{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/lp-sparsemap-differentiable-relaxed","title":"LP-SparseMAP: Differentiable Relaxed Optimization for Sparse Structured Prediction","arxiv_id":"2001.04437","date":"2020-01-13","proceeding":"ICML 2020 1","authors":["Vlad Niculae","André F. T. Martins"],"abstract":"Structured prediction requires manipulating a large number of combinatorial structures, e.g., dependency trees or alignments, either as latent or output variables. Recently, the SparseMAP method has been proposed as a differentiable, sparse alternative to maximum a posteriori (MAP) and marginal inference. SparseMAP returns a combination of a small number of structures, a desirable property in some downstream applications. However, SparseMAP requires a tractable MAP inference oracle. This excludes, e.g., loopy graphical models or factor graphs with logic constraints, which generally require approximate inference. In this paper, we introduce LP-SparseMAP, an extension of SparseMAP that addresses this limitation via a local polytope relaxation. LP-SparseMAP uses the flexible and powerful domain specific language of factor graphs for defining and backpropagating through arbitrary hidden structure, supporting coarse decompositions, hard logic constraints, and higher-order correlations. We derive the forward and backward algorithms needed for using LP-SparseMAP as a hidden or output layer. Experiments in three structured prediction tasks show benefits compared to SparseMAP and Structured SVM.","url_abs":"https://arxiv.org/abs/2001.04437v3","url_pdf":"https://arxiv.org/pdf/2001.04437v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"lp-sparsemap-differentiable-relaxed","repo_url":"https://github.com/deep-spin/lp-sparsemap","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"structured-prediction","task_name":"Structured Prediction"}],"methods":[{"method_slug":"svm","method_name":"SVM"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2001.04437","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}