{"paper":{"title":"Efficient Higher Order Derivatives of Objective Functions Composed of Matrix Operations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"cs.DS","authors_text":"Sebastian F. Walter","submitted_at":"2009-11-25T20:05:24Z","abstract_excerpt":"This paper is concerned with the efficient evaluation of higher-order derivatives of functions $f$ that are composed of matrix operations. I.e., we want to compute the $D$-th derivative tensor $\\nabla^D f(X) \\in \\mathbb R^{N^D}$, where $f:\\mathbb R^{N} \\to \\mathbb R$ is given as an algorithm that consists of many matrix operations. We propose a method that is a combination of two well-known techniques from Algorithmic Differentiation (AD): univariate Taylor propagation on scalars (UTPS) and first-order forward and reverse on matrices. The combination leads to a technique that we would like to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4940","kind":"arxiv","version":1},"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"}