Related papers: Classifying topological sector via machine learnin…
We demonstrate that there is significant redundancy in the parameterization of several deep learning models. Given only a few weight values for each feature it is possible to accurately predict the remaining values. Moreover, we show that…
Non-trivial spatial topology of the Universe may give rise to potentially measurable signatures in the cosmic microwave background. We explore different machine learning approaches to classify harmonic-space realizations of the microwave…
Mathematical morphology is a theory and technique to collect features like geometric and topological structures in digital images. Given a target image, determining suitable morphological operations and structuring elements is a cumbersome…
The topological analysis of four-dimensional (4D) image-type data is challenged by the immense size that these datasets can reach. This can render the direct application of methods, like persistent homology and convolutional neural networks…
Algebraic varieties are the geometric shapes defined by systems of polynomial equations; they are ubiquitous across mathematics and science. Amongst these algebraic varieties are Q-Fano varieties: positively curved shapes which have…
Neural networks possess formidable representational power, rendering them invaluable in solving complex quantum many-body systems. While they excel at analyzing static solutions, nonequilibrium processes, including critical dynamics during…
By considering specific limits in the gauge coupling constant of pure Yang--Mills dynamics, it is shown how there exist topological quantum field theory sectors in such systems defining nonperturbative topological configurations of the…
In this review I summarize how machine learning can be used in lattice gauge theory simulations and what ap\-proaches are currently available to improve the sampling of gauge field configurations, with a focus on applications in…
The published literature on topology optimization has exploded over the last two decades to include methods that use shape and topological derivatives or evolutionary algorithms formulated on various geometric representations and…
In Yang-Mills theory, the cumulants of the na\"ive lattice discretization of the topological charge evolved with the Yang-Mills gradient flow coincide, in the continuum limit, with those of the universal definition. We sketch in these…
Topological deep learning is a formalism that is aimed at introducing topological language to deep learning for the purpose of utilizing the minimal mathematical structures to formalize problems that arise in a generic deep learning…
In this survey, we provide an overview of category theory-derived machine learning from four mainstream perspectives: gradient-based learning, probability-based learning, invariance and equivalence-based learning, and topos-based learning.…
We calculate the topological susceptibility of the Yang-Mills vacuum using the field correlator method. Our estimate for the SU(3) gauge group, \chi^{1/4} = 196(7) MeV, is in a very good agreement with the results of recent numerical…
The topological charge density and topological susceptibility are determined by multi-probing approximation using overlap fermions in quenched SU(3) gauge theory. Then we investigate the topological structure of the quenched QCD vacuum, and…
The random vortex world-surface model is an infrared effective model of Yang-Mills dynamics based on center vortex degrees of freedom. These degrees of freedom carry topological charge through writhe and self-intersection of their…
We describe a quantum-assisted machine learning (QAML) method in which multivariate data is encoded into quantum states in a Hilbert space whose dimension is exponentially large in the length of the data vector. Learning in this space…
Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…
We show that deep neural networks can be integrated into, or fully replace, the Kohn-Sham density functional theory scheme for multi-electron systems in simple harmonic oscillator and random external potentials with no feature engineering.…
Machine learning techniques paired with the availability of massive datasets dramatically enhance our ability to explore the chemical compound space by providing fast and accurate predictions of molecular properties. However, learning on…
We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang-Mills theory. It gives a topological quantum model that has interesting and…