On the origin of finite entanglement scaling

• URL: http://arxiv.org/abs/2607.15124v1
• Date: Thu, 16 Jul 2026 15:33:30 GMT
• Title: On the origin of finite entanglement scaling
• Abstract summary: We develop a sparse linear solver to calculate the forward and backward derivatives of 2-dimensional tensor networks.<n>This algorithm is of independent interest as it provides a primitive for the variational optimization of projected entangled pair states.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The concept of finite entanglement scaling forms one of the pillars on which the tensor network ecosystem is built. In this paper, we resolve the open problem of determining the actual perturbations induced by matrix product state approximations of critical systems, and we demonstrate that these can be quite different than the ones predicted by conformal field theory. To that aim, we develop a sparse linear solver to calculate the forward and backward derivatives of 2-dimensional tensor networks with respect to their defining parameters in an implicit way. This algorithm is of independent interest as it provides a primitive for the variational optimization of projected entangled pair states that circumvents the instabilities plaguing traditional automatic differentiation methods.

Related papers

• Quantifying Uncertainty In Wide Two-Layer Neural Networks: On The Law Of The Limiting Fluctuation Process [3.0171175820634826]
  Uncertainty quantification in neural networks prediction is a main issue for usual applications.<n>Our approach seeks at reducing costs by directly evaluating uncertainty using PDE's information on the variance.<n>We thus study the law of the limiting process describing the random fluctuations around the mean-field limit of wide two-layer neural networks trained by gradient descent.
  arXiv  Detail & Related papers  (2026-06-04T10:25:23Z)
• Self-Supervised Coarsening of Unstructured Grid with Automatic Differentiation [55.88862563823878]
  In this work, we present an original algorithm to coarsen an unstructured grid based on the concepts of differentiable physics.<n>We demonstrate performance of the algorithm on two PDEs: a linear equation which governs slightly compressible fluid flow in porous media and the wave equation.<n>Our results show that in the considered scenarios, we reduced the number of grid points up to 10 times while preserving the modeled variable dynamics in the points of interest.
  arXiv  Detail & Related papers  (2025-07-24T11:02:13Z)
• Generalized Linear Mode Connectivity for Transformers [87.32299363530996]
  A striking phenomenon is linear mode connectivity (LMC), where independently trained models can be connected by low- or zero-loss paths.<n>Prior work has predominantly focused on neuron re-ordering through permutations, but such approaches are limited in scope.<n>We introduce a unified framework that captures four symmetry classes: permutations, semi-permutations, transformations, and general invertible maps.<n>This generalization enables, for the first time, the discovery of low- and zero-barrier linear paths between independently trained Vision Transformers and GPT-2 models.
  arXiv  Detail & Related papers  (2025-06-28T01:46:36Z)
• Universal Sequence Preconditioning [15.021303911702121]
  We study the problem of preconditioning in sequential prediction.<n>We show that convolving the target sequence corresponds to applying a lens of the hidden transition matrix.<n>We prove that this approach reduces regret for prediction algorithms.
  arXiv  Detail & Related papers  (2025-02-10T15:10:06Z)
• A primal-dual perspective for distributed TD-learning [6.663174194579773]
  The goal of this paper is to investigate distributed temporal difference (TD) learning for a networked multi-agent Markov decision process.<n>The proposed approach is based on distributed optimization algorithms, which can be interpreted as primal-dual Ordinary differential equation (ODE) dynamics subject to null-space constraints.
  arXiv  Detail & Related papers  (2023-10-01T10:38:46Z)
• Variational Laplace Autoencoders [53.08170674326728]
  Variational autoencoders employ an amortized inference model to approximate the posterior of latent variables. We present a novel approach that addresses the limited posterior expressiveness of fully-factorized Gaussian assumption. We also present a general framework named Variational Laplace Autoencoders (VLAEs) for training deep generative models.
  arXiv  Detail & Related papers  (2022-11-30T18:59:27Z)
• A Variational Inference Approach to Inverse Problems with Gamma Hyperpriors [60.489902135153415]
  This paper introduces a variational iterative alternating scheme for hierarchical inverse problems with gamma hyperpriors. The proposed variational inference approach yields accurate reconstruction, provides meaningful uncertainty quantification, and is easy to implement.
  arXiv  Detail & Related papers  (2021-11-26T06:33:29Z)
• Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control [0.0]
  We present a new approach to using neural networks to approximate the solutions of variational equations. We use a sequence of finite-dimensional subspaces whose basis functions are realizations of a sequence of neural networks.
  arXiv  Detail & Related papers  (2021-05-28T20:25:40Z)
• Error Bounds of the Invariant Statistics in Machine Learning of Ergodic It\^o Diffusions [8.627408356707525]
  We study the theoretical underpinnings of machine learning of ergodic Ito diffusions. We deduce a linear dependence of the errors of one-point and two-point invariant statistics on the error in the learning of the drift and diffusion coefficients.
  arXiv  Detail & Related papers  (2021-05-21T02:55:59Z)
• Joint Network Topology Inference via Structured Fusion Regularization [70.30364652829164]
  Joint network topology inference represents a canonical problem of learning multiple graph Laplacian matrices from heterogeneous graph signals. We propose a general graph estimator based on a novel structured fusion regularization. We show that the proposed graph estimator enjoys both high computational efficiency and rigorous theoretical guarantee.
  arXiv  Detail & Related papers  (2021-03-05T04:42:32Z)
• Eigendecomposition-Free Training of Deep Networks for Linear Least-Square Problems [107.3868459697569]
  We introduce an eigendecomposition-free approach to training a deep network. We show that our approach is much more robust than explicit differentiation of the eigendecomposition. Our method has better convergence properties and yields state-of-the-art results.
  arXiv  Detail & Related papers  (2020-04-15T04:29:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.