{"paper":{"title":"Graphical Newton","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.RO","cs.SY"],"primary_cat":"math.OC","authors_text":"Akshay Srinivasan, Emanuel Todorov","submitted_at":"2015-08-05T01:46:30Z","abstract_excerpt":"Computing the Newton step for a generic function $f: \\mathbb{R}^N \\rightarrow \\mathbb{R}$ takes $O(N^{3})$ flops. In this paper, we explore avenues for reducing this bound, when the computational structure of $f$ is known beforehand. It is shown that the Newton step can be computed in time, linear in the size of the computational-graph, and cubic in its tree-width."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00952","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}