Related papers: TensorNet: Cartesian Tensor Representations for Ef…

Quantum and quantum-inspired machine learning has emerged as a promising and challenging research field due to the increased popularity of quantum computing, especially with near-term devices. Theoretical contributions point toward…

Progress in the application of machine learning techniques to the prediction of solid-state and molecular materials properties has been greatly facilitated by the development state-of-the-art feature representations and novel deep learning…

Accurate prediction of molecular properties in complex chemical systems is crucial for accelerating material discovery and chemical innovation. However, current computational methods often struggle to capture the intricate compositional…

Symmetry-aware architectures are central to geometric deep learning. We present a systematic approach for constructing continuous rotationally invariant and equivariant functions using symmetric tensor networks. The proposed framework…

Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models…

Density based representations of atomic environments that are invariant under Euclidean symmetries have become a widely used tool in the machine learning of interatomic potentials, broader data-driven atomistic modelling and the…

Computational materials discovery is limited by the high cost of first-principles calculations. Machine learning (ML) potentials that predict energies from crystal structures are promising, but existing methods face computational…

Quantum computers are expected to enable fast solving of large-scale combinatorial optimization problems. However, their limitations in fidelity and the number of qubits prevent them from handling real-world problems. Recently, a…

Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine…

Convolutional neural networks show outstanding results in a variety of computer vision tasks. However, a neural network architecture design usually faces a trade-off between model performance and computational/memory complexity. For some…

Many learning tasks, including learning potential energy surfaces from ab initio calculations, involve global spatial symmetries and permutational symmetry between atoms or general particles. Equivariant graph neural networks are a standard…

A universal interatomic potential for an arbitrary set of chemical elements is urgently needed in computational materials science. Graph convolution neural network (GCN) has rich expressive power, but previously was mainly employed to…

Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…

Tensor network algorithms seek to minimize correlations to compress the classical data representing quantum states. Tensor network algorithms and similar tools---called tensor network methods---form the backbone of modern numerical methods…

We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise…

Inspired by the ConvNets with structured hidden representations, we propose a Tensor-based Neural Network, TCNN. Different from ConvNets, TCNNs are composed of structured neurons rather than scalar neurons, and the basic operation is neuron…

With the increasing adoption of machine learning tools like neural networks across several domains, interesting connections and comparisons to concepts from other domains are coming to light. In this work, we focus on the class of Tensor…

Tensor cores, along with tensor processing units, represent a new form of hardware acceleration specifically designed for deep neural network calculations in artificial intelligence applications. Tensor cores provide extraordinary…

The combinations of machine learning with ab initio methods have attracted much attention for their potential to resolve the accuracy-efficiency dilemma and facilitate calculations for large-scale systems. Recently, equivariant message…

This paper presents the Tensor Product Network (TPNet), a novel neural architecture for efficient and accurate function approximation and PDE solving. The core of the proposal involves constructing the solution explicitly as a linear…