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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 resolves this limitation by ensuring","title":"Long Range Frequency Tuning for QML","url":"https://arxiv.org/abs/2602.23409","vendor":"arxiv_cs_ai"},"summary":"arXiv:2602.23409v2 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 resolves this limitation by ensuring","title":"Long Range Frequency Tuning for QML","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-18T04:43:11Z","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":"ed25519:5ffbbb72dfb2632f6bebafe80b112224e501d1d6070ca5d532ddbb97a42a9f7ac48d57f73f8d82db9d307b76d6940401630e1282927163481af26fb8079efd03","signer":"crovia.substrate","subject":{"observed_at":"2026-05-18T04:43:11Z","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":"4445001b8f978d71987b07e2b4b959d545a3a34a97a0e9db0e6ccf9cbc549d55","leaf_index":140791,"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":"bbc89dbb1c5fbcc8749ecb0d3667ca211ae91e750445ccadda944b0bd44673a7","side":"left"},{"sibling":"73fba1d7ff000ee10e23143d3a100a2fdfb3345925314a04f2acc7834b46f605","side":"left"},{"sibling":"de79dc13783c616c9e443afb2c11c4bb804c6ac4dd0e097156ccb35dc37c9997","side":"left"},{"sibling":"0f0efec9f4fadf19583bcd1b704d7037b8cc87c55aed687565716b5f1a943a41","side":"right"},{"sibling":"1030005f0dffd7184c294c1675687c2f7200ac641111290389abd489bb5ac4af","side":"left"},{"sibling":"b59f5b6589804050df943e9de027b74c1fffb33440b7e6dfcf198d1d29863180","side":"left"},{"sibling":"518d2c79e4bbff1e18ea05bbb3663a3fb58b3b1682a658f34e706ea23e091089","side":"left"},{"sibling":"30c60828b6b0ade79197e585b88c06ccf4f348c1e62fbf6710d89ae2c2e9dcfb","side":"left"},{"sibling":"6bedf73520cf3dd8758d8bdedf3be245de9aea97abd42934aae25539176ae1b2","side":"left"},{"sibling":"07abc3bad689e74e6304772503dc9372a118e6f66883b8e88c43414efddac063","side":"right"},{"sibling":"28b78fb112bcf26b6801664db97eb8f52a9bccbf0a7ae6766e11845d443692df","side":"left"},{"sibling":"68d0a4634c1460a19c92edd9480df3aa733b814463e7420d1e14471bf61b2f83","side":"right"},{"sibling":"8af64f275b862349aa3bbb9d5cd7fa9a7fdd5620af3bf1b36b2a4519b0b53bdf","side":"right"},{"sibling":"8f4c0fbe56b6c010fbb8c782ebcd478079bb3f991d8704e2534209a075d9163c","side":"left"},{"sibling":"b98c2afadb358e5387e88f19588f8343a81b488d9b44a6f7e57a032db3a1b030","side":"right"},{"sibling":"11b0c1591747f09f7c8971a6caa19befcd81317ca9dfd417b143234df4e10c79","side":"right"},{"sibling":"87206f3bcc342797c990d87f7235c01f78d32ca59cfaf8ad18d71afc879ba477","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":140892,"merkle_root":"6cca56ead155990456b8a014cc50bddbe710f409b26e3d1bfa6fb12b0bfcf6bf","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260518T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-18T05:37:30Z","sig_algorithm":"ed25519","signature":"1e1135f7595f79b14fb11f5fa81a2e17ad31b11b44b427a5e40a7d511cd86447daf492babd368ab571cf26404c8c74c450d460130fca4b064eb2760367489a0f","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_61952eeadf354de8f3aa3befc2313e7290bfbfc5d6791edfe19b6273175c9c9b"}}