# Tucker Tensor Decomposition on FPGA

## TL;DR

This paper introduces a FPGA-based hardware accelerator for Tucker tensor decomposition, optimizing key modules and demonstrating significant speedups over CPU and GPU implementations on real and synthetic data.

## Contribution

It presents a novel FPGA implementation of Tucker decomposition modules, including a warm-start SVD algorithm, for resource-constrained hardware acceleration.

## Key findings

- Achieved 2.16 to 30.2x speedup over CPU and GPU implementations.
- Validated the design using synthetic and real MRI data sets.
- Demonstrated effective hardware optimization for tensor computations on FPGA.

## Abstract

Tensor computation has emerged as a powerful mathematical tool for solving high-dimensional and/or extreme-scale problems in science and engineering. The last decade has witnessed tremendous advancement of tensor computation and its applications in machine learning and big data. However, its hardware optimization on resource-constrained devices remains an (almost) unexplored field. This paper presents an hardware accelerator for a classical tensor computation framework, Tucker decomposition. We study three modules of this architecture: tensor-times-matrix (TTM), matrix singular value decomposition (SVD), and tensor permutation, and implemented them on Xilinx FPGA for prototyping. In order to further reduce the computing time, a warm-start algorithm for the Jacobi iterations in SVD is proposed. A fixed-point simulator is used to evaluate the performance of our design. Some synthetic data sets and a real MRI data set are used to validate the design and evaluate its performance. We compare our work with state-of-the-art software toolboxes running on both CPU and GPU, and our work shows 2.16 - 30.2x speedup on the cardiac MRI data set.