Symmetric eigenvalue decomposition (EVD) is a fundamental analytic and numerical tool used in many scientific areas. The state-of-the-art algorithm in terms of performance is typically the two-stage tridiagonalization method. The first stage in the two-stage tridiagonalization is called successive band reduction (SBR), which reduces a symmetric matrix to a band form, and its computational cost usually dominates. When Tensor Core (specialized matrix computational accelerator) is used to accelerate the expensive EVD, the conventional ZY-representation-based method results in suboptimal performance due to unfavorable shapes of the matrix computations. In this paper, we propose a new method that uses WY representation instead of ZY representation (see Section 3.2 for details), which can provide a better combination of locality and parallelism so as to perform better on Tensor Cores. Experimentally, the proposed method can bring up to 3.7x speedup in SBR and 2.3x in the entire EVD compared to state-of-the-art implementations.

This paper explores the use of Tensor Engines to accelerate nonlinear and linear SVM training. Support Vector Machine(SVM) is a classical machine learning model for classification and regression and remains to be the state-of-the-art model for some tasks such as text classification and bioinformatics. However large scale SVM training is still challenging because of its high computational complexity. This is especially severe for non-linear SVM with kernel tricks. On the other hand, the surging importance of neural networks fuels the emergence of specialized processors called Tensor Units (TensorCore in GPU and Tensor Processing Unit of Google) which are characterized by extreme efficiency and very limited precision and range. This paper proposes a TensorCore GPU based SVM algorithm and software system that is faster and more scalable than state-of-the-art SVM solvers. It includes a fast, accurate low-rank Gram matrix approximation that effectively utilizes the TensorCore in GPU and a primal-dual interior-point method to solve the quadratic program with a fast and predictable convergence rate. The random projection based Gram matrix approximation can be substantially accelerated by TensorCore on GPU.

Kernel Support Vector Machine (SVM) is a popular machine learning model for classification and regression. A significant challenge of large scale Kernel SVM is the size of the Gram matrix (n × n), which cannot be stored or processed efficiently when training data-set is large (e.g. n in the millions). This paper proposes a novel SVM training algorithm and its parallelization strategy that can efficiently train on data-sets with millions of samples on thousands of processors. It consists of an accurate, fast, and scalable low rank matrix approximation based on random projection, and a primal-dual interior point method to solve the approximated optimization problem. We demonstrate that xSVM is fast, scalable, and accurate on large scale data-sets and computing nodes. Compared to state-of-the-art distributed Kernel L1-SVM system xSVM is consistently several times faster, with comparable accuracy to the exact model trained by LIBSVM.