# BEAST: Efficient Tokenization of B-Splines Encoded Action Sequences for Imitation Learning

arXiv: https://arxiv.org/abs/2506.06072 · HTML: https://mlsanity.com/paper/2506.06072/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Placed in Robot manipulation imitation learning, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 47 of its 61 references that are in the map.
- First posted on arXiv 6 Jun 2025.

## Placed in

- Offline RL and imitation learning from data / [Robot manipulation imitation learning](https://mlsanity.com/offlinerl/robot-manipulation-imitation-learning/)

## Builds on (most cited first, 30 of 47)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023)
- [Neural Machine Translation of Rare Words with Subword Units](https://mlsanity.com/paper/1508.07909/) (2015)
- [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)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [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)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [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)
- [BC-Z: Zero-Shot Task Generalization with Robotic Imitation Learning](https://mlsanity.com/paper/2202.02005/) (2022)
- [SpatialVLA: Exploring Spatial Representations for Visual-Language-Action Model](https://mlsanity.com/paper/2501.15830/) (2025)
- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [CogACT: A Foundational Vision-Language-Action Model for Synergizing Cognition and Action in Robotic Manipulation](https://mlsanity.com/paper/2411.19650/) (2024)
- [Florence-2: Advancing a Unified Representation for a Variety of Vision Tasks](https://mlsanity.com/paper/2311.06242/) (2023)
- [TinyVLA: Towards Fast, Data-Efficient Vision-Language-Action Models for Robotic Manipulation](https://mlsanity.com/paper/2409.12514/) (2024)
- [Behavior Transformers: Cloning k modes with one stone](https://mlsanity.com/paper/2206.11251/) (2022)
- [Video Prediction Policy: A Generalist Robot Policy with Predictive Visual Representations](https://mlsanity.com/paper/2412.14803/) (2024)
- [3D Diffuser Actor: Policy Diffusion with 3D Scene Representations](https://mlsanity.com/paper/2402.10885/) (2024)
- [Goal-Conditioned Imitation Learning using Score-based Diffusion Policies](https://mlsanity.com/paper/2304.02532/) (2023)
- [Language Conditioned Imitation Learning over Unstructured Data](https://mlsanity.com/paper/2005.07648/) (2020)
- [DaViT: Dual Attention Vision Transformers](https://mlsanity.com/paper/2204.03645/) (2022)
- [RoboAgent: Generalization and Efficiency in Robot Manipulation via Semantic Augmentations and Action Chunking](https://mlsanity.com/paper/2309.01918/) (2023)

## Built on by (most cited first, 27 of 27)

- [QuantVLA: Scale-Calibrated Post-Training Quantization for Vision-Language-Action Models](https://mlsanity.com/paper/2602.20309/) (2026)
- [FASTer: Toward Efficient Autoregressive Vision Language Action Modeling via Neural Action Tokenization](https://mlsanity.com/paper/2512.04952/) (2025)
- [G0.5: One Autoregressive Stream for Robot Reasoning and Action](https://mlsanity.com/paper/2608.11739/) (2026)
- [ABPolicy: Asynchronous B-Spline Flow Policy for Real-Time and Smooth Robotic Manipulation](https://mlsanity.com/paper/2602.23901/) (2026)
- [Revisiting Embodied Chain-of-Thought for Generalizable Robot Manipulation](https://mlsanity.com/paper/2606.03784/) (2026)
- [AR-VLA: True Autoregressive Action Expert for Vision-Language-Action Models](https://mlsanity.com/paper/2603.10126/) (2026)
- [OmniSAT: Compact Action Token, Faster Auto Regression](https://mlsanity.com/paper/2510.09667/) (2025)
- [Mimic Intent, Not Just Trajectories](https://mlsanity.com/paper/2602.08602/) (2026)
- [Neural Implicit Action Fields: From Discrete Waypoints to Continuous Functions for Vision-Language-Action Models](https://mlsanity.com/paper/2603.01766/) (2026)
- [FLASH: Efficient Visuomotor Policy via Sparse Sampling](https://mlsanity.com/paper/2605.15492/) (2026)
- [Enabling Dynamic Tracking in Vision-Language-Action Models via Time-Discrete and Time-Continuous Velocity Feedforward](https://mlsanity.com/paper/2603.16218/) (2026)
- [General Covariant Action Modeling: Constructing Generalized Manifolds via Spatio-Temporal Decoupling](https://mlsanity.com/paper/2606.00110/) (2026)
- [LAST: Bridging Vision-Language and Action Manifolds via Gromov-Wasserstein Alignment](https://mlsanity.com/paper/2606.11221/) (2026)
- [Hermite Curves as Trajectory Priors for Vision-Language-Action Models](https://mlsanity.com/paper/2608.01265/) (2026)
- [Beyond World-Frame Action Heads: Motion-Centric Action Frames for Vision-Language-Action Models](https://mlsanity.com/paper/2605.11809/) (2026)
- [Real-Time Execution with Autoregressive Policies](https://mlsanity.com/paper/2606.13355/) (2026)
- [SMILE: Smooth Motion for Improved Long-Horizon VLA Execution](https://mlsanity.com/paper/2608.29432/) (2026)
- [LieSpline-DP: Lie-Group B-Spline Diffusion Policy for Smooth Robot Manipulation](https://mlsanity.com/paper/2609.15162/) (2026)
- [VLN on the Fly: An Onboard Vision-Language Navigation Stack for Aerial Robots](https://mlsanity.com/paper/2609.20191/) (2026)
- [Direction-Scale Decomposition in Action Representation: Rethinking What to Tokenize for Vision-Language-Action Models](https://mlsanity.com/paper/2609.28865/) (2026)
- [Rethinking Causal Action Tokenization with Conditional Annealing in Flow Matching](https://mlsanity.com/paper/2609.35469/) (2026)
- [LexiconVLA: Learning Reusable Atomic Action Codebooks for Unseen Tasks](https://mlsanity.com/paper/2609.36774/) (2026)
- [Toward Real-Time VLAs: Stage-Aware Two-Step Flow Denoising and System-Level Evaluation](https://mlsanity.com/paper/2609.39822/) (2026)
- [SplineWAM: Adaptive Action Horizons for World Action Models via B-Spline Representations](https://mlsanity.com/paper/2609.39873/) (2026)
- [TOAST: Stochastic Robot Action Tokenization for Autoregressive Vision-Language-Action Models](https://mlsanity.com/paper/2610.00899/) (2026)
- [Triggering Generalist Reasoning via Predictive Uncertainty for Dual-System VLA](https://mlsanity.com/paper/2610.05025/) (2026)
- [Vela: Scaling Vision-Language-Action Models with Adaptive Action Curve Parametrization](https://mlsanity.com/paper/2610.05230/) (2026)

## Abstract (arXiv)

We present the B-spline Encoded Action Sequence Tokenizer (BEAST), a novel action tokenizer that encodes action sequences into compact discrete or continuous tokens using B-splines. In contrast to existing action tokenizers based on vector quantization or byte pair encoding, BEAST requires no separate tokenizer training and consistently produces tokens of uniform length, enabling fast action sequence generation via parallel decoding. Leveraging our B-spline formulation, BEAST inherently ensures generating smooth trajectories without discontinuities between adjacent segments. We extensively evaluate BEAST by integrating it with three distinct model architectures: a Variational Autoencoder (VAE) with continuous tokens, a decoder-only Transformer with discrete tokens, and Florence-2, a pretrained Vision-Language Model with an encoder-decoder architecture, demonstrating BEAST's compatibility and scalability with large pretrained models. We evaluate BEAST across three established benchmarks consisting of 166 simulated tasks and on three distinct robot settings with a total of 8 real-world tasks. Experimental results demonstrate that BEAST (i) significantly reduces both training and inference computational costs, and (ii) consistently generates smooth, high-frequency control signals suitable for continuous control tasks while (iii) reliably achieves competitive task success rates compared to state-of-the-art methods.