E2Former-V2: On-the-Fly Equivariant Attention with Linear Activation Memory

Equivariant Graph Neural Networks (EGNNs) have become a widely used approach for modeling 3D atomistic systems. However, mainstream architectures face critical scalability bottlenecks due to the explicit construction of geometric features or dense tensor products on \textit{every} edge. To overcome this, we introduce \textbf{E2Former-V2}, a scalable architecture that integrates algebraic sparsity with hardware-aware execution. We introduce \textbf{Equivariant Axis-Aligned Sparsification (EAAS)}, which leverages an $\mathrm{SO}(3)\!\rightarrow\!\mathrm{SO}(2)$ change of basis to convert dense Wigner-$6j$ tensor contractions into sparse, parity-based re-indexing operations. Building on this representation, we propose \textbf{On-the-Fly Equivariant Attention}, a fully node-centric mechanism implemented via a fused Triton kernel. By eliminating materialized edge tensors and maximizing SRAM utilization, our kernel achieves up to \textbf{20$\times$ higher TFLOPS} than standard implementations. Experiments on SPICE and OMol25 show that E2Former-V2 preserves predictive accuracy while substantially accelerating inference, demonstrating the practical feasibility of large equivariant transformers on commodity GPUs.