{"paper":{"title":"A Unified Fractional Regularization Framework for Sparse Recovery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The ℓ1/ℓp^q fractional regularizer has first-order stationary points equivalent to those of the subtractive ℓ1 - α ℓp model and admits a new RIP recovery condition for high-coherence matrices.","cross_cats":["cs.LG","math.IT"],"primary_cat":"cs.IT","authors_text":"Chuanqi Ma, Hao Wang, Haoyu He, Yinhao Zhao","submitted_at":"2026-04-25T07:32:39Z","abstract_excerpt":"We propose a unified fractional regularization framework for sparse signal recovery based on the $\\ell_1/\\ell_p^q$ model. This model generalizes several widely used sparsity-promoting regularizers and provides additional flexibility through the parameters $p$ and $q$. Our main theoretical contribution is the characterization of the equivalence between the first-order stationary points of the $\\ell_1/\\ell_p^q$ formulation and the subtractive $\\ell_1-\\alpha\\ell_p$ model, thereby offering a unified perspective on these nonconvex regularizers. In addition, we establish a new sufficient recovery co"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The first-order stationary points of the ℓ1/ℓp^q formulation are equivalent to those of the subtractive ℓ1 - α ℓp model, and the framework admits a new sufficient recovery condition under the RIP that holds even for high-coherence sensing matrices.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The RIP-based recovery condition and the equivalence both rely on the parameters p and q being chosen in (0,1) and on the sensing matrix satisfying a restricted isometry property whose constants are not quantified in the abstract; the abstract does not state how sensitive the guarantees are to the choice of these parameters.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A unified ℓ1/ℓp^q fractional regularizer equates to the subtractive ℓ1 - α ℓp model at stationary points, supplies a new RIP-based recovery condition, and is solved by a provably convergent majorization-minimization algorithm.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The ℓ1/ℓp^q fractional regularizer has first-order stationary points equivalent to those of the subtractive ℓ1 - α ℓp model and admits a new RIP recovery condition for high-coherence matrices.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"360b2d2576aa8ddf267a454d47eaa9c579153cd02e9af4c3c92caf8cc5ae67c7"},"source":{"id":"2604.23184","kind":"arxiv","version":2},"verdict":{"id":"845969f0-5ae0-4708-a12d-8b927f9816c7","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T07:14:22.039409Z","strongest_claim":"The first-order stationary points of the ℓ1/ℓp^q formulation are equivalent to those of the subtractive ℓ1 - α ℓp model, and the framework admits a new sufficient recovery condition under the RIP that holds even for high-coherence sensing matrices.","one_line_summary":"A unified ℓ1/ℓp^q fractional regularizer equates to the subtractive ℓ1 - α ℓp model at stationary points, supplies a new RIP-based recovery condition, and is solved by a provably convergent majorization-minimization algorithm.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The RIP-based recovery condition and the equivalence both rely on the parameters p and q being chosen in (0,1) and on the sensing matrix satisfying a restricted isometry property whose constants are not quantified in the abstract; the abstract does not state how sensitive the guarantees are to the choice of these parameters.","pith_extraction_headline":"The ℓ1/ℓp^q fractional regularizer has first-order stationary points equivalent to those of the subtractive ℓ1 - α ℓp model and admits a new RIP recovery condition for high-coherence matrices."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.23184/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T09:37:52.517841Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:24:17.173014Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"0a50de17d435d386cdba8577949636c2b8660b79532ba4b227ed06b4ef2c8242"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}