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Trainable-frequency (TF) circuits promise a reduction by learning the data-encoding prefactors alongside the ansatz parameters, adapting the accessible frequency spectrum to the target during training. We identify a practical barrier that prevents this promise from being realized: the prefactor gradient is suppressed by the spectral gap between the circuit's accessible frequencies and the target spectrum, independently of the ansatz parameters, confining gradient-driven prefactor movement to a narrow neighborhood of initialization. We propose \\emph{ternary grid initialization} -- setting prefactors to $\\{1, 3, 9, \\ldots, 3^{k-1}\\}$ -- which ensures every target frequency withi","title":"Long Range Frequency Tuning for QML","url":"https://arxiv.org/abs/2602.23409","vendor":"arxiv_cs_ai"},"summary":"arXiv:2602.23409v3 Announce Type: replace-cross \nAbstract: Angle-encoded variational quantum circuits admit a truncated Fourier series representation of their output, but approximating functions with maximum frequency $\\omega_{\\max}$ using fixed unary encoding requires $\\mathcal{O}(\\omega_{\\max})$ encoding gates. Trainable-frequency (TF) circuits promise a reduction by learning the data-encoding prefactors alongside the ansatz parameters, adapting the accessible frequency spectrum to the target during training. We identify a practical barrier that prevents this promise from being realized: the prefactor gradient is suppressed by the spectral gap between the circuit's accessible frequencies and the target spectrum, independently of the ansatz parameters, confining gradient-driven prefactor movement to a narrow neighborhood of initialization. We propose \\emph{ternary grid initialization} -- setting prefactors to $\\{1, 3, 9, \\ldots, 3^{k-1}\\}$ -- which ensures every target frequency withi","title":"Long Range Frequency Tuning for QML","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-21T04:43:35Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2602.23409"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:ede0cdbe99bc4c72eede716959f48b1363933d635f838c7abc3e25c7ba7d22ff10c926c09c08aa736a5139751f299ca3b56519180680b823454fc797bb41a005","signer":"crovia.substrate","subject":{"observed_at":"2026-07-21T04:43:35Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2602.23409"},"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":"06ecf7e257d77c39cafa2ed693c5a67acad27097935f1f5a771c4a1c35a05a93","leaf_index":336952,"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":"f32add44a04756b6aeea42cbfc6a43177c0db19082d8bdefecae3764e9d27645","side":"right"},{"sibling":"e3989dcb3d3eac180d50fa78fc79220429245cf50f3dedff273c746a24e98cac","side":"right"},{"sibling":"37064b3772d0b6ab1b8abcf98cb68a7dbbab3b8eacddaa7f184cc6b362b6c9fa","side":"right"},{"sibling":"90317a295fd4599ba107de25d5eaa63397e9cb09072f156719cfb0e8f91bc763","side":"left"},{"sibling":"24d5ee4978268aeb8f558ef20aad366b0953b3bf3f0cf558fab499d1678ecc80","side":"left"},{"sibling":"bfabfb8c7ddd2bdc7b69e0e90130c2fa87e5e86c2ab6eb510187bf548726b65c","side":"left"},{"sibling":"950013dbd7f9f5861e4c5ff582a4f28f41529fee5ece541adb6d424c9cbd1f75","side":"right"},{"sibling":"45255096c5a08e740a615b6e3c262589a170dbfc373bdeaceae175916dd2ab97","side":"right"},{"sibling":"1298242aa509bc13b92160250ead2d95a721941ca6310e33b9eb0bf0821557d0","side":"right"},{"sibling":"61d44c6d16b87de577db53cff0dba2f003c50c036d92dc335120aa70124c8788","side":"right"},{"sibling":"5d0b792dbe69fd0a7cd8d79b467aa10204d1f25be602c06190f3423bc22727b8","side":"left"},{"sibling":"9eb5077edfb3dc553857d4794b925bfce117e0f8a1d049af5d0dd9026b470eef","side":"right"},{"sibling":"414b1a70fd1dcb25489a194714b97492b066684b15d0b7a48a176c4b9b5bc713","side":"right"},{"sibling":"21d66dd41003813f710b7617944f1bfba3258658a5d3370c21cad8f9e945bc99","side":"left"},{"sibling":"613f015699131eb89bd755dee67133be95af25cf5f16c1c8ce4b99d963b8dd86","side":"right"},{"sibling":"a729b574b1135956436ded5eef1fe8f08014ff6a0729749d307ab1bca93fcdc9","side":"right"},{"sibling":"77025bcb374a7ad74f520643e20a8ae1205a7ee78507b0beb93117760f1c29d3","side":"left"},{"sibling":"4bf21052e085e8ac81f1dec1d2b310bd12bf948992de6177d12e9d2fda8d39f0","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","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":337144,"merkle_root":"5e969cc01afa67e4dbe5d37b712cdb10f4aa1fd74404e02eab724cf487c8d6d9","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260721T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-21T05:38:38Z","sig_algorithm":"ed25519","signature":"5c0c1a8dd2793d787ccd5e49e8b4d70eed136352555518589f05c74be357fc171702e42a76c3a556d90e3d51ff36cb3d292aaac83c66566de7b943f318bda50c","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_ec8eea56274d0db97a33e6a7aed76126bc4fdcd407a1b862967308cd2bbf78c1"}}