ACM Transactions on Mathematical Software· 2026Q1
Mixed Precision Compression of Tucker Decomposition
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- Q1SCImago
- 2026year
Short summary
A new mixed-precision algorithm improves Tucker decomposition-based lossy compression of multiway data by storing parameters at different precisions, achieving up to 2x and 4x compression gains over single and double precision approximations, respectively.
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Key points
- Introduces a mixed-precision approach for Tucker decomposition lossy compression.
- Automatically determines optimal parameter precision to maximize compression.
- Achieves up to 2x compression improvement over single precision approximations.
- Achieves up to 4x compression improvement over double precision approximations.
- Validated by theoretical error bounds and numerical experiments on real-world data.
AI-generated from the title and abstract; the full text is not read.
Abstract
We present a mixed precision approach for improving Tucker-based lossy compression of multiway data. Current Tucker decomposition algorithms use a uniform floating-point precision and obtain compression by minimizing the multilinear ranks of the representation subject to the target error tolerance. Our algorithm automatically determines which parameters of the representation can be stored in lower precision to improve the compression ratio without exceeding the error tolerance. Crucially, we show that the opportunities to reduce precision are not uniform across parameters, and thus using multiple precisions allows for smoothly transitioning across tolerances between the precisions of standard formats. Theoretical error bounds and numerical experiments validate the approach, and we obtain up to \(2\times\) and \(4\times\) compression improvement factors over initial Tucker approximations of single and double precision real-world numerical simulation data, respectively.
The authors' abstract, as published at the source. ACM Transactions on Mathematical Software, 2026 · DOI ↗
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Field: Computational Mathematics
Computational MathematicsMathematics