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The Price of Freedom: Exploring Expressivity and Runtime Tradeoffs in Equivariant Tensor Products

Created by
  • Haebom

Author

YuQing Xie, Ameya Daigavane, Mit Kotak, Tess Smidt

Outline

In this paper, we systematically analyze various methods to reduce the computational complexity of tensor product, a key operation in $E(3)$-equivariant neural networks. In particular, we highlight that the speedups reported in previous studies may come at the expense of expressiveness, and present metrics to measure expressiveness and interactivity. We propose a simplified implementation of the Gaunt tensor product (GTP) that uses a spherical lattice directly, and experimentally show that this method yields a 30% speedup over the existing MACE inter-atomic potential learning. Finally, we present the first systematic microbenchmark results for various tensor product operations, highlighting the gap between theoretical time complexities and practical performance.

Takeaways, Limitations

Takeaways:
We clarify the trade-off between the speed and expressiveness of tensor multiplication operations in $E(3)$-equivariant neural networks.
A novel approach to simplify the implementation of GTP and improve its performance (utilizing a spherical grid).
Provides systematic micro-benchmarks for various tensor multiplication operations.
Emphasizes the importance of choosing the optimal tensor multiplication operation depending on the application.
Limitations:
Further research is needed on the generality and limitations of the proposed expressiveness and interactivity metrics.
The generalizability of the results to limited benchmark datasets needs to be examined.
Generalizability to various $E(3)$-equivariant neural network architectures needs to be examined.
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