FlashAttention on a Napkin: A Diagrammatic Approach to Deep Learning IO-Awareness

Optimizing deep learning algorithms currently requires slow, manual derivation, potentially leaving much performance untapped. Methods like FlashAttention have achieved a x6 performance improvement over native PyTorch by avoiding unnecessary data transfers, but required three iterations over three years. Automated compiled methods have consistently lagged behind. GPUs are limited by both transfers to processors and available compute, with transfer bandwidth having improved at a far slower pace. Already, transfer bandwidth accounts for 46% of GPU energy costs. This indicates the future of energy and capital-efficient algorithms relies on improved consideration of transfer costs (IO-awareness) and a systematic method for deriving optimized algorithms. In this paper, we present a diagrammatic approach to deep learning models which, with simple relabelings, derive optimal implementations and performance models that consider low-level memory. Diagrams generalize down the GPU hierarchy, providing a universal performance model for comparing hardware and quantization choices. Diagrams generate pseudocode, which reveals the application of hardware-specific features such as coalesced memory access, tensor core operations, and overlapped computation. We present attention algorithms for Ampere, which fits 13 warps per SM (FlashAttention fits 8), and for Hopper, which has improved overlapping and may achieve 1.32 PFLOPs.

Neural Circuit Diagrams: Robust Diagrams for the Communication, Implementation, and Analysis of Deep Learning Architectures

Diagrams matter. Unfortunately, the deep learning community has no standard method for diagramming architectures. The current combination of linear algebra notation and ad-hoc diagrams fails to offer the necessary precision to understand architectures in all their detail. However, this detail is critical for faithful implementation, mathematical analysis, further innovation, and ethical assurances. I present neural circuit diagrams, a graphical language tailored to the needs of communicating deep learning architectures. Neural circuit diagrams naturally keep track of the changing arrangement of data, precisely show how operations are broadcast over axes, and display the critical parallel behavior of linear operations. A lingering issue with existing diagramming methods is the inability to simultaneously express the detail of axes and the free arrangement of data, which neural circuit diagrams solve. Their compositional structure is analogous to code, creating a close correspondence between diagrams and implementation. In this work, I introduce neural circuit diagrams for an audience of machine learning researchers. After introducing neural circuit diagrams, I cover a host of architectures to show their utility and breed familiarity. This includes the transformer architecture, convolution (and its difficult-to-explain extensions), residual networks, the U-Net, and the vision transformer. I include a Jupyter notebook that provides evidence for the close correspondence between diagrams and code. Finally, I examine backpropagation using neural circuit diagrams. I show their utility in providing mathematical insight and analyzing algorithms' time and space complexities.