Related papers: Extracting a functional representation from a dict…
When functional data manifest amplitude and phase variations, a commonly-employed framework for analyzing them is to take away the phase variation through a function alignment and then to apply standard tools to the aligned functions. A…
Principal Component Analysis (PCA) finds the best linear representation of data, and is an indispensable tool in many learning and inference tasks. Classically, principal components of a dataset are interpreted as the directions that…
Functional decomposition is the process of breaking down a function $f$ into a composition $f=g(f_1,\dots,f_k)$ of simpler functions $f_1,\dots,f_k$ belonging to some class $\mathcal{F}$. This fundamental notion can be used to model…
Mechanistic interpretability aims to understand the internal mechanisms learned by neural networks. Despite recent progress toward this goal, it remains unclear how best to decompose neural network parameters into mechanistic components. We…
Mapping parallel threads onto non-box-shaped domains is a known challenge in GPU computing; efficient mapping prevents performance penalties from unnecessary resource allocation. Currently, achieving this requires significant analytical…
We introduce a new framework for learning dense correspondence between deformable 3D shapes. Existing learning based approaches model shape correspondence as a labelling problem, where each point of a query shape receives a label…
Neural models learn data representations that lie on low-dimensional manifolds, yet modeling the relation between these representational spaces is an ongoing challenge. By integrating spectral geometry principles into neural modeling, we…
In a fully-Bayesian Functional Principal Components Analysis (FPCA) the principal components are treated as unknown infinite-dimensional parameters. By projecting the functional principal components on a rich orthonormal spline basis, we…
The recently proposed CP language adopts Compositional Programming: a new modular programming style that solves challenging problems such as the Expression Problem. CP is implemented on top of a polymorphic core language with disjoint…
In recent times, functional data analysis (FDA) has been successfully applied in the field of high dimensional data classification. In this paper, we present a novel classification framework using functional data and classwise Principal…
Shape matching has been a long-studied problem for the computer graphics and vision community. The objective is to predict a dense correspondence between meshes that have a certain degree of deformation. Existing methods either consider the…
A data table which is arranged according to two factors can often be considered as a compositional table. An example is the number of unemployed people, split according to gender and age classes. Analyzed as compositions, the relevant…
Part of the theory of logic programming and nonmonotonic reasoning concerns the study of fixed-point semantics for these paradigms. Several different semantics have been proposed during the last two decades, and some have been more…
In recent years, several efforts have been made to enhance conceptual data modelling with automated reasoning to improve the model's quality and derive implicit information. One approach to achieve this in implementations, is to constrain…
An important property of high-performance, low complexity codes is the existence of highly efficient algorithms for their decoding. Many of the most efficient, recent graph-based algorithms, e.g. message passing algorithms and decoding…
We introduce the proper orthogonal descriptors for efficient and accurate interatomic potentials of multi-element chemical systems. The potential energy surface of a multi-element system is represented as a many-body expansion of…
The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (harmonic vector fields), and fluid dynamics (vesicle…
Representation learning is a pivotal area in the field of machine learning, focusing on the development of methods to automatically discover the representations or features needed for a given task from raw data. Unlike traditional feature…
The task of establishing correspondences between two 3D shapes is a long-standing challenge in computer vision. While numerous studies address full-full and partial-full 3D shape matching, only a limited number of works have explored the…
Establishing dense correspondence across 3D shapes is crucial for fundamental downstream tasks, including texture transfer, shape interpolation, and robotic manipulation. However, learning these mappings without manual supervision remains a…