FlashKAT: Understanding and Addressing Performance Bottlenecks in the Kolmogorov-Arnold Transformer

The Kolmogorov-Arnold Network (KAN) has been gaining popularity as an alternative to the multi-layer perceptron (MLP) with its increased expressiveness and interpretability. Even so, the KAN suffers from being orders of magnitude slower due to its increased computational cost and training instability, limiting its applicability to larger-scale tasks. Recently, the Kolmogorov-Arnold Transformer (KAT) has been proposed, which can achieve FLOPs similar to the traditional Transformer with MLPs by leveraging Group-Rational KAN (GR-KAN). Unfortunately, despite the comparable FLOPs, our testing reveals that the KAT is still 123x slower in training speeds, indicating that there are other performance bottlenecks beyond FLOPs. In this paper, we conduct a series of experiments to understand the root cause of the slowdown in KAT. We uncover that the slowdown can be isolated to memory stalls, linked more specifically to inefficient gradient accumulations in the backward pass of GR-KAN. To address this memory bottleneck, we propose FlashKAT, which minimizes accesses to slow memory and the usage of atomic adds through a restructured kernel. Evaluations demonstrate that FlashKAT can achieve a training speedup of 86.5x compared with the state-of-the-art KAT, while reducing rounding errors in the computation of the gradients.