[2605.19269] CODA: Rewriting Transformer Blocks as GEMM-Epilogue Programs

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Computer Science > Machine Learning

arXiv:2605.19269 (cs)

[Submitted on 19 May 2026 (v1), last revised 20 May 2026 (this version, v2)]

Title:CODA: Rewriting Transformer Blocks as GEMM-Epilogue Programs

Authors:Han Guo, Jack Zhang, Arjun Menon, Driss Guessous, Vijay Thakkar, Yoon Kim, Tri Dao<br>View a PDF of the paper titled CODA: Rewriting Transformer Blocks as GEMM-Epilogue Programs, by Han Guo and 6 other authors

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Abstract:Transformer training systems are built around dense linear algebra, yet a nontrivial fraction of end-to-end time is spent on surrounding memory-bound operators. Normalization, activations, residual updates, reductions, and related computations repeatedly move large intermediate tensors through global memory while performing little arithmetic, making data movement an increasingly important bottleneck in otherwise highly optimized training stacks. We introduce CODA, a GPU kernel abstraction that expresses these computations as GEMM-plus-epilogue programs. CODA is based on the observation that many Transformer operators exposed as separate framework kernels can be algebraically reparameterized to execute while a GEMM output tile remains on chip, before it is written to memory. The abstraction fixes the GEMM mainloop and exposes a small set of composable epilogue primitives for scaling, reductions, pairwise transformations, and accumulation. This constrained interface preserves the performance structure of expert-written GEMMs while remaining expressive enough to cover nearly all non-attention computation in the forward and backward pass of a standard Transformer block. Across representative Transformer workloads, both human- and LLM-authored CODA kernels achieve high performance, suggesting that GEMM-plus-epilogue programming offers a practical path toward combining framework-level productivity with hardware-level efficiency.

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Machine Learning (cs.LG)

Cite as:<br>arXiv:2605.19269 [cs.LG]

(or<br>arXiv:2605.19269v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2605.19269

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arXiv-issued DOI via DataCite

Submission history<br>From: Han Guo [view email]<br>[v1]<br>Tue, 19 May 2026 02:30:43 UTC (1,121 KB)

[v2]<br>Wed, 20 May 2026 17:38:24 UTC (493 KB)

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