Related papers: DMRjulia: Tensor recipes for entanglement renormal…
We demonstrate the use of tensor networks for image classification with the TensorNetwork open source library. We explain in detail the encoding of image data into a matrix product state form, and describe how to contract the network in a…
Recursive neural networks have widely been used by researchers to handle applications with recursively or hierarchically structured data. However, embedded control flow deep learning frameworks such as TensorFlow, Theano, Caffe2, and MXNet…
We introduce the MathGR package, written in Mathematica. The package can manipulate tensor and GR calculations with either abstract or explicit indices, simplify tensors with permutational symmetries, decompose tensors from abstract indices…
We consider denoising and deblurring problems for tensors. While images can be discretized as matrices, the analogous procedure for color images or videos leads to a tensor formulation. We extend the classical ROF functional for variational…
Tensors are higher-order extensions of matrices. While matrix methods form the cornerstone of machine learning and data analysis, tensor methods have been gaining increasing traction. However, software support for tensor operations is not…
The purpose of this paper is (i) to present a generic and fully functional implementation of the density-matrix renormalization group (DMRG) algorithm, and (ii) to describe how to write additional strongly-correlated electron models and…
In this work, we introduce pixel wise tensor normalization, which is inserted after rectifier linear units and, together with batch normalization, provides a significant improvement in the accuracy of modern deep neural networks. In…
We present the implementation of binary and ternary neural networks in the hls4ml library, designed to automatically convert deep neural network models to digital circuits with FPGA firmware. Starting from benchmark models trained with…
The paper surveys the topic of tensor decompositions in modern machine learning applications. It focuses on three active research topics of significant relevance for the community. After a brief review of consolidated works on multi-way…
We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017)]. By encoding the truth table of each vertex…
We propose a real-space renormalization group algorithm for accurately coarse-graining two-dimensional tensor networks. The central innovation of our method lies in utilizing variational boundary tensors as a globally optimized environment…
This paper covers two major subjects: First, the presentation of a new open-source library called FMI.jl for integrating FMI into the Julia programming environment by providing the possibility to load, parameterize and simulate FMUs.…
Purpose: The aim of this work is to develop a high-performance, flexible and easy-to-use MRI reconstruction framework using the scientific programming language Julia. Methods: Julia is a modern, general purpose programming language with…
InvertibleNetworks.jl is a Julia package designed for the scalable implementation of normalizing flows, a method for density estimation and sampling in high-dimensional distributions. This package excels in memory efficiency by leveraging…
Large Language Models (LLMs) have shown impressive capabilities in complex reasoning tasks. However, current approaches employ uniform language density for both intermediate reasoning and final answers, leading to computational…
Low-Rank Adaptation (LoRA) is widely used to efficiently adapt Transformers by adding trainable low-rank matrices to attention projections. While effective, these matrices are considered independent for each attention projection (Query,…
Recurrent Neural Networks (RNNs) and their variants, such as Long-Short Term Memory (LSTM) networks, and Gated Recurrent Unit (GRU) networks, have achieved promising performance in sequential data modeling. The hidden layers in RNNs can be…
The tensor notation used in several areas of mathematics is a useful one, but it is not widely available to the functional programming community. In a practical sense, the (embedded) domain-specific languages (DSLs) that are currently in…
Sparse tensors are prevalent in many data-intensive applications, yet existing differentiable programming frameworks are tailored towards dense tensors. This presents a significant challenge for efficiently computing gradients through…
Most contemporary multi-task learning methods assume linear models. This setting is considered shallow in the era of deep learning. In this paper, we present a new deep multi-task representation learning framework that learns cross-task…