Q-curvature and Path Integral Complexity

• URL: http://arxiv.org/abs/2201.00562v2
• Date: Fri, 15 Apr 2022 13:08:41 GMT
• Title: Q-curvature and Path Integral Complexity
• Authors: Hugo A. Camargo, Pawel Caputa, Pratik Nandy
• Abstract summary: We discuss the interpretation of path integral optimization as a uniformization problem in even dimensions. This perspective allows for a systematical construction of the higher-dimensional path integral complexity in holographic conformal field theories.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We discuss the interpretation of path integral optimization as a uniformization problem in even dimensions. This perspective allows for a systematical construction of the higher-dimensional path integral complexity in holographic conformal field theories in terms of Q-curvature actions. We explore the properties and consequences of these actions from the perspective of the optimization programme, tensor networks and penalty factors. Moreover, in the context of recently proposed holographic path integral optimization, we consider higher curvature contributions on the Hartle-Hawking bulk slice and study their impact on the optimization as well as their relation to Q-curvature actions and finite cut-off holography.

Related papers

• Designing Algorithms for Entropic Optimal Transport from an Optimisation Perspective [12.343553053539976]
  We develop a collection of novel methods for the entropic-regularised optimal transport problem.<n>We are inspired by existing mirror interpretations of the Sinkhorn problem.<n>The broader we develop based on over the joint distributions also finds an analogue in the Schr"odinger bridge problem.
  arXiv  Detail & Related papers  (2025-07-16T13:56:11Z)
• Sharper Convergence Rates for Nonconvex Optimisation via Reduction Mappings [34.309687104447114]
  We show that well-designed reduction mappings improve curvature properties of the objective, leading to better-conditioned problems and theoretically faster convergence for gradient-based methods.<n>Our analysis unifies a range of scenarios where structural information at optimality is leveraged to accelerate convergence, offering a principled explanation for the empirical gains observed in such optimisation algorithms.
  arXiv  Detail & Related papers  (2025-06-10T04:03:59Z)
• Efficient Design of Compliant Mechanisms Using Multi-Objective Optimization [50.24983453990065]
  We address the synthesis of a compliant cross-hinge mechanism capable of large angular strokes. We formulate a multi-objective optimization problem based on kinetostatic performance measures.
  arXiv  Detail & Related papers  (2025-04-23T06:29:10Z)
• Remarks on the Polyak-Lojasiewicz inequality and the convergence of gradient systems [0.3277163122167434]
  This work explores generalizations of the Polyak-Lojasiewicz inequality (PLI) This work shows that while weaker conditions are sufficient for global convergence to, and optimality of the set of critical points of the cost function, the "profile" of the gradient flow solution can change significantly depending on which "flavor" of inequality the cost satisfies.
  arXiv  Detail & Related papers  (2025-03-31T00:59:56Z)
• Hallmarks of Optimization Trajectories in Neural Networks: Directional Exploration and Redundancy [75.15685966213832]
  We analyze the rich directional structure of optimization trajectories represented by their pointwise parameters. We show that training only scalar batchnorm parameters some while into training matches the performance of training the entire network.
  arXiv  Detail & Related papers  (2024-03-12T07:32:47Z)
• Analyzing and Enhancing the Backward-Pass Convergence of Unrolled Optimization [50.38518771642365]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an optimization problem, which often lacks a closed form. This paper provides theoretical insights into the backward pass of unrolled optimization, showing that it is equivalent to the solution of a linear system by a particular iterative method. A system called Folded Optimization is proposed to construct more efficient backpropagation rules from unrolled solver implementations.
  arXiv  Detail & Related papers  (2023-12-28T23:15:18Z)
• Optimal Sets and Solution Paths of ReLU Networks [56.40911684005949]
  We develop an analytical framework to characterize the set of optimal ReLU networks. We establish conditions for the neuralization of ReLU networks to be continuous, and develop sensitivity results for ReLU networks.
  arXiv  Detail & Related papers  (2023-05-31T18:48:16Z)
• Backpropagation of Unrolled Solvers with Folded Optimization [55.04219793298687]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. One typical strategy is algorithm unrolling, which relies on automatic differentiation through the operations of an iterative solver. This paper provides theoretical insights into the backward pass of unrolled optimization, leading to a system for generating efficiently solvable analytical models of backpropagation.
  arXiv  Detail & Related papers  (2023-01-28T01:50:42Z)
• A theoretical and empirical study of new adaptive algorithms with additional momentum steps and shifted updates for stochastic non-convex optimization [0.0]
  It is thought that adaptive optimization algorithms represent the key pillar behind the of the Learning field. In this paper we introduce adaptive momentum techniques for different non-smooth objective problems.
  arXiv  Detail & Related papers  (2021-10-16T09:47:57Z)
• Optimization on manifolds: A symplectic approach [127.54402681305629]
  We propose a dissipative extension of Dirac's theory of constrained Hamiltonian systems as a general framework for solving optimization problems. Our class of (accelerated) algorithms are not only simple and efficient but also applicable to a broad range of contexts.
  arXiv  Detail & Related papers  (2021-07-23T13:43:34Z)
• Combinatorial Optimization for Panoptic Segmentation: An End-to-End Trainable Approach [23.281726932718232]
  We propose an end-to-end trainable architecture for simultaneous semantic and instance segmentation. Our approach shows the utility of using optimization in tandem with deep learning in a challenging large scale real-world problem.
  arXiv  Detail & Related papers  (2021-06-06T17:39:13Z)
• Holographic Path-Integral Optimization [0.0]
  We show that metrics that maximize gravity wave functions in holographic geometries precisely match those in the path-integral optimization procedure for their dual CFT states. We generalize the analysis to Lorentzian Anti-de Sitter and de Sitter geometries and use it to shed light on path-integral optimization in Lorentzian CFTs.
  arXiv  Detail & Related papers  (2021-03-31T18:00:01Z)
• Zeroth-Order Hybrid Gradient Descent: Towards A Principled Black-Box Optimization Framework [100.36569795440889]
  This work is on the iteration of zero-th-order (ZO) optimization which does not require first-order information. We show that with a graceful design in coordinate importance sampling, the proposed ZO optimization method is efficient both in terms of complexity as well as as function query cost.
  arXiv  Detail & Related papers  (2020-12-21T17:29:58Z)
• Path-Integral Optimization from Hartle-Hawking Wave Function [0.0]
  We show that the variation of the wave function leads to a constraint, equivalent to the Neumann boundary condition on a bulk slice. We reproduce the path-integral complexity action in two dimensions as well as its higher and lower dimensional generalizations.
  arXiv  Detail & Related papers  (2020-11-16T19:00:00Z)

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.