# PermVLA: Factorization Order as a Regularizer for VLA Learning

arXiv: https://arxiv.org/abs/2610.04659 · HTML: https://mlsanity.com/paper/2610.04659/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in VLA architectures and generalization, one of 13 directions in Vision-language-action models.
- Builds on 24 of its 25 references that are in the map.
- First posted on arXiv 3 Oct 2026.

## Placed in

- Vision-language-action models / [VLA architectures and generalization](https://mlsanity.com/vla/vla-architectures-and-generalization/)

## Builds on (most cited first, 24 of 24)

- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [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)
- [Fine-Tuning Vision-Language-Action Models: Optimizing Speed and Success](https://mlsanity.com/paper/2502.19645/) (2025)
- [FAST: Efficient Action Tokenization for Vision-Language-Action Models](https://mlsanity.com/paper/2501.09747/) (2025)
- [CALVIN: A Benchmark for Language-Conditioned Policy Learning for Long-Horizon Robot Manipulation Tasks](https://mlsanity.com/paper/2112.03227/) (2021)
- [SmolVLA: A Vision-Language-Action Model for Affordable and Efficient Robotics](https://mlsanity.com/paper/2506.01844/) (2025)
- [WorldVLA: Towards Autoregressive Action World Model](https://mlsanity.com/paper/2506.21539/) (2025)
- [Autoregressive Diffusion Models](https://mlsanity.com/paper/2110.02037/) (2021)
- [PaliGemma 2: A Family of Versatile VLMs for Transfer](https://mlsanity.com/paper/2412.03555/) (2024)
- [Interactive Post-Training for Vision-Language-Action Models](https://mlsanity.com/paper/2505.17016/) (2025)
- [A Deep and Tractable Density Estimator](https://mlsanity.com/paper/1310.1757/) (2013)
- [Efficient Diffusion Transformer Policies with Mixture of Expert Denoisers for Multitask Learning](https://mlsanity.com/paper/2412.12953/) (2024)
- [Masked Autoencoding for Scalable and Generalizable Decision Making](https://mlsanity.com/paper/2211.12740/) (2022)
- [Masked Trajectory Models for Prediction, Representation, and Control](https://mlsanity.com/paper/2305.02968/) (2023)
- [AVA-VLA: Improving Vision-Language-Action models with Active Visual Attention](https://mlsanity.com/paper/2511.18960/) (2025)
- [UniMASK: Unified Inference in Sequential Decision Problems](https://mlsanity.com/paper/2211.10869/) (2022)

## Abstract (arXiv)

Vision-language-action (VLA) policies commonly learn action chunks through a fixed left-to-right (LTR) factorization, although the same expert trajectory distribution admits many valid chain-rule factorizations. We identify factorization order as an overlooked regularization choice and introduce causally anchored permutation (CAP), which samples action reveal orders with a tunable chronological prefix. Its auxiliary objective trains one shared policy to predict actions from different known subsets of the same expert chunk, while deployment retains deterministic LTR control. We call this conditional-set augmentation: it creates multiple conditional prediction problems from one expert chunk without adding demonstrations. This discourages reliance on the single chronological prefix used by ordinary teacher forcing. Controlled experiments show that CAP consistently outperforms standard LTR training on LIBERO and LIBERO-Plus, with the same advantage appearing in cross-dataset CALVIN evaluation. A diagnostic that measures the expected squared difference between a chunk's joint log likelihood under two reveal orders verifies that CAP training internalizes agreement across reveal orders. These findings position sampled subset-conditioned auxiliary objectives as a general recipe for constructing VLA regularizers, illustrated by an extension to diffusion action generators.