Related papers: The Multiscale Loop Vertex Expansion

Learning latent representations that are simultaneously expressive, geometrically well-structured, and reliably calibrated remains a central challenge for Variational Autoencoders (VAEs). Standard VAEs typically assume a diagonal Gaussian…

Multipole expansion of an incident radiation field - that is, representation of the fields as sums of vector spherical wavefunctions - is essential for theoretical light scattering methods such as the T-matrix method and generalised…

Variational Autoencoders (VAE) are widely used for dimensionality reduction of large-scale tabular and image datasets, under the assumption of independence between data observations. In practice, however, datasets are often correlated, with…

This paper devises a novel lowest-order conforming virtual element method (VEM) for planar linear elasticity with the pure displacement/traction boundary condition. The main trick is to view a generic polygon $K$ as a new one…

The Learning with Errors (LWE) problem is the fundamental backbone of modern lattice based cryptography, allowing one to establish cryptography on the hardness of well-studied computational problems. However, schemes based on LWE are often…

An inductive realization of Loop Vertex Expansion is proposed and is applied to the construction of the $\phi_1^4$ theory. It appears simpler and more natural than the standard one at least for some situations.

Model merging aims to combine multiple fine-tuned models into a single multi-task model without access to training data. Existing task-vector merging methods such as TIES, TSV-M, and Iso-C/CTS differ in their aggregation rules but treat all…

Vertex algebras provide an axiomatic algebraic description of the operator product expansion (OPE) of chiral fields in 2-dimensional conformal field theory. Vertex Lie algebras (= Lie conformal algebras) encode the singular part of the OPE,…

In this paper we introduce learnable lattice vector quantization and demonstrate its effectiveness for learning discrete representations. Our method, termed LL-VQ-VAE, replaces the vector quantization layer in VQ-VAE with lattice-based…

We propose a variational quantum eigensolver (VQE) for the simulation of strongly-correlated quantum matter based on a multi-scale entanglement renormalization ansatz (MERA) and gradient-based optimization. This MERA quantum eigensolver can…

Multivariate (MTV) porous materials exhibit unique structural complexities based on diverse spatial arrangements of multiple building block combinations. These materials possess potential synergistic functionalities that exceed the sum of…

The variational method is a powerful approach to solve many-body quantum problems non perturbatively. However, in the context of relativistic quantum field theory (QFT), it needs to meet 3 seemingly incompatible requirements outlined by…

We present a rigorous renormalization group scheme for lattice quantum field theories in terms of operator algebras. The renormalization group is considered as an inductive system of scaling maps between lattice field algebras. We construct…

We construct cumulants up to a finite order of a tensor field theory perturbed by a quartic term, nicknamed the $T_3^4$ model. The method we use is the multi-scale loop vertex expansion. We prove analyticity and Borel summability of the…

Contractor renormalization (CORE) is a real-space renormalization-group method to derive effective Hamiltionians for microscopic models. The original CORE method is based on a real-space decomposition of the lattice into small blocks and…

In this paper, the line spectral estimation (LSE) problem with multiple measurement vectors (MMVs) is studied utilizing the Bayesian methods. Motivated by the recently proposed variational line spectral estimation (VALSE) method, we develop…

Variable Elimination (VE) is a classical exact inference algorithm for probabilistic graphical models such as Bayesian Networks, computing the marginal distribution of a subset of the random variables in the model. Our goal is to understand…

In statistical physics, one of the standard methods to study second order phase transitions is the renormalization group that usually leads to an expansion around the corresponding fully connected solution. Unfortunately, often in…

Generalized linear models (GLMs) are fundamental tools for statistical modeling, with maximum likelihood estimation (MLE) serving as the classical approach for parameter inference. While MLE performs well for canonical GLMs, it can become…

We propose a composable framework for latent space image augmentation that allows for easy combination of multiple augmentations. Image augmentation has been shown to be an effective technique for improving the performance of a wide variety…