🤖 AI Summary
This work proposes CuTe, a novel mathematical framework for representing and manipulating hierarchical tensor layouts through a layout algebra that supports operations such as concatenation, tiling, and inversion. Modern high-performance computing and deep learning rely heavily on specialized tensor instructions whose performance and correctness are critically dependent on intricate, hardware-specific data layouts. CuTe enables unified compile-time derivation, verification, and thread mapping of these layouts, significantly simplifying GPU kernel development while supporting expressive, general-purpose tensor transformations. The framework has been integrated into production systems including the NVIDIA CUTLASS library and the CuTe DSL, effectively bridging the gap between hardware constraints and software flexibility.
📝 Abstract
Modern architectures for high-performance computing and deep learning increasingly incorporate specialized tensor instructions, including tensor cores for matrix multiplication and hardware-optimized copy operations for multi-dimensional data. These instructions prescribe fixed, often complex data layouts that must be correctly propagated through the entire execution pipeline to ensure both correctness and optimal performance. We present CuTe, a novel mathematical specification for representing and manipulating tensors. CuTe introduces two key innovations: (1) a hierarchical layout representation that directly extends traditional flat-shape and flat-stride tensor representations, enabling the representation of complex mappings required by modern hardware instructions, and (2) a rich algebra of layout operations -- including concatenation, coalescence, composition, complementation, division, tiling, and inversion -- that enables sophisticated layout manipulation, derivation, verification, and static analysis. CuTe layouts provide a framework for managing both data layouts and thread arrangements in GPU kernels, while the layout algebra enables powerful compile-time reasoning about layout properties and the expression of generic tensor transformations.
In this work, we demonstrate that CuTe's abstractions significantly aid software development compared to traditional approaches, promote compile-time verification of architecturally prescribed layouts, facilitate the implementation of algorithmic primitives that generalize to a wide range of applications, and enable the concise expression of tiling and partitioning patterns required by modern specialized tensor instructions.
CuTe has been successfully deployed in production systems, forming the foundation of NVIDIA's CUTLASS library and a number of related efforts including CuTe DSL.