Related papers: NSPT for $O(N)$ non-linear sigma model: the larger…
We study the $O(N)$ nonlinear $\sigma$ model on a three-dimensional compact space $S^1 \times S^2$ (of radii $L$ and $R$ respectively) by means of large $N$ expansion, focusing on the finite size effects and conformal symmetries of this…
We define in this paper a class of three indices tensor models, endowed with $O(N)^{\otimes 3}$ invariance ($N$ being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor…
Many machine learning models based on neural networks exhibit scaling laws: their performance scales as power laws with respect to the sizes of the model and training data set. We use large-N field theory methods to solve a model recently…
We calculate the power spectrum of density fluctuations in the statistical non-equilibrium field theory for classical, microscopic degrees of freedom to first order in the interaction potential. We specialise our result to cosmology by…
We present a statistical equilibrium model of self-organization in a class of focusing, nonintegrable nonlinear Schrodinger (NLS) equations. The theory predicts that the asymptotic-time behavior of the NLS system is characterized by the…
Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications…
We apply the methods of modern analytic bootstrap to the critical $O(N)$ model in a $1/N$ expansion. At infinite $N$ the model possesses higher spin symmetry which is weakly broken as we turn on $1/N$. By studying consistency conditions for…
Artificial neural networks are powerful models, which have been widely applied into many aspects of machine translation, such as language modeling and translation modeling. Though notable improvements have been made in these areas, the…
We study the evolution leading to (or regressing from) a large fluctuation in a Statistical Mechanical system. We introduce and study analytically a simple model of many identically and independently distributed microscopic variables $n_m$…
The dominating NLP paradigm of training a strong neural predictor to perform one task on a specific dataset has led to state-of-the-art performance in a variety of applications (eg. sentiment classification, span-prediction based question…
For a long time, detection and parameter estimation methods for signal processing have relied on asymptotic statistics as the number $n$ of observations of a population grows large comparatively to the population size $N$, i.e. $n/N\to…
The question of the asymptotic form of the perturbation expansion in scalar field theories is reconsidered. Renewed interest in the computation of terms in the epsilon-expansion, used to calculate critical exponents, has been frustrated by…
Neural Machine Translation (NMT) is a new approach to machine translation that has made great progress in recent years. However, recent studies show that NMT generally produces fluent but inadequate translations (Tu et al. 2016b; Tu et al.…
Several years ago it was found that perturbation theory for two-dimensional O(N) models depends on boundary conditions even after the infinite volume limit has been taken termwise, provided $N>2$. There ensued a discussion whether the…
We study the dual description of the $\eta$-deformed $OSP(N|2m)$ sigma model in the asymptotically free regime ($N>2m+2$). Compared to the case of classical Lie groups, for supergroups there are inequivalent $\eta$-deformations…
Interactions between actors are frequently represented using a network. The latent position model is widely used for analysing network data, whereby each actor is positioned in a latent space. Inferring the dimension of this space is…
Neural network field theory (NNFT) represents fields as neural networks and samples field configurations by drawing network parameters from a probability distribution. We identify a previously unexplored architectural freedom in NNFT,…
Unlike equilibrium statistical mechanics, with its well-established foundations, a similar widely-accepted framework for non-equilibrium statistical mechanics (NESM) remains elusive. Here, we review some of the many recent activities on…
Concerning Numerical Stochastic Perturbation Theory, we discuss the convergence of the stochastic process (idea of the proof, features of the limit distribution, rate of convergence to equilibrium). Then we also discuss the expected…
The spatial momentum dependence of the spectral function for pi and sigma at finite temperature is studied by employing the O(4) linear sigma model and adopting a resummation technique called optimized perturbation theory (OPT).