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1. Vector-mode Multiplexing For Photonic Tensor Accelerator

   Alireza Fardoost, Fatemeh Ghaedi (April 2022, OptoElectronics and Communications Conference (OECC) and International Conference on Photonics in Switching and Computing (PSC))

   We propose a coherent multi-dimensional (wavelength, spatial mode, polarization, etc.) photonic tensor accelerator capable of performing high-speed artificial neural network computation. High-speed matrix-vector and matrix-matrix multiplication were experimentally demonstrated. 

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2. Simple, fast, and flexible framework for matrix completion with infinite width neural networks

   https://doi.org/10.1073/pnas.2115064119  

   Radhakrishnan, Adityanarayanan; Stefanakis, George; Belkin, Mikhail; Uhler, Caroline (April 2022, Proceedings of the National Academy of Sciences)

   Matrix completion problems arise in many applications including recommendation systems, computer vision, and genomics. Increasingly larger neural networks have been successful in many of these applications but at considerable computational costs. Remarkably, taking the width of a neural network to infinity allows for improved computational performance. In this work, we develop an infinite width neural network framework for matrix completion that is simple, fast, and flexible. Simplicity and speed come from the connection between the infinite width limit of neural networks and kernels known as neural tangent kernels (NTK). In particular, we derive the NTK for fully connected and convolutional neural networks for matrix completion. The flexibility stems from a feature prior, which allows encoding relationships between coordinates of the target matrix, akin to semisupervised learning. The effectiveness of our framework is demonstrated through competitive results for virtual drug screening and image inpainting/reconstruction. We also provide an implementation in Python to make our framework accessible on standard hardware to a broad audience. 

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3. Decoherence: a numerical study

   https://doi.org/10.1088/1751-8121/acb977  

   Nagele, Chris; Janssen, Oliver; Kleban, Matthew (February 2023, Journal of Physics A: Mathematical and Theoretical)

   Abstract We study quantum decoherence numerically in a system consisting of a relativistic quantum field theory coupled to a measuring device that is itself coupled to an environment. The measuring device and environment are treated as quantum, non-relativistic particles. We solve the Schrödinger equation for the wave function of this tripartite system using exact diagonalization. Although computational limitations on the size of the Hilbert space prevent us from exploring the regime where the device and environment consist of a truly macroscopic number of degrees of freedom, we nevertheless see clear evidence of decoherence: after tracing out the environment, the density matrix describing the system and measuring device evolves quickly towards a matrix that is close to diagonal in a subspace of pointer states. We measure the speed with which decoherence spreads in the relativistic quantum field theory for a range of parameters. We find that it is less than the speed of light but faster than the speed of the massive charges in the initial state. 

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4. Matrix sketching framework for linear mixed models in association studies

   https://doi.org/10.1101/gr.279230.124  

   Burch, Myson; Bose, Aritra; Dexter, Gregory; Parida, Laxmi; Drineas, Petros (September 2024, Genome Research)

   Linear mixed models (LMMs) have been widely used in genome-wide association studies to control for population stratification and cryptic relatedness. However, estimating LMM parameters is computationally expensive, necessitating large-scale matrix operations to build the genetic relationship matrix (GRM). Over the past 25 years, Randomized Linear Algebra has provided alternative approaches to such matrix operations by leveragingmatrix sketching, which often results in provably accurate fast and efficient approximations. We leverage matrix sketching to develop a fast and efficient LMM method calledMatrix-Sketching LMM (MaSk-LMM) by sketching the genotype matrix to reduce its dimensions and speed up computations. Our framework comes with both theoretical guarantees and a strong empirical performance compared to the current state-of-the-art for simulated traits and complex diseases. 

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5. Random Sampling for Distributed Coded Matrix Multiplication

   https://doi.org/10.1109/ICASSP.2019.8682895  

   Chang, Wei-Ting; Tandon, Ravi (May 2019, ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP))

   Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix multiplication, that are robust to stragglers (i.e., machines that may perform slower computations). In many scenarios, instead of exact computation, approximate matrix multiplication, i.e., allowing for a tolerable error is also sufficient. Such approximate schemes make use of randomization techniques to speed up the computation process. In this paper, we initiate the study of approximate coded matrix multiplication, and investigate the joint synergies offered by randomization and coding. Specifically, we propose two coded randomized sampling schemes that use (a) codes to achieve a desired recovery threshold and (b) random sampling to obtain approximation of the matrix multiplication. Tradeoffs between the recovery threshold and approximation error obtained through random sampling are investigated for a class of coded matrix multiplication schemes. 

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