Related papers: Fully tensorial approach to hypercomplex-valued ne…

Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…

We extend our previous work on a semi-Lagrangian adaptive rank (SLAR) integrator, in the finite difference framework for nonlinear Vlasov-Poisson systems, to the general high-order tensor setting. The proposed scheme retains the high-order…

We provide a novel analysis of low-rank tensor completion based on hypergraph expanders. As a proxy for rank, we minimize the max-quasinorm of the tensor, which generalizes the max-norm for matrices. Our analysis is deterministic and shows…

We show the existence of a deep neural network capable of approximating a wide class of high-dimensional approximations. The construction of the proposed neural network is based on a quasi-optimal polynomial approximation. We show that this…

Neural networks (NNs) are known for their high predictive accuracy in complex learning problems. Beside practical advantages, NNs also indicate favourable theoretical properties such as universal approximation (UA) theorems. Binarized…

This paper explores learned-context neural networks. It is a multi-task learning architecture based on a fully shared neural network and an augmented input vector containing trainable task parameters. The architecture is interesting due to…

A systematic method is presented for the construction and classification of algebras of gauge transformations for arbitrary high rank tensor gauge fields. For every tensor gauge field of a given rank, the gauge transformation will be…

The paper introduces two new aggregation functions to encode structural knowledge from tree-structured data. They leverage the Canonical and Tensor-Train decompositions to yield expressive context aggregation while limiting the number of…

The development of efficient machine learning models for molecular systems representation is becoming crucial in scientific research. We introduce TensorNet, an innovative O(3)-equivariant message-passing neural network architecture that…

Most machine learning models for structured data encode the structural knowledge of a node by leveraging simple aggregation functions (in neural models, typically a weighted sum) of the information in the node's neighbourhood. Nevertheless,…

Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…

This paper introduces Multidimensional Task Learning (MTL), a unified mathematical framework based on Generalized Einstein MLPs (GE-MLPs) that operate directly on tensors via the Einstein product. We argue that current computer vision task…

We study the complexity of functions computable by deep feedforward neural networks with piecewise linear activations in terms of the symmetries and the number of linear regions that they have. Deep networks are able to sequentially map…

We solve high-dimensional steady-state Fokker-Planck equations on the whole space by applying tensor neural networks. The tensor networks are a linear combination of tensor products of one-dimensional feedforward networks or a linear…

Deep learning has been widely applied and brought breakthroughs in speech recognition, computer vision, and many other domains. The involved deep neural network architectures and computational issues have been well studied in machine…

We introduce T-Basis, a novel concept for a compact representation of a set of tensors, each of an arbitrary shape, which is often seen in Neural Networks. Each of the tensors in the set is modeled using Tensor Rings, though the concept…

We propose a novel perspective to understand deep neural networks in an interpretable disentanglement form. For each semantic class, we extract a class-specific functional subnetwork from the original full model, with compressed structure…

The inherent diversity of computation types within the deep neural network (DNN) models often requires a variety of specialized units in hardware processors, which limits computational efficiency, increasing both inference latency and power…

Advanced algorithms for large-scale electronic structure calculations are mostly based on processing multi-dimensional sparse data. Examples are sparse matrix-matrix multiplications in linear-scaling Kohn-Sham calculations or the efficient…

In contrast to regular (simple) networks, hyper networks possess the ability to depict more complex relationships among nodes and store extensive information. Such networks are commonly found in real-world applications, such as in social…