Related papers: The LG Fibration
Let $L$ be an oriented link with an alternating diagram $D$. It is known that $L$ is a fibered link if and only if the surface $R$ obtained by applying Seifert's algorithm to $D$ is a Hopf plumbing. Here, we call $R$ a Hopf plumbing if $R$…
Automatic detection of faults in optical fibers is an active area of research that plays a significant role in the design of reliable and stable optical networks. A fiber measurement system that combines automated data acquisition and…
Laser-induced breakdown spectroscopy (LIBS) is a popular, fast elemental analysis technique used to determine the chemical composition of target samples, such as in industrial analysis of metals or in space exploration. Recently, there has…
The unprecedented predictive success of deep generative models in complex many-body systems, such as AlphaFold3, raises an epistemological question: do these networks merely memorize data distributions via high-dimensional interpolation, or…
In this paper we first identify a basic limitation in gradient descent-based optimization methods when used in conjunctions with smooth kernels. An analysis based on the spectral properties of the kernel demonstrates that only a vanishingly…
Geometry-aware optimizers such as Newton and natural gradient can improve conditioning in deep learning, but scalable variants such as K-FAC, Shampoo, and related preconditioners usually impose structural approximations early, often…
Given a closed hyperbolic surface $S$, let $\cQF$ denote the space of quasifuchsian hyperbolic metrics on $S\times\R$ and $\cGH_{-1}$ the space of maximal globally hyperbolic anti-de Sitter metrics on $S\times\R$. We describe natural maps…
Grasping is one of the most fundamental challenging capabilities in robotic manipulation, especially in unstructured, cluttered, and semantically diverse environments. Recent researches have increasingly explored language-guided…
Understanding how deep neural networks learn useful internal representations from data remains a central open problem in the theory of deep learning. We introduce Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based…
Sensing is an integral part of 6G and beyond systems, providing exceptional environmental perception along with communication. Radio frequency (RF)-based sensing often relies on simplified geometric assumptions (e.g., point scatterers or…
We derive the universal R-matrix of the quantum-deformed enveloping algebra of centrally extended sl(2|2) using Drinfeld's quantum double construction. We are led to enlarging the algebra by additional generators corresponding to an sl(2)…
Inverse scattering problems, such as those in electromagnetic imaging using phaseless data (PD-ISPs), involve imaging objects using phaseless measurements of wave scattering. Such inverse problems can be highly non-linear and ill-posed…
This paper proposes Stochastic Geographic Gradient Fusion (SGFusion), a novel training algorithm to leverage the geographic information of mobile users in Federated Learning (FL). SGFusion maps the data collected by mobile devices onto…
We present a new framework for the simultaneous optimiziation of both the topology as well as the relative density grading of cellular structures and materials, also known as lattices. Due to manufacturing constraints, the optimization…
We show how a Hopfield network with modifiable recurrent connections undergoing slow Hebbian learning can extract the underlying geometry of an input space. First, we use a slow/fast analysis to derive an averaged system whose dynamics…
We introduce the problem of hidden Hamiltonian cycle recovery, where there is an unknown Hamiltonian cycle in an $n$-vertex complete graph that needs to be inferred from noisy edge measurements. The measurements are independent and…
The aim of this paper is to describe the obstruction for an almost Lagrangian fibration to be Lagrangian, a problem which is central to the classification of Lagrangian fibrations and, more generally, to understanding the obstructions to…
We derive a family of linear inference algorithms that generalize existing graph-based label propagation algorithms by allowing them to propagate generalized assumptions about "attraction" or "compatibility" between classes of neighboring…
A degree 1 non-negative graded super manifold equipped with a degree 1 vector field Q satisfying [Q, Q]=1, namely a so-called NQ-1 manifold is, in plain differential geometry language, a Lie algebroid. We introduce a notion of fibration for…
Modelling information from complex systems such as humans social interaction or words co-occurrences in our languages can help to understand how these systems are organized and function. Such systems can be modelled by networks, and network…