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.
Communications on Pure and Applied Mathematics , volume=
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The annealed TAP complexity is the Legendre transform of a Parisi variational functional constrained by zero overlap mass, with a matching lower bound from Kac-Rice computation.
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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.
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The Legendre structure of the TAP complexity for the Ising spin glass
The annealed TAP complexity is the Legendre transform of a Parisi variational functional constrained by zero overlap mass, with a matching lower bound from Kac-Rice computation.