Related papers: Learning from Topology: Cosmological Parameter Est…
The Hessian of a neural network captures parameter interactions through second-order derivatives of the loss. It is a fundamental object of study, closely tied to various problems in deep learning, including model design, optimization, and…
A neural network with fixed topology can be regarded as a parametrization of functions, which decides on the correlations between functional variations when parameters are adapted. We propose an analysis, based on a differential geometry…
Using tools from topology and functional analysis, we provide a framework where artificial neural networks, and their architectures, can be formally described. We define the notion of machine in a general topological context and show how…
Determination of cosmological parameters is a major goal in cosmology at present. The availability of improved data sets necessitates the development of novel statistical tools to interpret the inference from a cosmological model. In this…
Persistent homology is an effective method for extracting topological information, represented as persistent diagrams, of spatial structure data. Hence it is well-suited for the study of protein structures. Attempts to incorporate…
Making use of the wealth of new observational data coming from the sky it is possible to constrain particle physics theories beyond the Standard Model. One way to do this is illustrated in this article: a subset of theories admits cosmic…
Topological Machine Learning (TML) is an emerging field that leverages techniques from algebraic topology to analyze complex data structures in ways that traditional machine learning methods may not capture. This tutorial provides a…
Constraints on the main cosmological parameters using CMB or large scale structure data are usually based on power-law assumption of the primordial power spectrum (PPS). However, in the absence of a preferred model for the early universe,…
Persistent Homology (PH) has been successfully used to train networks to detect curvilinear structures and to improve the topological quality of their results. However, existing methods are very global and ignore the location of topological…
Deep learning is a powerful analysis technique that has recently been proposed as a method to constrain cosmological parameters from weak lensing mass maps. Due to its ability to learn relevant features from the data, it is able to extract…
Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs). Concurrently, topological descriptors based on persistent…
We study the accuracy with which cosmological parameters can be determined from real space power spectrum of matter density contrast at weakly nonlinear scales using analytical approaches. From power spectra measured in $N$-body simulations…
Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…
Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neural network models still struggle to capture higher-order…
Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first…
Mapping is an essential task for mobile robots and topological representation often works as a basis for the various applications. In this paper, a novel framework that can build topological maps incrementally is proposed. The algorithm is…
Network tomography, a classic research problem in the realm of network monitoring, refers to the methodology of inferring unmeasured network attributes using selected end-to-end path measurements. In the research community, network…
I will briefly present my work on cosmological parameters estimation. Classical methods for parameters estimation involve the exploration of the parameter space on a precalculated grid of cosmological models. Here we try to estimate the…
A nontrivial topology of the spatial section of the universe is an observable, which can be probed for all locally homogeneous and isotropic universes, without any assumption on the cosmological density parameters. We discuss how one can…
Supervised machine learning pipelines trained on features derived from persistent homology have been experimentally observed to ignore much of the information contained in a persistence diagram. Computing persistence diagrams is often the…