Platonic Transformers: A Solid Choice For Equivariance
This addresses the problem of inefficient equivariant methods for researchers in computer vision and scientific domains, though it appears incremental as it builds on existing Transformer frameworks.
The paper tackles the lack of geometric symmetry inductive biases in Transformers by introducing the Platonic Transformer, which achieves competitive performance on benchmarks like CIFAR-10, ScanObjectNN, QM9, and OMol25 while preserving the standard Transformer's architecture and computational cost.
While widespread, Transformers lack inductive biases for geometric symmetries common in science and computer vision. Existing equivariant methods often sacrifice the efficiency and flexibility that make Transformers so effective through complex, computationally intensive designs. We introduce the Platonic Transformer to resolve this trade-off. By defining attention relative to reference frames from the Platonic solid symmetry groups, our method induces a principled weight-sharing scheme. This enables combined equivariance to continuous translations and Platonic symmetries, while preserving the exact architecture and computational cost of a standard Transformer. Furthermore, we show that this attention is formally equivalent to a dynamic group convolution, which reveals that the model learns adaptive geometric filters and enables a highly scalable, linear-time convolutional variant. Across diverse benchmarks in computer vision (CIFAR-10), 3D point clouds (ScanObjectNN), and molecular property prediction (QM9, OMol25), the Platonic Transformer achieves competitive performance by leveraging these geometric constraints at no additional cost.