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Tensor decomposition has emerged as a prominent technique to learn low-dimensional representation under the supervision of reconstruction error, primarily benefiting data inference tasks like completion and imputation, but not…

Convolutional neural networks (CNNs) have gained widespread usage across various fields such as weather forecasting, computer vision, autonomous driving, and medical image analysis due to its exceptional ability to extract spatial…

We propose a kernelized classification layer for deep networks. Although conventional deep networks introduce an abundance of nonlinearity for representation (feature) learning, they almost universally use a linear classifier on the learned…

The accuracy and complexity of kernel learning algorithms is determined by the set of kernels over which it is able to optimize. An ideal set of kernels should: admit a linear parameterization (tractability); be dense in the set of all…

PELICAN is a novel permutation equivariant and Lorentz invariant or covariant aggregator network designed to overcome common limitations found in architectures applied to particle physics problems. Compared to many approaches that use…

Convolutional Neural Networks (CNNs) excel at extracting local features hierarchically, but their performance in capturing complex correlations hinges heavily on deep architectures, which are usually computationally demanding and difficult…

Irregularly sampled multivariate time series are ubiquitous in several application domains, leading to sparse, not fully-observed and non-aligned observations across different variables. Standard sequential neural network architectures,…

Geometric deep learning (GDL) models have demonstrated a great potential for the analysis of non-Euclidian data. They are developed to incorporate the geometric and topological information of non-Euclidian data into the end-to-end deep…

Tensor Network (TN) Kernel Machines speed up model learning by representing parameters as low-rank TNs, reducing computation and memory use. However, most TN-based Kernel methods are deterministic and ignore parameter uncertainty. Further,…

Recently, methods have been developed to accurately predict the testing performance of a Deep Neural Network (DNN) on a particular task, given statistics of its underlying topological structure. However, further leveraging this newly found…

Convolutional neural networks have had a great success in numerous tasks, including image classification, object detection, sequence modelling, and many more. It is generally assumed that such neural networks are translation invariant,…

The large spatial/temporal/frequency scale of geoscience and remote-sensing datasets causes memory issues when using convolutional neural networks for (sub-) surface data segmentation. Recently developed fully reversible or fully invertible…

This paper introduces an adaptive convolutional neural network (CNN) architecture capable of automating various topology optimization (TO) problems with diverse underlying physics. The proposed architecture has an encoder-decoder-type…

Tensor-valued data arise naturally in neuroimaging, genomics, climate science, and spatiotemporal networks, where multilinear dependencies across modes carry information that is destroyed under vectorization. Existing approaches either…

We study criteria for and properties of boundary-to-boundary holography in a class of spin network states defined by analogy to projected entangled pair states (PEPS). In particular, we consider superpositions of states corresponding to…

We show that discrete synaptic weights can be efficiently used for learning in large scale neural systems, and lead to unanticipated computational performance. We focus on the representative case of learning random patterns with binary…

The Computable Cross Norm (CCNR) was recently discussed in Ref.~\cite{Yin:2022toc} as a measure of multipartite entanglement in a condensed matter context. In this short note, we point out that it is closely related to the $(2,n)$-R\'enyi…

The success of tensor network approaches in simulating strongly correlated quantum systems crucially depends on whether the many body states that are relevant for the problem can be encoded in a local tensor network. Despite numerous…

This paper accompanies with our recent work on quantum error correction (QEC) and entanglement spectrum (ES) in tensor networks (arXiv:1806.05007). We propose a general framework for planar tensor network state with tensor constraints as a…

Making accurate predictions of chaotic time series is a complex challenge. Reservoir computing, a neuromorphic-inspired approach, has emerged as a powerful tool for this task. It exploits the memory and nonlinearity of dynamical systems…