{"paper":{"title":"Automatic Differentiation for Tensor Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.SC","authors_text":"Patrick van der Smagt, Sebastian Urban","submitted_at":"2017-11-03T22:24:47Z","abstract_excerpt":"Kjolstad et. al. proposed a tensor algebra compiler. It takes expressions that define a tensor element-wise, such as $f_{ij}(a,b,c,d) = \\exp\\left[-\\sum_{k=0}^4 \\left((a_{ik}+b_{jk})^2\\, c_{ii} + d_{i+k}^3 \\right) \\right]$, and generates the corresponding compute kernel code.\n  For machine learning, especially deep learning, it is often necessary to compute the gradient of a loss function $l(a,b,c,d)=l(f(a,b,c,d))$ with respect to parameters $a,b,c,d$. If tensor compilers are to be applied in this field, it is necessary to derive expressions for the derivatives of element-wise defined tensors, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01348","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"}