FlashFFTConv: Efficient Convolutions for Long Sequences with Tensor Cores

Convolution models with long filters have demonstrated state-of-the-art reasoning abilities in many long-sequence tasks but lag behind the most optimized Transformers in wall-clock time. A major bottleneck is the Fast Fourier Transform (FFT)--which allows long convolutions to run in $O(N logN)$ time in sequence length $N$ but has poor hardware utilization. In this paper, we study how to optimize the FFT convolution. We find two key bottlenecks: the FFT does not effectively use specialized matrix multiply units, and it incurs expensive I/O between layers of the memory hierarchy. In response, we propose FlashFFTConv. FlashFFTConv uses a matrix decomposition that computes the FFT using matrix multiply units and enables kernel fusion for long sequences, reducing I/O. We also present two sparse convolution algorithms--1) partial convolutions and 2) frequency-sparse convolutions--which can be implemented simply by skipping blocks in the matrix decomposition, enabling further opportunities for memory and compute savings. FlashFFTConv speeds up exact FFT convolutions by up to 7.93$\times$ over PyTorch and achieves up to 4.4$\times$ speedup end-to-end. Given the same compute budget, FlashFFTConv allows Hyena-GPT-s to achieve 2.3 points better perplexity on the PILE and M2-BERT-base to achieve 3.3 points higher GLUE score--matching models with twice the parameter count. FlashFFTConv also achieves 96.1% accuracy on Path-512, a high-resolution vision task where no model had previously achieved better than 50%. Furthermore, partial convolutions enable longer-sequence models--yielding the first DNA model that can process the longest human genes (2.3M base pairs)--and frequency-sparse convolutions speed up pretrained models while maintaining or improving model quality

On the Virtualization of CUDA Based GPU Remoting on ARM and X86 Machines in the GVirtuS Framework

The astonishing development of diverse and different hardware platforms is twofold: on one side, the challenge for the exascale performance for big data processing and management; on the other side, the mobile and embedded devices for data collection and human machine interaction. This drove to a highly hierarchical evolution of programming models. GVirtuS is the general virtualization system developed in 2009 and firstly introduced in 2010 enabling a completely transparent layer among GPUs and VMs. This paper shows the latest achievements and developments of GVirtuS, now supporting CUDA 6.5, memory management and scheduling. Thanks to the new and improved remoting capabilities, GVirtus now enables GPU sharing among physical and virtual machines based on x86 and ARM CPUs on local workstations, computing clusters and distributed cloud appliances