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This paper shows that drawing fresh sketches at every iteration of under-constrained iterative ridge regression yields provably better convergence than reusing a single sketch, deriving residual-aware sampling rules and an oracle sampling distribution, with experiments including ridge probes on Qwen2.5 representations supporting the theory.
A neurosurgery resident at Peking College Hospital uses GPT 5.6 Sol to prove a two-decades-old conjecture in numerical linear algebra, supporting research on transcranial ultrasound.
The article derives the column elimination tree for the right-looking sparse Cholesky algorithm, explaining how it predicts fill-in and task dependencies without performing dense factorization.