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We present a method of computing any one-loop integral in lattice perturbation theory by systematically expanding around its continuum limit. At any order in the expansion in the lattice spacing, the result can be written as a sum of…
The library LINPRO which provides solution to the linear inverse problem for data contaminated by a statistical noise is presented. The library makes use of two methods: Maximum Entropy Method and Singular Value Decomposition. As an example…
As state of the art neural networks (NNs) continue to grow in size, their resource-efficient implementation becomes ever more important. In this paper, we introduce a compression scheme that reduces the number of computations required for…
Solving linear systems of polynomial equations is a ubiquitous problem in both mathematics and physics. The standard approach, Gaussian elimination, scales cubically with system size and often constitutes a computational bottleneck. The…
We present ensmallen, a fast and flexible C++ library for mathematical optimization of arbitrary user-supplied functions, which can be applied to many machine learning problems. Several types of optimizations are supported, including…
Recurrent neural networks (RNN) are the backbone of many text and speech applications. These architectures are typically made up of several computationally complex components such as; non-linear activation functions, normalization,…
Emerging Learned image Compression (LC) achieves significant improvements in coding efficiency by end-to-end training of neural networks for compression. An important benefit of this approach over traditional codecs is that any optimization…
Large Language Models (LLMs) often exhibit a gap between their internal knowledge and their explicit linguistic outputs. In this report, we empirically investigate whether Looped Transformers (LTs)--architectures that increase computational…
Winograd convolution is originally proposed to reduce the computing overhead by converting multiplication in neural network (NN) with addition via linear transformation. Other than the computing efficiency, we observe its great potential in…
A polynomial-time algorithm for 0-1 integer linear programmings has been proposed. This method continues the classic idea of solving ILP with its LP relaxation. The innovation is that every constraint in the LP is reconstructed into a…
This paper explores the integration of Diophantine equations into neural network (NN) architectures to improve model interpretability, stability, and efficiency. By encoding and decoding neural network parameters as integer solutions to…
The linear noise approximation is commonly used to obtain intrinsic noise statistics for biochemical networks. These estimates are accurate for networks with large numbers of molecules. However it is well known that many biochemical…
We present an algorithm for the optimization of a class of finite element integration loop nests. This algorithm, which exploits fundamental mathematical properties of finite element operators, is proven to achieve a locally optimal…
Training convolutional neural networks (CNNs) with a strict 1-Lipschitz constraint under the $l_{2}$ norm is useful for adversarial robustness, interpretable gradients and stable training. 1-Lipschitz CNNs are usually designed by enforcing…
Low-light image enhancement (LLIE) aims to improve low-illumination images. However, existing methods face two challenges: (1) uncertainty in restoration from diverse brightness degradations; (2) loss of texture and color information caused…
Advancements in Natural Language Processing are heavily reliant on the Transformer architecture, whose improvements come at substantial resource costs due to ever-growing model sizes. This study explores optimization techniques, including…
We present methods for the numerical evaluation of the master integrals that appear in the calculation of scattering amplitudes at higher order in perturbative quantum field theory. We follow the general strategy of solving first-order…
We present the library Moore, which implements Interval Arithmetic in modern C++. This library is based on a new feature in the C++ language called concepts, which reduces the problems caused by template meta programming, and leads to a new…
Optical neural network (ONN) is emerging as an attractive proposal for machine-learning applications, enabling high-speed computation with low-energy consumption. However, there are several challenges in applying ONN for industrial…
This paper proposes a composite inner-product computation unit based on left-to-right (LR) arithmetic for the acceleration of convolution neural networks (CNN) on hardware. The efficacy of the proposed L2R-CIPU method has been shown on the…