arXiv subjects

Yanick Thurn

Publications and source records attributed to Yanick Thurn.

5 recordsLinked to original sources

arXiv2026

Analytic continuation of Green's functions with a neural network

An important problem in many-body physics is to reconstruct the spectral density from the imaginary-time domain Green's function. Typically, the imaginary-time Green's function is generated by Monte Carlo methods. As the one-point fermionic kernel diverges exponentially for large frequencies, numerical noise generically causes instabilities. We use a convolutional neural network to obtain the spectral density for a given imaginary time Green's function. The network is trained by data which we generate using random Gaussians. We improve the training data set available by including collision centers for the Gaussians rather than employing uniformly distributed Gaussians. Our network is constructed in such a way that its output fulfills positive semidefiniteness. We compare the results of our network with results of the Maximum Entropy method (MaxEnt), a standard method for the same reconstruction problem for the spectral density. This comparison is performed for three different cases, namely our Gaussian based test data as well as two physical models, the 1d Hubbard model showing spin-charge separation, and the two-dimensional SSH model in the self-consistent Born approximation. We find that the network outperforms MaxEnt when presented data close to the training set. For the physical models considered, MaxEnt recognizes physical features more precisely as compared to our network prediction. While it is hard to improve MaxEnt, the quality of the network depends on the training data set which can be systematically enhanced and improved.

cond-mat.str-el↗

arXiv2025

Hyperbolic tiling neighborhoods in O(1) time

Tilings of the hyperbolic plane are of significant interest among many branches of mathematics, physics and computer science. Yet, their construction remains a non-trivial task. Current approaches primarily use tree-based recursive algorithms, which are fundamentally limited: they do not readily yield the neighborhood graph representing cell adjacencies, which is however required for many applications. We introduce a novel approach that allows to build hyperbolic tilings and their associated graph structure simultaneously, using only combinatoric rules without requiring an explicit coordinate representation. This allows to generate arbitrarily large, exact hyperbolic graphs, with an algorithmic complexity that does not depend on the lattice size. We provide an easy-to-use implementation which substantially outperforms existing methods, hence rendering ultra large-scale numerical simulations on these geometric structures accessible for the scientific community.

physics.comp-ph↗

arXiv2024

Discrete JT gravity as an Ising model

Inspired by the program of discrete holography, we show that Jackiw-Teitelboim (JT) gravity on a hyperbolic tiling of Euclidean AdS$_2$ gives rise to an Ising model on the dual lattice, subject to a topological constraint. The Ising model involves an asymptotic boundary condition with spins pointing opposite to the magnetic field. The topological constraint enforces a single domain wall between the spins of opposite direction, with the topology of a circle. The resolvent of JT gravity is related to the free energy of this Ising model, and the classical limit of JT gravity corresponds to the Ising low-temperature limit. We study this Ising model through a Monte Carlo approach and a mean-field approximation. For finite truncations of the infinite hyperbolic lattice, the map between both theories is only valid in a regime in which the domain wall has a finite size. For the extremal cases of large positive or negative coupling, the domain wall either shrinks to zero or touches the boundary of the lattice. This behavior is confirmed by the mean-field analysis. We expect that our results may be used as a starting point for establishing a holographic matrix model duality for discretized gravity.

hep-th↗

arXiv2024

Opening the Black Box: predicting the trainability of deep neural networks with reconstruction entropy

An important challenge in machine learning is to predict the initial conditions under which a given neural network will be trainable. We present a method for predicting the trainable regime in parameter space for deep feedforward neural networks (DNNs) based on reconstructing the input from subsequent activation layers via a cascade of single-layer auxiliary networks. We show that a single epoch of training of the shallow cascade networks is sufficient to predict the trainability of the deep feedforward network on a range of datasets (MNIST, CIFAR10, FashionMNIST, and white noise), thereby providing a significant reduction in overall training time. We achieve this by computing the relative entropy between reconstructed images and the original inputs, and show that this probe of information loss is sensitive to the phase behaviour of the network. We further demonstrate that this method generalizes to residual neural networks (ResNets) and convolutional neural networks (CNNs). Moreover, our method illustrates the network's decision making process by displaying the changes performed on the input data at each layer, which we demonstrate for both a DNN trained on MNIST and the vgg16 CNN trained on the ImageNet dataset. Our results provide a technique for significantly accelerating the training of large neural networks.

cs.LG↗

arXiv2023

HYPERTILING -- a high performance Python library for the generation and visualization of hyperbolic lattices

HYPERTILING is a high-performance Python library for the generation and visualization of regular hyperbolic lattices embedded in the Poincar\'e disk model. Using highly optimized, efficient algorithms, hyperbolic tilings with millions of vertices can be created in a matter of minutes on a single workstation computer. Facilities including computation of adjacent vertices, dynamic lattice manipulation, refinements, as well as powerful plotting and animation capabilities are provided to support advanced uses of hyperbolic graphs. In this manuscript, we present a comprehensive exploration of the package, encompassing its mathematical foundations, usage examples, applications, and a detailed description of its implementation.

physics.comp-ph↗