An efficient black-box reduction from PQ to TDS learning for any Boolean concept class in the distribution-free setting implies hardness for TDS learning of halfspaces, while membership queries enable efficient PQ learning of halfspaces via iterative Forster transforms.
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4 Pith papers cite this work. Polarity classification is still indexing.
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Deterministic (1+ε)-approximation algorithm for the volume of the unit hypercube truncated by k sums-of-univariate-convex constraints, running in poly_k(n, 1/ε, L, L_o) time.
Polynomial-time algorithm samples the Sherrington-Kirkpatrick Gibbs measure at beta < 1/2 with o(1) TVD error by combining potential Hessian ascent, stochastic localization, covariance estimates, and Jarzynski equality with rejection sampling.
Lower bounds are derived for the ground-state eigenvalues of -Δ + R/4 + V and the drifted operator -Δ_f + V on Ricci shrinkers, in terms of integrals involving V and the shrinker entropy, with generalizations via Perelman's μ-functional.
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Potential Hessian Ascent III: Sampling the Sherrington--Kirkpatrick Model at Beta < 1/2
Polynomial-time algorithm samples the Sherrington-Kirkpatrick Gibbs measure at beta < 1/2 with o(1) TVD error by combining potential Hessian ascent, stochastic localization, covariance estimates, and Jarzynski equality with rejection sampling.