FAST - Efficient Robot Action Tokenization

Paper Link: https://arxiv.org/pdf/2501.09747

FAST’s goal is to train policies $\pi (a_{1:H}|o)$ that map an observation $o$ to a sequence of future robot actions $a_{1:H}$

Time Series Compression §

Key takeaway: Any sufficiently effective compression approach when applied to the action targets is suited to improve the training speed of VLA models

In the paper they use DCT, purpose of this algorithm is to transform continuous signal into a sum of cosine elements of various frequencies

Low frequencies capture shape, high frequency reflect sharp jumps

Compared to learn compression approaches DCT compression is analytical approach thus simple and fast

FAST Tokenization Algorithm §

1. Normalize the input actions, s.t 1st and 99th quantile of values in the training dataset for each action maps to range $[-1,\dots ,1]$
   1. Purpose of this is to make tokenization of cross-embodied datasets with different action scales easier
2. Apply DCT to each action dimension separately
   1. To compress DCT converted signal we simply omit insignificant coefficients, implemented using scale-and-round operation, scaling coefficient is a hyperparam
   2. Scale and Round = take a real number/constant x, scale it by a constant s, then round to nearest integer
3. Flatten the matrix into 1-D vector of integers
4. Use BPE to merge tokens, making action dense tokens

Note: Order of flattening DCT coefficient matrix prior to BPE can have a significant impact, the paper goes with column first flattening

The tokenizer only has 2 hyperparameters, scale applied to DCT coefficients before rounding and vocab size of BPE compression step. Paper uses rounding scale 10 and BPE vocab size 1024

DCT based tokenization has shown to be much better and a lot less tedious to train compared to Vector Quantization

Universal Robot Action Tokenizer §

The only learned part of the tokenizer is the vocabulary of BPE encoder, which needs to be trained for each new dataset the tokenizer is being applied to

The learning process is usually fast (only a few minutes), since it adds friction Physical Intelligence aims to train a universal action tokenizer that can encode chunks of robot actions from any robot

For best results, normalize input action range $[-1,\dots ,1]$ via quantile normalization and tokenizing 1-second action chunk at a time

Inference Speeds: ${\pi }_0-FAST$ matches the performance of diffusion ${\pi }_0$ but is slower at inference time