Related papers: Polytopes and Machine Learning
We introduce reflexive polytopes of index l as a natural generalisation of the notion of a reflexive polytope of index 1. These l-reflexive polytopes also appear as dual pairs. In dimension two we show that they arise from reflexive…
Diverse many-body systems, from soap bubbles to suspensions to polymers, learn and remember patterns in the drives that push them far from equilibrium. This learning may be leveraged for computation, memory, and engineering. Until now,…
The machine learning of lattice operators has three possible bottlenecks. From a statistical standpoint, it is necessary to design a constrained class of operators based on prior information with low bias, and low complexity relative to the…
We discuss an experimental approach to open problems in toric geometry: are smooth projective toric varieties (i) projectively normal and (ii) defined by degree 2 equations? We discuss the creation of lattice polytopes defining smooth toric…
We propose a new class of deep reinforcement learning (RL) algorithms that model latent representations in hyperbolic space. Sequential decision-making requires reasoning about the possible future consequences of current behavior.…
Deep learning is a form of machine learning for nonlinear high dimensional pattern matching and prediction. By taking a Bayesian probabilistic perspective, we provide a number of insights into more efficient algorithms for optimisation and…
In [1, 2], we have explored the theoretical aspects of feature extraction optimization processes for solving largescale problems and overcoming machine learning limitations. Majority of optimization algorithms that have been introduced in…
We propose a novel machine learning method for sampling from the high-dimensional probability distributions of Lattice Field Theories, which is based on a single neural ODE layer and incorporates the full symmetries of the problem. We test…
Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects in stochastic geometry. A natural geometric question is…
There is a growing consensus that solutions to complex science and engineering problems require novel methodologies that are able to integrate traditional physics-based modeling approaches with state-of-the-art machine learning (ML)…
Accurate volume estimation of objects from visual data is a long-standing challenge in computer vision with significant applications in robotics, logistics, and smart health. Existing methods often rely on complex 3D reconstruction…
Polygon representation learning is essential for diverse applications, encompassing tasks such as shape coding, building pattern classification, and geographic question answering. While recent years have seen considerable advancements in…
Two-dimensional materials are a class of atomically thin materials with assorted electronic and quantum properties. Accurate identification of layer thickness, especially for a single monolayer, is crucial for their characterization. This…
There are (at least) two reasons to study random polytopes. The first is to understand the combinatorics and geometry of random polytopes especially as compared to other classes of polytopes, and the second is to analyze average-case…
Many machine learning problems involve regressing variables on a non-Euclidean manifold -- e.g. a discrete probability distribution, or the 6D pose of an object. One way to tackle these problems through gradient-based learning is to use a…
We develop information geometric techniques to understand the representations learned by deep networks when they are trained on different tasks using supervised, meta-, semi-supervised and contrastive learning. We shed light on the…
The many ways in which machine and deep learning are transforming the analysis and simulation of data in particle physics are reviewed. The main methods based on boosted decision trees and various types of neural networks are introduced,…
We present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that…
We investigate different approaches to machine learning of line bundle cohomology on complex surfaces as well as on Calabi-Yau three-folds. Standard function learning based on simple fully connected networks with logistic sigmoids is…
Machine learning (ML) methods can expand our ability to construct, and draw insight from large datasets. Despite the increasing volume of planetary observations, our field has seen few applications of ML in comparison to other sciences. To…