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We introduce the \\textbf{Hybrid Hierarchical SAE (HH-SAE)} to resolve this by factorizing manifolds into a nested hierarchy of \\textbf{Contextual} ($L_0$), \\textbf{Atomic} ($f_1$), and \\textbf{Compository} ($f_2$) tiers. Evaluating across disparate manifolds, HH-SAE demonstrates superior resolution by \\textbf{``fracturing'' administrative clinical labels into physiological modes} and achieving a peak \\textbf{cross-domain zero-shot AUC of 0.9156 in fraud detection}. Path ablation confirms the architecture's structural necessity, revealing a 13.46\\% utility collapse when contextual subtraction is removed. Finally, knowledge-steered synthesis achieves a +9.9\\% AUPRC lift over state-of-the-art generators, proving that HH-SAE effectively prioritizes high-order me","title":"HH-SAE: Discovering and Steering Hierarchical Knowledge of Complex Manifolds","url":"https://arxiv.org/abs/2605.10536","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.10536v1 Announce Type: cross \nAbstract: Rare semantic innovations in high-dimensional, mission-critical domains are often obscured by dense background contexts, a challenge we define as \\textit{feature density conflict}. We introduce the \\textbf{Hybrid Hierarchical SAE (HH-SAE)} to resolve this by factorizing manifolds into a nested hierarchy of \\textbf{Contextual} ($L_0$), \\textbf{Atomic} ($f_1$), and \\textbf{Compository} ($f_2$) tiers. 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Finally, knowledge-steered synthesis achieves a +9.9\\% AUPRC lift over state-of-the-art generators, proving that HH-SAE effectively prioritizes high-order me","title":"HH-SAE: Discovering and Steering Hierarchical Knowledge of Complex Manifolds","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-12T04:43:42Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.10536"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:3213f31355f47ae37b7fc6a45c7441cd42e946af99ecf8527b90b5be296399eb83601f07859cca210aa454f85eb0fa2edd5667d2b573e5fbd751ab69bbfbe30e","signer":"crovia.substrate","subject":{"observed_at":"2026-05-12T04:43:42Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.10536"},"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":"9130f51367cf6bd1d787c6349bad68cb535d89a3ecf8ca38b610dfb7e1514d12","leaf_index":128884,"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":"bff4160051ac21b4b1ac5fc44cb9e9cada5bdb7f94bb59a18baa0b2225275cef","side":"right"},{"sibling":"6df3f3adede1ed19f810e828ae843a69a4dc74ccc61655b8d289d19b09494f78","side":"right"},{"sibling":"a331fff27a96146f9d8463169eb0faf5b5f835bdd9c433f9e1853312533aadbf","side":"left"},{"sibling":"8178ef5517d750d7e33d38587bb7bf0d259674a36cb5669caa7c3e53eb3af44e","side":"right"},{"sibling":"096f26885af6e2b415095978b8e79153500455870f3b0ed5fe35ed15213ee754","side":"left"},{"sibling":"810f061c10e36b6799e34a835d3b337a068f6963a6daea1e25f4b79bb263c897","side":"left"},{"sibling":"35de91831a229ebffda43a52472669e391dfea2fabdcbb02a5ed218458366227","side":"left"},{"sibling":"17788012ee9d23c33d35ead8be5aa8d08d73dd70833c55b77c06f0f8d286c3ef","side":"right"},{"sibling":"9b7895252355a8c8a373671590682bbf4d36d41befce49b5e889eaf896415156","side":"left"},{"sibling":"1d74b0fb79eace68949b4d82b0e430b1d9eb122c125f67f5be7d50c074c228e7","side":"left"},{"sibling":"c6eaf7a4fcab2db96e9e9423acb6922c80f64882d0f3f50d09e53a4807d23084","side":"left"},{"sibling":"df12eaabc0a370aff5d0488478f48d2b3f90d025c903643f98ea804b017688ec","side":"right"},{"sibling":"ffc4d51379293bc3e1910c7d612f409dc610fd9acf8241793fb89f82e1bad4ef","side":"left"},{"sibling":"62ac6554017807bd83187f5a3e5f4f72d6c482616429c2780e9fff1f4845fa04","side":"left"},{"sibling":"3a5e69cf0803f4c91f3895ed7c9a95748fef240bec4422e167c05300f79f06c0","side":"left"},{"sibling":"f2817ab288b5324fe49770372c7a10f33f7cd11005f8d4c0a730316f5229dc98","side":"left"},{"sibling":"725fac972e772ca0dc598810ea1abc70df472f72d2d6ab8a0baee2b80e5d2f4c","side":"left"},{"sibling":"98fc57dfef8873b512edc8340f7181df57302bb96777625e072235c62d7c5895","side":"right"}]},"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":134292,"merkle_root":"77fc9c28fae777b81da5b495b3115474df6592dfac590333213d3bdf8b94a9b3","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260515T023701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-15T02:37:25Z","sig_algorithm":"ed25519","signature":"68107a834b00b24f5d4501e5ec727445311f132a486567ecc4c72a4e6dff24c8c21f2de3105293353ba5fdbe370d032819af6aa70f694e2e39b6af6737507009","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_b7ed0d5fb9a1a5e57d97941df08945c372fb68975f5ec6839a0096ee3040607a"}}