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

arXiv: https://arxiv.org/abs/2609.09925 · HTML: https://mlsanity.com/paper/2609.09925/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Efficient VLA inference and adaptation, one of 13 directions in Vision-language-action models.
- Builds on 17 of its 24 references that are in the map.
- First posted on arXiv 9 Sep 2026.

## Placed in

- Vision-language-action models / [Efficient VLA inference and adaptation](https://mlsanity.com/vla/efficient-vla-inference-and-adaptation/)

## Builds on (most cited first, 17 of 17)

- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [Octo: An Open-Source Generalist Robot Policy](https://mlsanity.com/paper/2405.12213/) (2024)
- [LIBERO: Benchmarking Knowledge Transfer for Lifelong Robot Learning](https://mlsanity.com/paper/2306.03310/) (2023)
- [GR00T N1: An Open Foundation Model for Generalist Humanoid Robots](https://mlsanity.com/paper/2503.14734/) (2025)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Fine-Tuning Vision-Language-Action Models: Optimizing Speed and Success](https://mlsanity.com/paper/2502.19645/) (2025)
- [RDT-1B: a Diffusion Foundation Model for Bimanual Manipulation](https://mlsanity.com/paper/2410.07864/) (2024)
- [SpatialVLA: Exploring Spatial Representations for Visual-Language-Action Model](https://mlsanity.com/paper/2501.15830/) (2025)
- [RoboTwin 2.0: A Scalable Data Generator and Benchmark with Strong Domain Randomization for Robust Bimanual Robotic Manipulation](https://mlsanity.com/paper/2506.18088/) (2025)
- [X-VLA: Soft-Prompted Transformer as Scalable Cross-Embodiment Vision-Language-Action Model](https://mlsanity.com/paper/2510.10274/) (2025)
- [ReZero is All You Need: Fast Convergence at Large Depth](https://mlsanity.com/paper/2003.04887/) (2020)
- [Clifford Neural Layers for PDE Modeling](https://mlsanity.com/paper/2209.04934/) (2022)

## Abstract (arXiv)

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.