The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.
Powers of tensors and fast matrix multiplication
Abstract
This paper presents a method to analyze the powers of a given trilinear form (a special kind of algebraic construction also called a tensor) and obtain upper bounds on the asymptotic complexity of matrix multiplication. Compared with existing approaches, this method is based on convex optimization, and thus has polynomial-time complexity. As an application, we use this method to study powers of the construction given by Coppersmith and Winograd [Journal of Symbolic Computation, 1990] and obtain the upper bound ω < 2.3728639 on the exponent of square matrix multiplication, which slightly improves the best known upper bound.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601
Gaussian elimination is not optimal
Strassen, V. (1969) · Numerische Mathematik · doi:10.1007/bf02165411 · Cited by 2,509
Matrix multiplication via arithmetic progressions
Coppersmith, D., & Winograd, S. (1990) · Journal of Symbolic Computation · doi:10.1016/s0747-7171(08)80013-2 · Cited by 2,248
Improved bound for complexity of matrix multiplication
Davie, A. M., & Stothers, A. J. (2013) · Proceedings of the Royal Society of Edinburgh: Section A Mathematics · doi:10.1017/s0308210511001648 · Cited by 152
Cited by
Discovering faster matrix multiplication algorithms with reinforcement learning
Fawzi, A., Balog, M., Huang, A., Hubert, T., Romera-Paredes, B., Barekatain, M., Novikov, A., R. Ruiz, F. J., Schrittwieser, J., Swirszcz, G., et al. (2022) · Nature · doi:10.1038/s41586-022-05172-4 · Cited by 478
Why Does Deep and Cheap Learning Work So Well?
Lin, H. W., Tegmark, M., & Rolnick, D. (2017) · Journal of Statistical Physics · doi:10.1007/s10955-017-1836-5 · Cited by 393
Improved Quantum Algorithm for Triangle Finding via Combinatorial Arguments
Gall, F. L. (2014) · 2014 IEEE 55th Annual Symposium on Foundations of Computer Science · doi:10.1109/focs.2014.31 · Cited by 56
Privacy-Preserving Deep Learning Based on Multiparty Secure Computation: A Survey
Zhang, Q., Xin, C., & Wu, H. (2021) · IEEE Internet of Things Journal · doi:10.1109/jiot.2021.3058638 · Cited by 53
New applications of the polynomial method: The cap set conjecture and beyond
Grochow, J. (2018) · Bulletin of the American Mathematical Society · doi:10.1090/bull/1648 · Cited by 16
Metadata
- Authors
- Le Gall, F.
- Venue
- Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation
- Publisher
- ACM
- Published
- 2014-07-23
- Pages
- 296-303
- OpenAlex
- W2120248756
- Cited by
- 856
- References
- 4
- FWCI
- 60.19
- Type
- conference paper
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Powers of tensors and fast matrix multiplication. https://app.cochat.ai/papers/10.1145/2608628.2608664
- The paper
- Le Gall, F. (2014). Powers of tensors and fast matrix multiplication. Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation. https://doi.org/10.1145/2608628.2608664
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
