Time-Frequency Geometric Cross-Attention for Chunked Vision-Language-Action Models

Abstract: Modern vision-language-action (VLA) policies predict a whole chunk of actions: one to two seconds of coordinated motion emitted in a single forward pass. Yet an action chunk is essentially a short multivariate trajectory, but inside these models it is a sequence of generic per-timestep hidden tokens decoded by a linear head. This under-serves two motion structures. First, frequency: a chunk superimposes a smooth global trend and fine corrective motion across time scales, and a single token entangles them. Second, cross-phase geometry: motions of different phases (reach, contact, grasp adjustment, settling) unfold along very different, near-orthogonal directions in representation space, yet are tightly related for the task and arise across the time axis. Dot-product attention scores alignment by an inner product, so it favors aligned tokens and is least sensitive near orthogonality, leaving such relationships for the network to recover through a detour. We introduce Time-Frequency Geometric Cross-Attention (TFGCA), a drop-in module repairing both blind spots. TFGCA uses a per-dimension learnable stationary wavelet transform to decompose the action chunk into time-frequency tokens, and each time token retrieves information from them via a cross-attention that fuses the dot product (similarity) with the wedge-product magnitude (sensitive to near-orthogonality) through a learnable weight. A zero-initialized residual reproduces the base behavior at initialization, so it can be dropped onto a pretrained VLA and fine-tuned jointly. Relative to the same-source base, TFGCA improves in-distribution LIBERO by +1.5 on average, the OOD LIBERO-Plus by +6.3, the randomized average under RoboTwin domain randomization by +28.5, and the overall success rate on three real-robot AgiBot A2 tasks by +11.67 points, with larger gains out of distribution.