Related papers: Machine Learning Line Bundle Cohomology

We use reinforcement learning as a means of constructing string compactifications with prescribed properties. Specifically, we study heterotic SO(10) GUT models on Calabi-Yau three-folds with monad bundles, in search of phenomenologically…

Optical two-dimensional (2D) coherent spectroscopy excels in studying coupling and dynamics in complex systems. The dynamical information can be learned from lineshape analysis to extract the corresponding linewidth. However, it is usually…

We introduce a new method to study mixed characteristic deformation of line bundles. In particular, for sufficiently large smooth projective families $f : \mathscr{X} \to \mathscr{S}$ defined over the ring of $N$-integers…

Understanding the dynamics of neural networks in different width regimes is crucial for improving their training and performance. We present an exact solution for the learning dynamics of a one-hidden-layer linear network, with…

Layered hybrid halide compounds offer promising functional properties, particularly tunable band gaps, conductivity, light harvesting thus making them prospective for applications in photovoltaics and optoelectronics. This study exemplifies…

Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…

The classification problem for principal fibre bundles over two-dimensional CW-complexes is considered. Using the Postnikov factorization for the base space of a universal bundle a Puppe sequence that gives an implicit solution for the…

We propose a new algorithm to learn a one-hidden-layer convolutional neural network where both the convolutional weights and the outputs weights are parameters to be learned. Our algorithm works for a general class of (potentially…

The study of topological bandstructures is an active area of research in condensed matter physics and beyond. Here, we combine recent progress in this field with developments in machine-learning, another rising topic of interest.…

The latest techniques from Neural Networks and Support Vector Machines (SVM) are used to investigate geometric properties of Complete Intersection Calabi-Yau (CICY) threefolds, a class of manifolds that facilitate string model building. An…

Machine learning (ML) tasks are becoming ubiquitous in today's network applications. Federated learning has emerged recently as a technique for training ML models at the network edge by leveraging processing capabilities across the nodes…

Covariance matrices have attracted attention for machine learning applications due to their capacity to capture interesting structure in the data. The main challenge is that one needs to take into account the particular geometry of the…

Dense prediction tasks typically employ encoder-decoder architectures, but the prevalent convolutions in the decoder are not image-adaptive and can lead to boundary artifacts. Different generalized convolution operations have been…

In the present note we describe geometrically the homology classes in the total space of a surface bundle over a surface in terms of the holonomy map. We treat the cases where the base surface is closed or has one boundary component. We…

By redefining the conventional notions of layers, we present an alternative view on finitely wide, fully trainable deep neural networks as stacked linear models in feature spaces, leading to a kernel machine interpretation. Based on this…

Multiparameter persistent homology has been largely neglected as an input to machine learning algorithms. We consider the use of lattice-based convolutional neural network layers as a tool for the analysis of features arising from…

We explore algebro-geometric properties of the moduli space of holomorphic Lie algebroid ($ \mathcal{L} $) connections on a compact Riemann surface $X$ of genus $g \,\geq\, 3$. A smooth compactification of the moduli space of…

We present an explicit method for translating between the linear sigma model and the spectral cover description of SU(r) stable bundles over an elliptically fibered Calabi-Yau manifold. We use this to investigate the 4-dimensional duality…

Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great…