FastRank: Fast Tensor Rank Approximation based on Spectral Energy

Konstantinos Bougiatiotis, Georgios Paliouras
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:1873-1881, 2026.

Abstract

Complex multi-dimensional data are often represented as tensors, analyzed through tensor decompositions. A central challenge is selecting the right number of components for the decomposition. In the Canonical Polyadic Decomposition (CPD), this means determining the canonical rank, which directly impacts decomposition quality. Existing methods typically estimate rank by repeatedly computing CPDs, an expensive process. We introduce $FastRank$, a theoretically grounded method that estimates rank without CPD computation. By applying Singular Value Decomposition (SVD) to a sum-reduced matrix of the tensor and analyzing its eigenspectrum, FastRank achieves over $1000\times$ speedup and surpasses state-of-the-art accuracy. We validate it using both synthetic and real data, including noisy settings, and highlight its scalability in knowledge graph completion, where prior methods fail due to computational limitations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-bougiatiotis26a, title = { FastRank: Fast Tensor Rank Approximation based on Spectral Energy }, author = {Bougiatiotis, Konstantinos and Paliouras, Georgios}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {1873--1881}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/bougiatiotis26a/bougiatiotis26a.pdf}, url = {https://proceedings.mlr.press/v300/bougiatiotis26a.html}, abstract = { Complex multi-dimensional data are often represented as tensors, analyzed through tensor decompositions. A central challenge is selecting the right number of components for the decomposition. In the Canonical Polyadic Decomposition (CPD), this means determining the canonical rank, which directly impacts decomposition quality. Existing methods typically estimate rank by repeatedly computing CPDs, an expensive process. We introduce $FastRank$, a theoretically grounded method that estimates rank without CPD computation. By applying Singular Value Decomposition (SVD) to a sum-reduced matrix of the tensor and analyzing its eigenspectrum, FastRank achieves over $1000\times$ speedup and surpasses state-of-the-art accuracy. We validate it using both synthetic and real data, including noisy settings, and highlight its scalability in knowledge graph completion, where prior methods fail due to computational limitations. } }
Endnote
%0 Conference Paper %T FastRank: Fast Tensor Rank Approximation based on Spectral Energy %A Konstantinos Bougiatiotis %A Georgios Paliouras %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-bougiatiotis26a %I PMLR %P 1873--1881 %U https://proceedings.mlr.press/v300/bougiatiotis26a.html %V 300 %X Complex multi-dimensional data are often represented as tensors, analyzed through tensor decompositions. A central challenge is selecting the right number of components for the decomposition. In the Canonical Polyadic Decomposition (CPD), this means determining the canonical rank, which directly impacts decomposition quality. Existing methods typically estimate rank by repeatedly computing CPDs, an expensive process. We introduce $FastRank$, a theoretically grounded method that estimates rank without CPD computation. By applying Singular Value Decomposition (SVD) to a sum-reduced matrix of the tensor and analyzing its eigenspectrum, FastRank achieves over $1000\times$ speedup and surpasses state-of-the-art accuracy. We validate it using both synthetic and real data, including noisy settings, and highlight its scalability in knowledge graph completion, where prior methods fail due to computational limitations.
APA
Bougiatiotis, K. & Paliouras, G.. (2026). FastRank: Fast Tensor Rank Approximation based on Spectral Energy . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:1873-1881 Available from https://proceedings.mlr.press/v300/bougiatiotis26a.html.

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