Research references

These sources explain the compiler and GPU-programming ideas that inform meTile. Citing a project does not imply that meTile matches its feature coverage or performance.

Tiled programming and layouts

Triton introduced a compiler and intermediate language for tiled neural-network kernels. meTile’s Python kernel language takes its cue from Triton’s programming model. CuTe’s layout algebra informs the separation of logical coordinates from memory and execution layouts.

For distributed ownership, see Triton’s Gluon layout tutorial and the Linear Layouts paper. meTile’s ThreadLayout is a narrower register/thread-bit permutation model, not an implementation of every Gluon or CuTe layout.

Selecting compiler rewrites

Lap Chi Lau’s CS 341 notes cover maximum flow, minimum cut and project selection. The project author attended CS 341 with Lap Chi Lau in Spring 2025; the course’s treatment of project selection helped shape meTile’s rewrite selector.

Horace He’s AOTAutograd discussion shows min-cut applied to a different compiler problem: choosing activations to save or recompute.

meTile represents overlapping rewrite candidates as a conflict graph. For each bipartite component, an s-t min-cut selects a maximum-weight independent set. Non-bipartite components use a deterministic greedy fallback. The implementation does not solve arbitrary maximum-weight independent set problems with min-cut. See Compute-Graph Fusion and Compiler Architecture.

Metal and compiler boundaries

The Metal Shading Language specification defines shader types, address spaces and synchronization rules. Apple’s Metal Performance Primitives guide describes the native tensor operations used by eligible backends.

Compiler Bypasses and Native Code explains the boundary between supported Metal compilation and AIR or native-ISA research. Neither a vector expression in MSL nor a change to AIR guarantees a particular final GPU instruction sequence.

Bibliography

@misc{he2022mincut,
    title={Min-cut optimal(*) recomputation (i.e. activation checkpointing) with AOTAutograd},
    author={Horace He},
    year={2022},
    howpublished={PyTorch Dev Discussions},
    url={https://dev-discuss.pytorch.org/t/min-cut-optimal-recomputation-i-e-activation-checkpointing-with-aotautograd/467}
}

@misc{lau2025cs341,
    title={CS 341: Algorithms, Lectures 15 and 16: Maximum Flow, Minimum Cut, and Applications},
    author={Lap Chi Lau},
    year={2025},
    howpublished={University of Waterloo course notes},
    url={https://cs.uwaterloo.ca/~lapchi/cs341-2025/notes.html}
}

@misc{cecka2026cute,
    title={CuTe Layout Representation and Algebra},
    author={Cris Cecka},
    year={2026},
    eprint={2603.02298},
    archivePrefix={arXiv},
    primaryClass={cs.MS},
    url={https://arxiv.org/abs/2603.02298}
}

@inproceedings{tillet2019triton,
    title={Triton: An Intermediate Language and Compiler for Tiled Neural Network Computations},
    author={Philippe Tillet and H. T. Kung and David Cox},
    booktitle={Proceedings of the 3rd ACM SIGPLAN International Workshop on Machine Learning and Programming Languages},
    year={2019},
    doi={10.1145/3315508.3329973}
}