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This paper asks under what conditions a content-adaptive patching operator should outperform a tuned uniform one. Local heterogeneity alone is not enough: under pointwise forecasting losses, a complex-looking region is not automatically one where finer patching reduces the loss. We model patching as a budgeted bitrate allocation and derive an explicit threshold that a dynamic patching rule must satisfy to beat a well-tuned uniform baseline, then bound the achievable improvement both locally (a quadratic surrogate) and globally (a strong-convexity bound under the model's assumptions). Two structural results follow: without a coupling constraint, scalar local complexity cannot produce a non-uniform optimum under a common loss landscape; and once the backbone is trained to its representat","title":"Adaptive Patching Is Harder Than It Looks For Time-Series Forecasting","url":"https://arxiv.org/abs/2606.04074","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.04074v1 Announce Type: cross \nAbstract: Adaptive patching is a recent and compelling proposal for time-series Transformers: allocate finer patches where the sequence looks locally informative. This paper asks under what conditions a content-adaptive patching operator should outperform a tuned uniform one. Local heterogeneity alone is not enough: under pointwise forecasting losses, a complex-looking region is not automatically one where finer patching reduces the loss. We model patching as a budgeted bitrate allocation and derive an explicit threshold that a dynamic patching rule must satisfy to beat a well-tuned uniform baseline, then bound the achievable improvement both locally (a quadratic surrogate) and globally (a strong-convexity bound under the model's assumptions). Two structural results follow: without a coupling constraint, scalar local complexity cannot produce a non-uniform optimum under a common loss landscape; and once the backbone is trained to its representat","title":"Adaptive Patching Is Harder Than It Looks For Time-Series Forecasting","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-04T04:43:08Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.04074"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:7d5c7b679b6815378711861a739b8aba527214de019e7453b5a6b3e98d913f74edf76d4f701bff7baecd07a78130232a2c9afb980d94d8da248dd8b16a96940b","signer":"crovia.substrate","subject":{"observed_at":"2026-06-04T04:43:08Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.04074"},"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":"c782bbf2afceb2a1fad6da596cd041b5b491f05fb4f19c27cc79a09d695c124f","leaf_index":212625,"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":"5d1f955bd86f592305e6ec59ba55138dd6037d3a1430933d78ad15834cbc99fd","side":"left"},{"sibling":"65c87dd8f7616ba4443289364652e3e509abaa5afc8afcf3e450aecaa84f86d1","side":"right"},{"sibling":"a61db09c847df22093314022784ab79f2f08c6896b28689f5d543cc725d9bea3","side":"right"},{"sibling":"19651e5ca8d080dc0f2faac1ed1f179684cfac765a2c41f3784fc18ba66d83f4","side":"right"},{"sibling":"94accb9622dfb0b35aaabe0b377aeab967297202d7b813257223ef630cda6f58","side":"left"},{"sibling":"e45a00123eb622a9e74504132e353e625e4bbbd90046168a18f3faf0a8c32548","side":"right"},{"sibling":"d2014279f61fb9e0da911cabc2d3a32664afdbd198aebf9c06cb2b3f9176da97","side":"right"},{"sibling":"2943aa232ba1099978a3aeee29e3e0c39faa6231597512d9c82160e7a5a2db32","side":"left"},{"sibling":"c78f0d662697b816291c956749c41d06c16e4dc4c3d390f9a90590e3f2821765","side":"right"},{"sibling":"cfb460164a914d1f96a36aa17124b45bb5417829d2adbe5ca48375dbd842ec44","side":"left"},{"sibling":"a84ebc8e894a9893ee34d1afc942d15f28243b926f1e5f9d7f10a3de1e795262","side":"left"},{"sibling":"f8f6bd9da448fa097e2115b71146f61691d9f8807aca291c87c633192a7224e9","side":"left"},{"sibling":"2dca509b3eb767a47cf215d4315f230ce9103a76264412008ae23a349b519ef1","side":"left"},{"sibling":"24d1bb4b13e0e46131b27b70a48e65fcf4e2e14b95e3bb83ade821e9df530f6b","side":"left"},{"sibling":"422bcf7e281ca3a607f3726a5e6b8fabdb85e8b32199b4a86356998e260a0b34","side":"right"},{"sibling":"54a99163a4a62374c3ca6fb46294222f1d4b1a9d0b636e27256b0e093e98239a","side":"right"},{"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":213053,"merkle_root":"19d104b92c4d7299881c447fb8422611fc9cb8615d37a538959e34a2da7ef55f","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260604T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-04T05:37:49Z","sig_algorithm":"ed25519","signature":"630748e88645187aa3b4d4cb8c872cc146180d0301e4c6656f15f99081d7776432715cea2a997b32b7b3a5216f215d19c1b536c0b093100ec843fa0bd65f2101","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_26931a8a41b3312f167e2600ca6bade64280dcc5868ab6306e077fa8f91d85ee"}}