{"ID":2889447,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.20447","arxiv_id":"2507.20447","title":"WEEP: A Differentiable Nonconvex Sparse Regularizer via Weakly-Convex Envelope","abstract":"Sparse regularization is fundamental in signal processing and feature extraction but often relies on non-differentiable penalties, conflicting with gradient-based optimizers. We propose WEEP (Weakly-convex Envelope of Piecewise Penalty), a novel differentiable regularizer derived from the weakly-convex envelope framework. WEEP provides tunable, unbiased sparsity and a simple closed-form proximal operator, while maintaining full differentiability and L-smoothness, ensuring compatibility with both gradient-based and proximal algorithms. This resolves the tradeoff between statistical performance and computational tractability. We demonstrate superior performance compared to established convex and non-convex sparse regularizers on challenging compressive sensing and image denoising tasks.","short_abstract":"Sparse regularization is fundamental in signal processing and feature extraction but often relies on non-differentiable penalties, conflicting with gradient-based optimizers. We propose WEEP (Weakly-convex Envelope of Piecewise Penalty), a novel differentiable regularizer derived from the weakly-convex envelope framewo...","url_abs":"https://arxiv.org/abs/2507.20447","url_pdf":"https://arxiv.org/pdf/2507.20447v2","authors":"[\"Takanobu Furuhashi\",\"Hidekata Hontani\",\"Qibin Zhao\",\"Tatsuya Yokota\"]","published":"2025-07-28T00:40:48Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.CV\"]","methods":"[]","has_code":false}