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Convergence of linear programming hierarchies for Gibbs states of spin systems
Hamza Fawzi, Omar Fawzi
https://arxiv.org/abs/2506.06125 https://

Convergence of linear programming hierarchies for Gibbs states of spin systems
We consider the problem of computing expectation values of local functions under the Gibbs distribution of a spin system. In particular, we study two families of linear programming hierarchies for this problem. The first hierarchy imposes local spin flip equalities and has been considered in the bootstrap literature in high energy physics. For this hierarchy, we prove fast convergence under a spatial mixing (decay of correlations) condition. This condition is satisfied for example above the cri…

Stochastic Preconditioning for Neural Field Optimization
Selena Ling, Merlin Nimier-David, Alec Jacobson, Nicholas Sharp
https://arxiv.org/abs/2505.20473 h…

Stochastic Preconditioning for Neural Field Optimization
Neural fields are a highly effective representation across visual computing. This work observes that fitting these fields is greatly improved by incorporating spatial stochasticity during training, and that this simple technique can replace or even outperform custom-designed hierarchies and frequency space constructions. The approach is formalized as implicitly operating on a blurred version of the field, evaluated in-expectation by sampling with Gaussian-distributed offsets. Querying the blurr…