Information Limits of Low-Rank Approximation Certification
Quick summary
arXiv:2610.03321v1 Announce Type: cross Abstract: Low-rank approximation can require additional matrix--vector products to verify that its error meets a prescribed tolerance. We characterize this certification cost for both relative matrix error and mean-square output error. For a single approximation matrix candidate, we determine the exact dimension-uniform minimax query constant as the allowed failure probability vanishes. Our main result concerns reusing validation responses as the approximation space expands. For a candidate family constructed independently of validation, one batch suppor
Key takeaways
- arXiv:2610.03321v1 Announce Type: cross Abstract: Low-rank approximation can require additional matrix--vector products to verify that its error meets a prescribed tolerance.
- We characterize this certification cost for both relative matrix error and mean-square output error.
- For a single approximation matrix candidate, we determine the exact dimension-uniform minimax query constant as the allowed failure probability vanishes.
Why it matters
The importance of “Information Limits of Low-Rank Approximation Certification” will be measured by what changes in practice. User behavior, access conditions, verifiable performance and responsible-use outcomes are the signals worth following.
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