This paper introduces three new compiler transformations for representing and transforming sparse matrix computations and their data representations. In cooperation with run-time inspection, our compiler derives transformed matrix representations and associated transformed code to implement a variety of representations targeting different architecture platforms. This systematic approach to combining code and data transformations on sparse computations, which extends a polyhedral transformation and code generation framework, permits the compiler to compose these transformations with other transformations to generate code that is on average within 5% and often exceeds manually-tuned, highperformance sparse matrix libraries CUSP and OSKI. Additionally, the compiler-generated inspector codes are on average 1.5× faster than OSKI and perform comparably to CUSP, respectively.

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Deep learning (DL) is one of the most prominent branches of machine learning. Due to the immense computational cost of DL workloads, industry and academia have developed DL libraries with highly-specialized kernels for each workload/architecture, leading to numerous, complex code-bases that strive for performance, yet they are hard to maintain and do not generalize. In this work, we introduce the batch-reduce GEMM kernel and show how the most popular DL algorithms can be formulated with this kernel as the basic building-block. Consequently, the DL library-development degenerates to mere (potentially automatic) tuning of loops around this sole optimized kernel. By exploiting our new kernel we implement Recurrent Neural Networks, Convolution Neural Networks and Multilayer Perceptron training and inference primitives in just 3K lines of high-level code. Our primitives outperform vendoroptimized libraries on multi-node CPU clusters, and we also provide proof-of-concept CNN kernels targeting GPUs. Finally, we demonstrate that the batch-reduce GEMM kernel within a tensor compiler yields high-performance CNN primitives, further amplifying the viability of our approach.

This paper describes a compiler approach to communicationavoiding optimizations in geometric multigrid (GMG), one of the most popular methods for solving partial differential equations. Communication-avoiding optimizations reduce vertical communication through the memory hierarchy and horizontal communication across processes or threads, usually at the expense of introducing redundant computation. We focus on applying these optimizations to the smooth operator, which successively reduces the error and accounts for the largest fraction of the GMG execution time. Our compiler technology applies both novel and known transformations to derive an implementation comparable to manually-tuned code. To make the approach portable, an underlying autotuning system explores the tradeoff between reduced communication and increased computation, as well as tradeoffs in threading schemes, to automatically identify the best implementation for a particular architecture and at each computation phase. Results show that we are able to quadruple the performance of the smooth operation on the finest grids while attaining similar or better performance than manually-tuned code.

This paper presents a compiler and runtime framework for parallelizing sparse matrix computations that have loopcarried dependences. Our approach automatically generates a runtime inspector to collect data dependence information and achieves wavefront parallelization of the computation, where iterations within a wavefront execute in parallel, and synchronization is required across wavefronts. A key contribution of this paper involves dependence simplification, which reduces the time and space overhead of the inspector. This is implemented within a polyhedral compiler framework, extended for sparse matrix codes. Results demonstrate the feasibility of using automaticallygenerated inspectors and executors to optimize ILU factorization and symmetric Gauss-Seidel relaxations, which are part of the Preconditioned Conjugate Gradient (PCG) computation. Our implementation achieves a median speedup of 2.97× on 12 cores over the reference sequential PCG implementation, significantly outperforms PCG parallelized using Intel's Math Kernel Library (MKL), and is within 6% of the median performance of manually-parallelized PCG.