Life sciences · Preprint
arXiv · September 4, 2026
Posted before peer review. The findings may change or fail to hold.
This preprint describes a computational technique to accelerate Gaussian kernel sum calculations by leveraging optimised flash attention algorithms via input augmentation. The work demonstrates speed and memory improvements over existing libraries for feature dimensions >8 in fp16 precision but has not undergone peer review.
Preprint.
Gauss kernel sums with arbitrary signed weights can be evaluated via flash attention using two input augmentations For feature dimension D>8 in fp16, the approach beats compiled PyTorch code and PyKeOps kernels in speed, memory overhead and accuracy Memory scaling remains linear
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This is a computational methods paper on arXiv describing a software engineering approach to accelerate Gaussian kernel calculations; it has not been peer reviewed and does not report clinical or biological outcomes.
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Gaussian kernel sums are the computational core of maximum mean discrepancies (MMDs), kernel gradient flows, Stein variational gradient descent (SVGD), and many other kernel methods. At the same time, softmax attention has received an extraordinary amount of hardware-aware code engineering, culminating in flash attention. We show that Gauss kernel sums with arbitrary, signed weights can be evaluated via flash attention: two small input augmentations turn the normalized softmax reduction into the unnormalized Gauss sum, without writing a single line of custom GPU code. For feature dimension D>8 in fp16, this approach beats compiled PyTorch code as well as PyKeOps kernels (often significantly) in speed, memory-overhead and accuracy. Indeed, its memory scaling remains linear.
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