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Matrix libraries often focus on achieving high performance for problems considered to be either "small" or "large", as these two scenarios tend to respond best to different optimization strategies. We propose a unified technique for…
This work focuses on accelerating the multiplication of a dense random matrix with a (fixed) sparse matrix, which is frequently used in sketching algorithms. We develop a novel scheme that takes advantage of blocking and recomputation…
General Matrix Multiplication or GEMM kernels take centre place in high performance computing and machine learning. Recent NVIDIA GPUs include GEMM accelerators, such as NVIDIA's Tensor Cores. Their exploitation is hampered by the…
KBLAS is a new open source high performance library that provides optimized kernels for a subset of Level 2 BLAS functionalities on CUDA-enabled GPUs. Since performance of dense matrix-vector multiplication is hindered by the overhead of…
Dealing with asymmetry in the architecture opens a plethora of questions from the perspective of scheduling task-parallel applications, and there exist early attempts to address this problem via ad-hoc strategies embedded into a runtime…
As multicore systems continue to gain ground in the High Performance Computing world, linear algebra algorithms have to be reformulated or new algorithms have to be developed in order to take advantage of the architectural features on these…
To address the challenge of performance portability, and facilitate the implementation of electronic structure solvers, we developed the Basic Matrix Library (BML) and Parallel, Rapid O(N) and Graph-based Recursive Electronic Structure…
Mathematical operators whose transformation rules constitute the building blocks of a multi-linear algebra are widely used in physics and engineering applications where they are very often represented as tensors. In the last century, thanks…
Recent advances in deep learning (DL) have led to a shift from traditional 64-bit floating point (FP64) computations toward reduced-precision formats, such as FP16, BF16, and 8- or 16-bit integers, combined with mixed-precision arithmetic.…
Multilinear algebra kernel performance on modern massively-parallel systems is determined mainly by data movement. However, deriving data movement-optimal distributed schedules for programs with many high-dimensional inputs is a notoriously…
General matrix-matrix multiplication (GEMM) is a fundamental operation in machine learning (ML) applications. We present the first comprehensive performance acceleration of GEMM workloads on AMD's second-generation AIE-ML (AIE2)…
Sparse General Matrix Multiply (SpGEMM) is key for various High-Performance Computing (HPC) applications such as genomics and graph analytics. Using the semiring abstraction, many algorithms can be formulated as SpGEMM, allowing…
The Simplex tableau has been broadly used and investigated in the industry and academia. With the advent of the big data era, ever larger problems are posed to be solved in ever larger machines whose architecture type did not exist in the…
This paper describes REAP, a software-hardware approach that enables high performance sparse linear algebra computations on a cooperative CPU-FPGA platform. REAP carefully separates the task of organizing the matrix elements from the…
Weight-only quantization is widely used to mitigate the memory-bound nature of LLM inference. Codebook-based methods extend this trend by achieving strong accuracy in the extremely low-bit regime (e.g., 2-bit). However, current kernels rely…
We present tritonBLAS, a fast and deterministic analytical model that uses architectural parameters like the cache hierarchy, and relative code and data placement to generate performant GPU GEMM kernels. tritonBLAS explicitly models the…
This paper presents the Neural Cache architecture, which re-purposes cache structures to transform them into massively parallel compute units capable of running inferences for Deep Neural Networks. Techniques to do in-situ arithmetic in…
The current computer architecture has moved towards the multi/many-core structure. However, the algorithms in the current sequential dense numerical linear algebra libraries (e.g. LAPACK) do not parallelize well on multi/many-core…
Machine Learning compilers like TVM allow a fast and flexible deployment on embedded CPUs. This enables the use of non-standard operators, which are common in ML compression techniques. However, it is necessary to understand the limitations…
Emerging non-volatile main memory (NVRAM) technologies provide byte-addressability, low idle power, and improved memory-density, and are likely to be a key component in the future memory hierarchy. However, a critical challenge in achieving…