Related papers: Towards a double-scaling limit for tensor models: …
We study critical behaviors of the reduced fidelity susceptibility for two neighboring sites in the one-dimensional transverse field Ising model. It is found that the divergent behaviors of the susceptibility take the form of square of…
We discuss methods for visualizing neural network decision boundaries and decision regions. We use these visualizations to investigate issues related to reproducibility and generalization in neural network training. We observe that changes…
The next generation of cosmological observations will be sensitive to small deviations from a pure power law in the primordial power spectrum of the curvature perturbations. In the context of slow-roll inflation, these deviations are…
An extended study of scaling of the first and second kinds for inclusive electron scattering from nuclei is presented. Emphasis is placed on the transverse response in the kinematic region lying above the quasielastic peak. In particular,…
Amplitudes of ordinary tensor models are dominated at large $N$ by the so-called melonic graph amplitudes. Enhanced tensor models extend tensor models with special scalings of their interactions which allow, in the same limit, that the…
In this paper we give a field theory explanation of two confining dualities that have been proposed in the literature based on exact results from supersymmetric localization. The first confining model under investigation is 4d $SU(N_c+1)$…
We study the spectrum of the large $N$ quantum field theory of bosonic rank-$3$ tensors, whose quartic interactions are such that the perturbative expansion is dominated by the melonic diagrams. We use the Schwinger-Dyson equations to…
Octupolar order is described in two space dimensions in terms of the maxima (and conjugated minima) of the probability density associated with a third-rank, fully symmetric and traceless tensor. Such a representation is shown to be…
Deterministic rate equations are widely used in the study of stochastic, interacting particles systems. This approach assumes that the inherent noise, associated with the discreteness of the elementary constituents, may be neglected when…
We prove a lower bound on the rank of tensors constructed from families of linear maps that `expand' the dimension of every subspace. Such families, called {\em dimension expanders} have been studied for many years with several known…
This paper investigates the estimation problem in a regression-type model. To be able to deal with potential high dimensions, we provide a procedure called LOL, for Learning Out of Leaders with no optimization step. LOL is an auto-driven…
Scaling limits of critical percolation models show major differences between low and high dimensional models. The article discusses the formulation of the continuum limit for the former case. A mathematical framework is proposed for the…
The fine-tuning of deep pre-trained models has revealed compositional properties, with multiple specialized modules that can be arbitrarily composed into a single, multi-task model. However, identifying the conditions that promote…
This paper studies the computational challenges of large-scale attention-based models in artificial intelligence by utilizing importance sampling methods in the streaming setting. Inspired by the classical definition of the $\ell_2$ sampler…
We carry out next-to-leading order (NLO) parton model calculations for the standard hard ``QCD'' processes in the massless Schwinger model. The asymptotic expansion of the exact result for the deep inelastic cross section is used to infer…
Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…
Neural scaling laws define a predictable relationship between a model's parameter count and its performance after training in the form of a power law. However, most research to date has not explicitly investigated whether scaling laws can…
By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…
We propose a discrete model whose continuum limit reproduces the string susceptibility and the scaling dimensions of $(2,4m)$-minimal superconformal models coupled to $2D$-supergravity. The basic assumption in our presentation is a set of…
We study the double- and triple-scaling limits of a complex multi-matrix model, with $\mathrm{U}(N)^2\times \mathrm{O}(D)$ symmetry. The double-scaling limit amounts to taking simultaneously the large-$N$ (matrix size) and large-$D$ (number…