Paper: https://arxiv.org/abs/2311.05908
Code: https://github.com/HazyResearch/flash-fft-conv
Blog post: https://hazyresearch.stanford.edu/blog/2023-11-13-flashfftconv
Abstract:
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(NlogN) 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× over PyTorch and achieves up to 4.4× 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.
Flatten the image to 1D?
Then you lose the 2D grid structure of the image, which is why you want to use a CNN in the first place.
I think it’s possible to apply many of these optimizations to 2D convs as well though. This group is just more interested in language modeling than images.
Yeah they built this project because they have one previous work using fft to finish sequence modeling