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Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

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2 recordsLinked to original sources

arXiv2026

Operator-Guided Model Reduction for Generative Sampling in Lattice Field Theory

Neural generative samplers for lattice field theory can be costly to train and evaluate. When they miss modes or assign them incorrect relative weights, biased observables do not reveal which collective variables are responsible. We project a trained flow-matching velocity onto vector fields built from lattice operators and Fourier modes. In two-dimensional lattice $ϕ^4$ theory, the projection separates changes in the overall magnetization from the lowest nonzero-momentum fluctuations and guides an explicit invertible proposal that treats them separately. Allowing the amplitude of the lowest nonzero-momentum fluctuations to depend on the magnetization improves the overlap between the proposal and target distributions, while the same two-parameter modification at higher momenta gives smaller improvements. The Metropolis--Hastings correction defines a Markov chain with the target Boltzmann distribution as its stationary law, and the normalized proposal density yields finite-volume partition-function estimates consistent with an independent HMC calculation. At the larger tested volume, the overlap between the proposal and target distributions deteriorates substantially, limiting the range over which the same parameterization remains effective.

hep-lat↗

arXiv2026

What Neural Network Field Theory Can and Cannot Realise on a Computer

One aim of neural network field theory is to put a quantum or effective field theory on a computer, with the network ensemble itself as the theory. We ask how far that aim can be pushed for a function class regular enough to be computed with. Our main result is a no-go theorem with assumptions that hold for standard network architectures. We use it to separate four versions of neural network field theory, according to whether the defining object is the finite width ensemble or its infinite width limit, and whether the target we want to compute is a quantum or an effective field theory. Neither finite width interpretation is straightforwardly consistent. For finite width ensembles with finite variance at each point, the QFT interpretation fails reflection positivity, while the EFT interpretation establishes no scale separation by which the positivity violation can be placed outside its domain of validity. Of the two limit versions, one can be simulated in full and the other only in part, as only its smeared correlators are computable with a controlled error. As such, at the level of a controlled numerical computation, the QFT and EFT versions cannot be distinguished. One dimension escapes the obstruction, yet reflection positivity is shown to still fail there at every finite width for the cosine network. Two escapes from the theorem remain, giving up either finite variance at a point or exact rotation invariance, and we discuss both of these possibilities.

hep-th↗