fb56606f66812fae7317e09690b9acb18385f4ab117a981238","side":"right"},{"sibling":"0534329a7475dc9df51998c83c16892126679dade0fa34182f21e869599386c7","side":"right"},{"sibling":"2d24720928ead0e7670650eb55f558c4f20e4c18df376f47ba72cfa8cf0ed344","side":"right"},{"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":147301,"merkle_root":"08903d7159c3b38eeeeafc09eab15139ea417f1d94f02f1fbc87296b37db840a","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260521T183701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-21T18:37:33Z","sig_algorithm":"ed25519","signature":"905f2924632dfa2970c8690285f5b5d4a1d891d0e0ef1cbc404ebec2fd937215ac768e16f0a9f28b18977a55ae0bfd226db6833ae7ef588729054117d2da7303","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_02b2d069839ee020e8946036f1525a2607f77af485e7c57b3db52c0977966266"}}