Convolutional architectures have emerged as powerful alternatives to Transformers for sequence modeling. The primary advantage is that they offer improved theoretical sequence length complexity by leveraging the Fast Fourier Transform (FFT). However, this theoretical improvement does not always meaningfully land in practice. One critical obstacle is that applying standard FFTs is not amenable to the large-scale training pipeline wherein data is packed from different sources into a single sequence for hardware efficiency. Indeed, standard FFT algorithms are not easily amenable to document packing. Existing workarounds suffer from severe inefficiencies, crippling the practical performance of convolutional architectures. We close this gap with RubiConv, a novel algorithm for performing hardware-efficient, boundary-respecting convolutions on packed sequences. Extensive experiments show that RubiConv achieves significant speedups over both attention and standard FFT-based baselines. This work makes the theoretical efficiency of long convolutional models a practical reality for large-scale, real-world data packing.
@article{arxiv.2605.08451,
title = {RubiConv -- Efficient Boundary-Respecting Convolutions},
author = {Linda Friso and Annie Marsden and Xinyi Chen and Arushi Gupta and Peter Bartlett and Mark Braverman and Elad Hazan},
journal= {arXiv preprint arXiv:2605.08451},
year = {2026}
}