Related papers: The LG Fibration

Let X be a projective hyperk\"ahler manifold containing a Lagrangian subtorus L. We study intersections of deformations of L, defining a canonical almost holomorphic map called L-reduction, which is not birational if and only if X admits an…

Good representations for phylogenetic trees and networks are important for optimizing storage efficiency and implementation of scalable methods for the inference and analysis of evolutionary trees for genes, genomes and species. We…

Collagen fiber orientations in bones, visible with Second Harmonic Generation (SHG) microscopy, represent the inner structure and its alteration due to influences like cancer. While analyses of these orientations are valuable for medical…

In this work, we present a novel and practical approach to address one of the longstanding problems in computer vision: 2D and 3D affine invariant feature matching. Our Grassmannian Graph (GrassGraph) framework employs a two stage procedure…

We define the concept of \emph{companion automorphism} of a Hopf algebra $H$ as an automorphism $\sigma:H \rightarrow H$: $\sigma^2=S^2$ --where $S$ denotes the antipode--. A Hopf algebra is said to be \emph{almost involutive} (AI) if it…

Backpropagation of error (backprop) is a powerful algorithm for training machine learning architectures through end-to-end differentiation. However, backprop is often criticised for lacking biological plausibility. Recently, it has been…

Reinforcement Learning (RL) algorithms allow artificial agents to improve their action selections so as to increase rewarding experiences in their environments. Deep Reinforcement Learning algorithms require solving a nonconvex and…

In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…

We introduce a mapping framework for deep learning inference that takes advantage of predictable neural network behavior to plan both computation and communication ahead of time. The framework generates a unified stream of instructions and…

Let n>3, and let L be a Lagrangian embedding of an n-disk into the cotangent bundle of n-dimensional Euclidean space that agrees with the cotangent fiber over a non-zero point x outside a compact set. Assume that L is disjoint from the…

We present a Morphology-Informed Heterogeneous Graph Neural Network (MI-HGNN) for learning-based contact perception. The architecture and connectivity of the MI-HGNN are constructed from the robot morphology, in which nodes and edges are…

Deep learning is emerging as a new paradigm for solving inverse imaging problems. However, the deep learning methods often lack the assurance of traditional physics-based methods due to the lack of physical information considerations in…

Deep learning based on deep neural networks of various structures and architectures has been powerful in many practical applications, but it lacks enough theoretical verifications. In this paper, we consider a family of deep convolutional…

We study certain types of piecewise smooth Lagrangian fibrations of smooth symplectic manifolds, which we call stitched Lagrangian fibrations. We extend the classical theory of action-angle coordinates to these fibrations by encoding the…

We present a novel approach to robotic grasp planning using both a learned grasp proposal network and a learned 3D shape reconstruction network. Our system generates 6-DOF grasps from a single RGB-D image of the target object, which is…

While the animals' Fin-to-Limb evolution has been well-researched in biology, such morphological transformation remains under-adopted in the modern design of advanced robotic limbs. This paper investigates a novel class of overconstrained…

We study 3d $\mathcal{N}=2$ supersymmetric gauge theories on closed oriented Seifert manifold---circle bundles over an orbifold Riemann surface---, with a gauge group G given by a product of simply-connected and/or unitary Lie groups. Our…

We consider solving high-order semidefinite programming (SDP) relaxations of nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. Instead of solving the SDP alone, we propose a new…

We develop a correspondence between the orbits of the group of linear symplectomorphisms of a real finite dimensional symplectic vector space in the complex Lagrangian Grassmannian and the Grassmannians of linear subspaces of the real…

Feature representations, both hand-designed and learned ones, are often hard to analyze and interpret, even when they are extracted from visual data. We propose a new approach to study image representations by inverting them with an…