The field of neural networks is witnessing a significant shift towards incorporating equivariant principles and novel transformer architectures. Researchers are actively exploring ways to induce geometric symmetries and equivariances into neural network models, enabling them to better capture complex patterns in data. This trend is driven by the need for more efficient, flexible, and interpretable models that can effectively handle diverse tasks, such as computer vision, 3D point cloud processing, and molecular property prediction. Notably, the development of Platonic Transformers and Latent Mixture of Symmetries models has shown promising results in achieving combined equivariance to continuous translations and Platonic symmetries. Furthermore, innovative approaches like Wave-PDE Nets are emerging as alternatives to traditional attention mechanisms, offering improved efficiency and performance.

Some noteworthy papers in this area include: The PDE-Transformer paper, which introduces a novel analytical framework that reconceptualizes the Transformer's discrete structure as a continuous spatiotemporal dynamical system. The Platonic Transformers paper, which resolves the trade-off between efficiency and flexibility in equivariant methods by defining attention relative to reference frames from Platonic solid symmetry groups. The Wave-PDE Nets paper, which introduces a neural architecture whose elementary operation is a differentiable simulation of the second-order wave equation, providing a powerful alternative to attention and first-order state-space models.