Related papers: Adaptive Patching for Tensor Train Computations

Foundation models have impressive performance and generalization capabilities across a wide range of applications. The increasing size of the models introduces great challenges for the training. Tensor parallelism is a critical technique…

Time-independent quantum response calculations are performed using Tensor cores. This is achieved by mapping density matrix perturbation theory onto the computational structure of a deep neural network. The main computational cost of each…

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…

Topological quantum computing has recently proven itself to be a very powerful model when considering large- scale, fully error corrected quantum architectures. In addition to its robust nature under hardware errors, it is a software driven…

Recent convolutional neural network (CNN) development continues to advance the state-of-the-art model accuracy for various applications. However, the enhanced accuracy comes at the cost of substantial memory bandwidth and storage…

We propose a new method for low-rank approximation of Moore-Penrose pseudoinverses (MPPs) of large-scale matrices using tensor networks. The computed pseudoinverses can be useful for solving or preconditioning of large-scale overdetermined…

We consider sequential state and parameter learning in state-space models with intractable state transition and observation processes. By exploiting low-rank tensor train (TT) decompositions, we propose new sequential learning methods for…

This paper studies the efficiency problem for visual transformers by excavating redundant calculation in given networks. The recent transformer architecture has demonstrated its effectiveness for achieving excellent performance on a series…

The numerical approximation of partial differential equations (PDEs) poses formidable challenges in high dimensions since classical grid-based methods suffer from the so-called curse of dimensionality. Recent attempts rely on a combination…

Efficient parametrizations of quantum states are essential for trainable hybrid classical-quantum algorithms. A key challenge in their design consists in adapting to the available qubit connectivity of the quantum processor, which limits…

We give an algorithm that converts any tensor network (TN) into a sequence of local unitaries whose composition block-encodes the network contraction, suitable for Quantum Eigenvalue / Singular Value Transformation (QET/QSVT). The…

Tensor train decomposition is a powerful tool for dealing with high-dimensional, large-scale tensor data, which is not suffering from the curse of dimensionality. To accelerate the calculation of the auxiliary unfolding matrix, some…

We present a novel procedure for optimization based on the combination of efficient quantized tensor train representation and a generalized maximum matrix volume principle. We demonstrate the applicability of the new Tensor Train Optimizer…

Transformer architectures, particularly Diffusion Transformers (DiTs), have become widely used in diffusion and flow-matching models due to their strong performance compared to convolutional UNets. However, the isotropic design of DiTs…

In this paper, we propose a new adaptive technique, named adaptive trajectories sampling (ATS), which is used to select training points for the numerical solution of partial differential equations (PDEs) with deep learning methods. The key…

Neural-network quantum states (NQS) are powerful neural-network ans\"atzes that have emerged as promising tools for studying quantum many-body physics through the lens of the variational principle. These architectures are known to be…

In recent years, there have been an increasing number of applications of tensor completion based on the tensor train (TT) format because of its efficiency and effectiveness in dealing with higher-order tensor data. However, existing tensor…

In this article we propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this…

Despite advances using low-rank adapters and quantization, pretraining of large models on consumer hardware has not been possible without model sharding, offloading during training, or per-layer gradient updates. To address these…

A key challenge for molecular dynamics simulations is efficient exploration of free energy landscapes over relevant collective variables (CV). Common methods for enhancing sampling become prohibitively inefficient beyond only a few CVs; in…