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Life sciences · Preprint
arXiv · August 18, 2026
Raises a question worth testing. It does not answer one.
This is a theoretical paper answering a computational complexity question about feature priming in online linear regression by constructing lower bounds that show certain algorithms incur Ω(min{T,√d}) regret. The work establishes fundamental limits but does not address practical clinical or prediction tasks, and empirical validation is limited to exploratory diagnostics.
Theoretical analysis with lower-bound constructions.
Hadamard constructions force Ω(min{T,√d}) regret for all three feature-priming rules against a zero-loss one-sparse comparator Cheap nuisance interpolation causes the refit to underweight the truly predictive coordinate, limiting regret guarantees Univariate powered priming achieves regret controlled by data rank, matched by Euclidean-normalized triangular construction even under nonnegative ridge regularization
Safety was not reported in the material analysed. Check the source before drawing any conclusion about harm.
The source did not state who this applies to in practice.
Theoretical analysis of online regression algorithms with lower-bound constructions and limited empirical validation; raises questions about feature priming rather than settling clinical or practical questions.
As stated by the source record.
Quoted from the source exactly as published.
Graded across the dimensions that decide whether you should act, each from what the source actually supports. There is no single score, and where a dimension was not assessed it says so.
In high-dimensional online prediction, the best predictor may depend on only a few features, so regret should scale with sparsity rather than the ambient dimension. Feature priming pursues this goal by estimating feature weights from past data and refitting a minimum-norm predictor on the rescaled design. Warmuth and Amid asked at COLT 2023 whether any of three such rules admits a competitive online regret guarantee. Using the natural Moore--Penrose protocol based only on past data, we give a negative answer to the sparse-logarithmic form of this COLT open problem. Our analysis identifies a common obstruction: cheap nuisance interpolation causes the refit to underweight the truly predictive coordinate. An exact target-mass identity and a two-sign argument turn this effect into clipped prediction loss. Hadamard constructions force $Ω(\min\{T,\sqrt{d}\})$ regret for all three rules against a zero-loss one-sparse comparator, with extensions to fixed prime powers and selectors among the rules. Conversely, regret is controlled by data rank, and a Euclidean-normalized triangular construction matches this dependence for powered univariate priming, even under nonnegative second-stage ridge regularization; a paired ridge construction also covers all three powered rules. Exploratory diagnostics on frozen language-model activations exhibit the same relation among nuisance interpolation, target weight, and loss. The exact multivariate and Pearson frontiers remain open.
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