Exploitation of parallel architectures has become critical to scalable machine learning (ML). Since a wide range of ML algorithms employ linear algebraic operators, GPUs with BLAS libraries are a natural choice for such an exploitation. Two approaches are commonly pursued: (i) developing specific GPU accelerated implementations of complete ML algorithms; and (ii) developing GPU kernels for primitive linear algebraic operators like matrix-vector multiplication, which are then used in developing ML algorithms. This paper extends the latter approach by developing fused kernels for a combination of primitive operators that are commonly found in popular ML algorithms. We identify the generic pattern of computation (alpha * X^T (v * (X * y)) + beta * z) and its various instantiations. We develop a fused kernel to optimize this computation on GPUs -- with specialized techniques to handle both sparse and dense matrices. This approach not only reduces the cost of data loads due to improved temporal locality but also enables other optimizations like coarsening and hierarchical aggregation of partial results. We also present an analytical model that considers input data characteristics and available GPU resources to estimate near-optimal settings for kernel launch parameters. The proposed approach provides speedups ranging from 2 to 67 for different instances of the generic pattern compared to launching multiple operator-level kernels using GPU accelerated libraries. We conclude by demonstrating the effectiveness of the approach in improving end-to-end performance on an entire ML algorithm.

Sparse matrix-vector multiplication (SpMV) is one of the key operations in linear algebra. Overcoming thread divergence, load imbalance and non-coalesced and indirect memory access due to sparsity and irregularity are challenges to optimizing SpMV on GPUs.

Sparse matrix-vector multiplication (SpMV) is a widely used computational kernel. The most commonly used format for a sparse matrix is CSR (Compressed Sparse Row), but a number of other representations have recently been developed that achieve higher SpMV performance. However, the alternative representations typically impose a significant preprocessing overhead. While a high preprocessing overhead can be amortized for applications requiring many iterative invocations of SpMV that use the same matrix, it is not always feasible -- for instance when analyzing large dynamically evolving graphs. This paper presents ACSR, an adaptive SpMV algorithm that uses the standard CSR format but reduces thread divergence by combining rows into groups (bins) which have a similar number of non-zero elements. Further, for rows in bins that span a wide range of non zero counts, dynamic parallelism is leveraged. A significant benefit of ACSR over other proposed SpMV approaches is that it works directly with the standard CSR format, and thus avoids significant preprocessing overheads. A CUDA implementation of ACSR is shown to outperform SpMV implementations in the NVIDIA CUSP and cuSPARSE libraries on a set of sparse matrices representing power-law graphs. We also demonstrate the use of ACSR for the analysis of dynamic graphs, where the improvement over extant approaches is even higher.