Related papers: Unitary-Group Invariant Kernels and Features from …
This paper addresses the problem of unsupervised clustering which remains one of the most fundamental challenges in machine learning and artificial intelligence. We propose the clustered generator model for clustering which contains both…
Representation learning with small labeled data have emerged in many problems, since the success of deep neural networks often relies on the availability of a huge amount of labeled data that is expensive to collect. To address it, many…
Learning with kernels is an important concept in machine learning. Standard approaches for kernel methods often use predefined kernels that require careful selection of hyperparameters. To mitigate this burden, we propose in this paper a…
Quantum kernel methods offer significant theoretical benefits by rendering classically inseparable features separable in quantum space. Yet, the practical application of Quantum Machine Learning (QML), currently constrained by the…
Unsupervised and supervised learning methods conventionally use kernels to capture nonlinearities inherent in data structure. However experts have to ensure their proposed nonlinearity maximizes variability and capture inherent diversity of…
The goal of invariant theory is to find all the generators for the algebra of representations of a group that leave the group invariant. Such generators will be called \emph{basic invariants}. In particular, we set out to find the set of…
In this paper, we propose Complex Diffusion Maps (CDM), a novel diffusion mapping framework that aims to reveal the dominant complex harmonics of high-dimensional data. Inspired by the local Gaussian kernel relevant to the heat equation and…
We introduce and study a number of invariants of locally compact quantum groups defined by their scaling and modular groups and the spectrum of their modular elements. Focusing mainly on compact quantum groups we consider the question…
Deep kernel learning combines the non-parametric flexibility of kernel methods with the inductive biases of deep learning architectures. We propose a novel deep kernel learning model and stochastic variational inference procedure which…
We develop a new mathematical approach to diffeomorphism invariant quantum states for the quantisation of general field theories such as general relativity and modified gravity. Treating quantum fields as fibre bundles, we discuss operators…
An enumerative invariant theory in Algebraic Geometry, Differential Geometry, or Representation Theory, is the study of invariants which 'count' $\tau$-(semi)stable objects $E$ with fixed topological invariants $[E]=\alpha$ in some…
Symmetry learning has proven to be an effective approach for extracting the hidden structure of data, with the concept of equivariance relation playing the central role. However, most of the current studies are built on architectural theory…
Multi-band insulating Bloch Hamiltonians with internal or spatial symmetries, such as particle-hole or inversion, may have topologically disconnected sectors of trivial atomic-limit (momentum-independent) Hamiltonians. We present a…
Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite…
The ability to identify useful features or representations of the input data based on training data that achieves low prediction error on test data across multiple prediction tasks is considered the key to multitask learning success. In…
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line…
We study positive definite kernels pulled back along a finite family of self-maps under a subinvariance inequality for the associated branching operator. Iteration produces an increasing kernel tower with defect kernels. Under diagonal…
A modified gamma kernel should not be automatically preferred to the standard gamma kernel, especially for univariate convex densities with a pole at the origin. In the multivariate case, multiple combined gamma kernels, defined as a…
Distance metric learning aims to learn from the given training data a valid distance metric, with which the similarity between data samples can be more effectively evaluated for classification. Metric learning is often formulated as a…
Developing robust and interpretable vision systems is a crucial step towards trustworthy artificial intelligence. In this regard, a promising paradigm considers embedding task-required invariant structures, e.g., geometric invariance, in…