Related papers: Entangled Kernels -- Beyond Separability
Data similarity is a key concept in many data-driven applications. Many algorithms are sensitive to similarity measures. To tackle this fundamental problem, automatically learning of similarity information from data via self-expression has…
Neural networks use their hidden layers to transform input data into linearly separable data clusters, with a linear or a perceptron type output layer making the final projection on the line perpendicular to the discriminating hyperplane.…
The general perception is that kernel methods are not scalable, and neural nets are the methods of choice for nonlinear learning problems. Or have we simply not tried hard enough for kernel methods? Here we propose an approach that scales…
Applying new computing paradigms like quantum computing to the field of machine learning has recently gained attention. However, as high-dimensional real-world applications are not yet feasible to be solved using purely quantum hardware,…
Learned image reconstruction has become a pillar in computational imaging and inverse problems. Among the most successful approaches are learned iterative networks, which are formulated by unrolling classical iterative optimisation…
This papers introduces an algorithm for the solution of multiple kernel learning (MKL) problems with elastic-net constraints on the kernel weights. The algorithm compares very favourably in terms of time and space complexity to existing…
In quantum information, it is of high importance to efficiently detect entanglement. Generally, it needs quantum tomography to obtain state density matrix. However, it would consumes a lot of measurement resources, and the key is how to…
The convolution operator is the fundamental building block of modern convolutional neural networks (CNNs), owing to its simplicity, translational equivariance, and efficient implementation. However, its structure as a fixed, linear,…
This paper presents a general framework to integrate prior knowledge in the form of logic constraints among a set of task functions into kernel machines. The logic propositions provide a partial representation of the environment, in which…
We present a review of the problem of finding out whether a quantum state of two or more parties is entangled or separable. After a formal definition of entangled states, we present a few criteria for identifying entangled states and…
Quantum machine learning is a rapidly evolving field of research that could facilitate important applications for quantum computing and also significantly impact data-driven sciences. In our work, based on various arguments from complexity…
High-dimensional data in the form of tensors are challenging for kernel classification methods. To both reduce the computational complexity and extract informative features, kernels based on low-rank tensor decompositions have been…
We present a novel property-preserving kernel-based operator learning method for incompressible flows governed by the incompressible Navier--Stokes equations. Traditional numerical solvers incur significant computational costs to respect…
Kernel methods play a critical role in many machine learning algorithms. They are useful in manifold learning, classification, clustering and other data analysis tasks. Setting the kernel's scale parameter, also referred to as the kernel's…
This paper presents a two-phase method for learning interaction kernels of stochastic many-particle systems. After transforming stochastic trajectories of every particle into the particle density function by the kernel density estimation…
Kernel methods are powerful machine learning techniques which implement generic non-linear functions to solve complex tasks in a simple way. They Have a solid mathematical background and exhibit excellent performance in practice. However,…
Building on a specific formalization of analogical relationships of the form "A relates to B as C relates to D", we establish a connection between two important subfields of artificial intelligence, namely analogical reasoning and…
We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…
Entanglement is a fundamental aspect of quantum physics, both conceptually and for its many applications. Classifying an arbitrary multipartite state as entangled or separable -- a task referred to as the separability problem -- poses a…
We propose a localized approach to multiple kernel learning that can be formulated as a convex optimization problem over a given cluster structure. For which we obtain generalization error guarantees and derive an optimization algorithm…