1h ago

MMLU Benchmark Redundancy Solved via 2008 Submodular Optimization

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Original post
OPAlex Smola#292Alex Smola@SMOLIX

This is the Gaussian process sensor placement problem Krause, Singh and Guestrin solved in 2008. Entropy and mutual information of the score covariance are both submodular, with the standard (1 − 1/e) guarantee for greedy. Cheap, principled, exact in closed form.

5:36 PM · May 25, 2026 View on X
REPLYAlex Smola#292Alex Smola@SMOLIX

Greedy entropy turns out to be exactly pivoted Cholesky on the score covariance. The residual trace gives a spectral diagnostic for free.

Paper: https://arxiv.org/abs/2605.02209 Blog: https://alex.smola.org/posts/34-benchmark-selection/

Alex SmolaAlex Smola@smolix

This is the Gaussian process sensor placement problem Krause, Singh and Guestrin solved in 2008. Entropy and mutual information of the score covariance are both submodular, with the standard (1 − 1/e) guarantee for greedy. Cheap, principled, exact in closed form.

12:36 AM · May 26, 2026 · 133 Views
12:36 AM · May 26, 2026 · 105 Views