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About this paper
Ahmed El Alaoui, Andrea Montanari, Mark Sellke
An algorithm for sampling from the Sherrington-Kirkpatrick Gibbs measure, based on stochastic localization and Approximate Message Passing, achieves efficient sampling for inverse temperatures β < 1/2. Additionally, the work demonstrates a fundamental limitation, showing that no stable algorithm can accurately sample the measure in the replica symmetry broken phase (β > 1).
Key insights
- Stochastic localization offers a novel algorithmic paradigm for sampling complex, high-dimensional probability distributions by progressively tilting the measure towards a single configuration.
- Approximate Message Passing (AMP) and Natural Gradient Descent (NGD) can efficiently and accurately compute the mean of dynamically tilted Gibbs measures, which is a critical subroutine for the algorithmic implementation of stochastic localization.
- The concept of 'algorithmic stability', when combined with the phenomenon of 'disorder chaos' in the replica symmetry broken phase (β > 1), provides a fundamental explanation for why certain algorithms cannot accurately sample the Sherrington-Kirkpatrick Gibbs measure at low temperatures.
Summary by alphaXiv.
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