Does Transolver really need a Transformer?

Abstract

The widely used Transolver family of neural operators is based on physics-attention, which softly assigns the points of an unstructured mesh to a small number of slices, applies self-attention among the resulting tokens, and broadcasts the result back to the points. We provide a comprehensive empirical and theoretical analysis to elucidate the mechanisms which are responsible for model performance. To this end, we perform careful ablations on a challenging suite of nine 3D fluid dynamics benchmarks to find that replacing token attention with a constant linear map does not affect the accuracy. Thus, Transolver does not need a Transformer at all. However, removing the global mixing (slicing/deslicing) or doing it only once leads to performance collapse. We leverage the theory of averaging neural operators to explain and corroborate our findings by showing that just slicing/deslicing, in conjunction with pointwise MLPs, already suffices for universal approximation of continuous operators and attention is redundant in this context. Finally, we provide a novel FlashAttention-style efficient implementation of the key slicing/deslicing module of Transolver. This flashslice kernel streams slice and deslice over the points without materializing the heavy slice-weight tensor, while reproducing the best available implementation to floating point error. At the same time, it leads to very significant memory and compute savings, particularly at large slice counts.