Related papers: On Representing (Anti)Symmetric Functions
Modelling functions of sets, or equivalently, permutation-invariant functions, is a long-standing challenge in machine learning. Deep Sets is a popular method which is known to be a universal approximator for continuous set functions. We…
The principle of translation equivariance (if an input image is translated an output image should be translated by the same amount), led to the development of convolutional neural networks that revolutionized machine vision. Other…
In this work, we establish a representation theorem for multivariable totally symmetric functions: a multisymmetric continuous function must be the composition of a continuous function and a set of generators of the multisymmetric…
We define two-parameter families of noncommutative symmetric functions and quasi-symmetric functions, which appear to be the proper analogues of the Macdonald symmetric functions in these settings.
The crucial role played by the underlying symmetries of high energy physics and lattice field theories calls for the implementation of such symmetries in the neural network architectures that are applied to the physical system under…
We propose semi-random features for nonlinear function approximation. The flexibility of semi-random feature lies between the fully adjustable units in deep learning and the random features used in kernel methods. For one hidden layer…
We study quantum corrections to hypersurfaces of dimension $d+1>2$ embedded in generic higher-dimensional spacetimes. Manifest covariance is maintained throughout the analysis and our methods are valid for arbitrary co-dimension and…
Four-dimensional N-extended superconformal symmetry and correlation functions of quasi-primary superfields are studied within the superspace formalism. A superconformal Killing equation is derived and its solutions are classified in terms…
Machine learning is among the most widely anticipated use cases for near-term quantum computers, however there remain significant theoretical and implementation challenges impeding its scale up. In particular, there is an emerging body of…
This paper presents a noncommutative theory of symmetric functions, based on the notion of quasi-determinant. We begin with a formal theory, corresponding to the case of symmetric functions in an infinite number of independent variables.…
The universality properties of kernels characterize the class of functions that can be approximated in the associated reproducing kernel Hilbert space and are of fundamental importance in the theoretical underpinning of kernel methods in…
Convolutional neural networks are the most widely used type of neural networks in applications. In mathematical analysis, however, mostly fully-connected networks are studied. In this paper, we establish a connection between both network…
Traditional supervised learning aims to learn an unknown mapping by fitting a function to a set of input-output pairs with a fixed dimension. The fitted function is then defined on inputs of the same dimension. However, in many settings,…
Symmetry is present in nature and science. In image processing, kernels for spatial filtering possess some symmetry (e.g. Sobel operators, Gaussian, Laplacian). Convolutional layers in artificial feed-forward neural networks have typically…
Encoding classical data into quantum states is considered a quantum feature map to map classical data into a quantum Hilbert space. This feature map provides opportunities to incorporate quantum advantages into machine learning algorithms…
Equivariant neural networks have proven to be effective for tasks with known underlying symmetries. However, optimizing equivariant networks can be tricky and best training practices are less established than for standard networks. In…
Universality of neural networks describes the ability to approximate arbitrary function, and is a key ingredient to keep the method effective. The established models for universal quantum neural networks(QNN), however, require the…
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…
We propose a novel class of neural network-like parametrized functions, i.e., general transformation neural networks (GTNNs), for high-dimensional approximation. Conventional deep neural networks sometimes perform less accurately on…
We present a novel framework to overcome the limitations of equivariant architectures in learning functions with group symmetries. In contrary to equivariant architectures, we use an arbitrary base model such as an MLP or a transformer and…