Related papers: Inferring relevant features: from QFT to PCA

Combining the advantages of quantum computing and neural networks, quantum neural networks (QNNs) have gained considerable attention recently. However, because of the lack of quantum resource, it is costly to train QNNs. In this work, we…

We present three generalisations of Kernel Principal Components Analysis (KPCA) which incorporate knowledge of the class labels of a subset of the data points. The first, MV-KPCA, penalises within class variances similar to Fisher…

Renormalization group (RG) methods are emerging as tools in biology and computer science to support the search for simplifying structure in distributions over high-dimensional spaces. We show that mixture models can be thought of as having…

Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success,…

Indistinguishability is an essential concept to understanding mysterious quantum features in the view point of the wave-particle duality of quantum mechanics. The fundamental physics of the indistinguishability lies in quantum superposition…

The identification and quantification of markers in medical images is critical for diagnosis, prognosis and management of patients in clinical practice. Supervised- or weakly supervised training enables the detection of findings that are…

We describe how randomized benchmarking can be used to reconstruct the unital part of any trace-preserving quantum map, which in turn is sufficient for the full characterization of any unitary evolution, or more generally, any unital…

Quantum machine learning (QML) shows promise for analyzing quantum data. A notable example is the use of quantum convolutional neural networks (QCNNs), implemented as specific types of quantum circuits, to recognize phases of matter. In…

At low energies, the microscopic characteristics and changes of physical systems as viewed at different distance scales are described by universal scale invariant properties investigated by the Renormalization Group (RG) apparatus, an…

Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on…

Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…

Learning an empirically effective model with generalization using limited data is a challenging task for deep neural networks. In this paper, we propose a novel learning framework called PurifiedLearning to exploit task-irrelevant features…

The accurate detection of small deviations in given density matrices is important for quantum information processing. Here we propose a new method based on the concept of data mining. We demonstrate that the proposed method can more…

Renormalization procedure is generalized to be applicable for non renormalizable theories. It is shown that introduction of an extra expansion parameter allows to get rid of divergences and express physical quantities as series of finite…

The importance and usefulness of renormalization are emphasized in nonrelativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin…

Unsupervised machine learning, and in particular data clustering, is a powerful approach for the analysis of datasets and identification of characteristic features occurring throughout a dataset. It is gaining popularity across scientific…

This paper concerns the critical decision process of extracting or selecting the features before applying a clustering algorithm. It is not obvious to evaluate the importance of the features since the most popular methods to do it are…

Contrastive learning is a powerful framework for learning self-supervised representations that generalize well to downstream supervised tasks. We show that multiple existing contrastive learning methods can be reinterpreted as learning…

Recent applications of kernel methods in machine learning have seen a renewed interest in the Laplacian kernel, due to its stability to the bandwidth hyperparameter in comparison to the Gaussian kernel, as well as its expressivity being…

Distribution shifts between sites can seriously degrade model performance since models are prone to exploiting unstable correlations. Thus, many methods try to find features that are stable across sites and discard unstable features.…