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Recent work by Tian and So (SODA 2025) shows that testing approximate stationarity notions for PA functions is computationally intractable in the worst case, and identifies fixed-dimensional tractability as an open direction.\n  We address this dire"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.10219","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-05-11T08:59:57Z","cross_cats_sorted":["cs.CC","cs.LG"],"title_canon_sha256":"632fd37e0d9554c4a1846e13e91fc71c4d49351b5a7fa58a22681c6a163b0546","abstract_canon_sha256":"eaeda1156351b7ffa91e17e4a4295db6964e268b1cd3ce9a530bd4af9e327e56"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:22.789355Z","signature_b64":"aizytQYy9XcQo2Q/BtEoJWQWVmQWzsRacflKHNB62zd00GSVpRrWpbIpr1DvDAr/WoHjGPTZADRxRRWXsblTCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3107d88e9b4b0b539346ad647e4c6a391c06840c0529e36b0797d6104ae2056a","last_reissued_at":"2026-05-25T02:01:22.788761Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:22.788761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parameterized Complexity of Stationarity Testing for Piecewise-Affine Functions and Shallow CNN Losses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Testing approximate stationarity for continuous piecewise-affine functions is XP-tractable in fixed dimension for some cases but W[1]-hard for others, with ETH lower bounds excluding subexponential dependence on dimension.","cross_cats":["cs.CC","cs.LG"],"primary_cat":"math.OC","authors_text":"Yuhan Ye","submitted_at":"2026-05-11T08:59:57Z","abstract_excerpt":"We study the parameterized complexity of testing approximate first-order stationarity at a prescribed point for continuous piecewise-affine (PA) functions, a basic task in nonsmooth optimization. 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