Yifeng Chu and I just posted our paper on chaining-type bounds for expected soft maxima of Gaussian processes. The analysis makes use of a nice blend of ideas from probability, statistical physics of disordered systems, and information theory. arxiv.org/abs/2606.22611
AI Weekly's analysis
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- The paper derives upper and lower bounds for soft maxima of centered Gaussian processes, defined as Gibbs averages at inverse temperature β > 0.
- The bounds retain the same multiscale structure as generic chaining expressions, with a truncation term governed by the inverse temperature β.
- As β → ∞, the bounds recover the majorizing measure theorem; applied to the Sherrington-Kirkpatrick model, they yield a finite-size Parisi formula.
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