VLA Notes (6): RT-1's Discrete-Action Route — TokenLearner, Causal Mask, and Cross-Entropy

1. Why RT-1 Chose Discrete Action Tokens

In Part 1 of this series we said there are two ways to represent robot actions:

Continuous generation: directly regress joint angles and velocities for smooth trajectories — the territory of π0 and Xiaomi Robotics today.
Discrete tokenization: quantize continuous actions into discrete symbols and generate them autoregressively, like an LLM writing a sentence.

RT-1 (Google Robotics, 2022) took the second path. The core idea is simple: if LLMs can learn language structure from trillions of text tokens, why not treat actions as tokens and reuse the whole language-model training stack — autoregression, Transformers, cross-entropy?

The downside is obvious: quantizing continuous motion throws away precision and can make trajectories jittery. But RT-1 proved the engineering simplicity and scalability of the route, paving the way for RT-2 and OpenVLA.

This post answers the two questions that most often confuse beginners:

How do 6 frames become 486 visual tokens, and how does TokenLearner squeeze them to 48?

In the decoder-only action decoder, what exactly are “standard causal mask + categorical cross-entropy loss”, and what variants exist?

2. Vision Side: EfficientNet + TokenLearner

2.1 From Image to Tokens: 81 per Frame

RT-1’s input is six consecutive robot-camera images.

Why six? At a control rate of 3 Hz, six frames cover roughly the last two seconds of observation. The model needs this short-term memory to judge where objects are moving, where the gripper is, and how the previous action is unfolding.

Each 300×300 RGB image first passes through an EfficientNet-B3 visual encoder:

The final feature map is 9×9×512.
Flattening the 9×9 spatial grid gives 81 visual tokens, each a 512-d vector.

So for one frame:

300×300 image  →  EfficientNet-B3  →  9×9×512  →  81 tokens (512-d)

2.2 Six Frames Explode the Token Count

Six frames, 81 tokens each, gives:

6 × 81 = 486 visual tokens

That is before language instruction tokens and special tokens. Four hundred and eighty-six visual tokens is too expensive for 3 Hz real-time inference — Transformer cost roughly scales with the square of sequence length.

2.3 TokenLearner: 81 Tokens → 8 Tokens

RT-1’s solution is TokenLearner (Google, 2021). Instead of uniformly downsampling the feature map, it lets the model decide which spatial locations matter.

How it works (element-wise attention):

For every spatial position in the 9×9 feature map, compute an importance score.
The score is element-wise: it looks not only at spatial location but also at which of the 512 channel responses are strong.
Use these scores to adaptively aggregate the 81 tokens into 8 representative tokens.

Intuitive analogy:

TokenLearner is like a photographer who doesn’t shrink the whole photo uniformly. Instead, it automatically zooms in on the few regions most relevant to the manipulation task and blurs the background.

Result:

6 frames × 81 tokens  →  TokenLearner  →  6 frames × 8 tokens = 48 visual tokens

In the RT-1 paper this raises inference speed by about 2.4×.

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  <text x="0" y="0" font-size="12" fill="#555">Input: 6 history frames (3 Hz ≈ 2 seconds)</text>
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<text x="95" y="168" text-anchor="middle" font-size="10" fill="#555">300×300 → 9×9×512</text>

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<text x="395" y="168" text-anchor="middle" font-size="10" fill="#555">Element-wise attn → 8/frame</text>

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  <text x="0" y="18" font-size="11" fill="#555">Compressed to 48 tokens</text>
  <text x="0" y="36" font-size="11" fill="#555">+ language + &lt;BOS&gt;</text>
  <text x="0" y="54" font-size="11" fill="#34A853">Inference speed ↑ 2.4×</text>
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<text x="340" y="248" text-anchor="middle" font-size="14" fill="#1a1a1a" font-family="monospace">300×300 × 6 frames  →  9×9×512 × 6 = 486 tokens  →  TokenLearner  →  8×6 = 48 tokens</text>

<text x="340" y="310" text-anchor="middle" font-size="12" fill="#1a73e8">6 frames = last ~2 seconds; TokenLearner adaptively keeps task-relevant regions.</text>

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Figure: RT-1 first turns each frame into 81 tokens with EfficientNet, then compresses each frame to 8 tokens with TokenLearner.

3. Action Side: Decoder-Only Transformer

After visual compression, the 48 visual tokens are concatenated with language instruction tokens and a special <BOS> start token, then fed into a decoder-only Transformer.

3.1 What Goes In and What Comes Out

Input sequence (left to right):

<BOS>  [language instruction tokens]  [visual tokens × 48]

Output sequence (generated autoregressively):

[mode token]  [arm action tokens ...]  [base action tokens ...]

RT-1 discretizes actions into three token types:

Type	Meaning	Examples
Mode	End-effector open/close / motion mode	open / close / move
Arm	Discretized 6–7 DOF joint angles	each dimension binned
Base	Mobile base velocity / heading	forward / back / turn

The model generates a string of action tokens, which are then decoded back into the robot’s actual control command.

3.2 Standard Causal Mask: Look Left Only

The signature of a decoder-only Transformer is the causal mask:

Position t can only attend to positions ≤ t; it cannot peek at the future.

This preserves autoregressive validity: when predicting the t-th action token, the model may only use positions 1 … t-1 plus the input-side history.

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<text x="340" y="150" text-anchor="middle" font-size="12" fill="#1a73e8">Lower-triangle green: predicting token t can only use positions 1…t.</text>

Figure: A standard causal mask is a lower-triangle matrix; it prevents the model from peeking at future tokens.

4. Common Forms of Causal Mask

In practice, “look left only” comes in several flavors.

4.1 Strict Causal Mask

The most common. Position t can only attend to positions ≤ t. Both training and inference use this lower-triangle pattern.

4.2 Mask with a Start Token

If the sequence begins with a special <BOS> or <PAD>, you sometimes want every position to attend to that start token (it carries no future information, just global context), while keeping everything else strictly causal. In matrix form, the first column is all green and the rest is lower-triangular.

4.3 Block Causal Mask

Actions are often generated in groups: first a “mode”, then a group of “arm joints”, then “base”. A block causal mask allows:

Strict causality inside each block;
Current block to attend to all previous blocks;
No peeking at later blocks.

This fits RT-1-style multi-field action tokens naturally: base tokens can see mode and arm tokens, but arm tokens cannot see base tokens.

4.4 KV-Cache Mask

At inference time, Keys and Values of already-generated tokens are cached. The mask then looks like:

Historical tokens (cached): marked with *, not recomputed;
Current new token: attends only to cache + its own row;
Future tokens: still masked.

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  <text x="60" y="90" text-anchor="middle" font-size="10" fill="#555">Most common</text>
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  <text x="60" y="0" text-anchor="middle" font-size="11" fill="#1a1a1a" font-weight="bold">4. KV-Cache</text>
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<text x="340" y="195" text-anchor="middle" font-size="12" fill="#1a73e8">Strict causal is default; BOS/block suit multi-field actions; KV-cache is an inference optimization.</text>

Figure: Four causal-mask variants. Green = visible, gray = masked, yellow = cached.

5. Categorical Cross-Entropy: Standard and Variants

Because action tokens are discrete categories, the training objective is categorical cross-entropy:

L = - Σ  y_t,v · log( p_hat_t,v )

Here y_t is the one-hot ground-truth action token and p_hat_t is the predicted probability distribution. Intuitively, the loss only cares about whether the probability mass on the true category is high.

5.1 Standard Cross-Entropy

The ground-truth label is one-hot: 1 at the true position and 0 elsewhere. Loss = -log(probability at the true position). This is the RT-1 baseline.

5.2 Label Smoothing

Standard cross-entropy can push the model to be over-confident and overfit. Label smoothing changes the one-hot target to:

true position = 1 - ε
all others    = ε / (V - 1)

The model no longer has to push the true class probability all the way to 1; it is allowed to leave a small probability for every other class. This usually improves generalization.

5.3 Weighted Cross-Entropy

Different action classes can be imbalanced — for example, “base motion” tokens may appear far less often than “arm” tokens. Weighted cross-entropy multiplies the loss of rare classes by a larger weight:

L_t = - w_y_t · log( p_hat_t, y_t )

This is very practical in robotics data, preventing the model from learning only the most common “safe” actions.

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  <text x="80" y="95" text-anchor="middle" font-size="10" fill="#555">True class probability = 1</text>
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  <text x="80" y="0" text-anchor="middle" font-size="11" fill="#1a1a1a" font-weight="bold">2. Label Smoothing</text>
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  <text x="80" y="95" text-anchor="middle" font-size="10" fill="#555">True = 1-ε, others split ε</text>
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  <text x="80" y="0" text-anchor="middle" font-size="11" fill="#1a1a1a" font-weight="bold">3. Weighted</text>
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  <text x="80" y="95" text-anchor="middle" font-size="10" fill="#555">Classes use weights w</text>
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<text x="340" y="173" text-anchor="middle" font-size="13" fill="#1a1a1a">Standard: L = -log p̂ₜ,ᵧₜ</text>
<text x="340" y="190" text-anchor="middle" font-size="13" fill="#1a1a1a">Weighted: L = -wᵧₜ · log p̂ₜ,ᵧₜ ｜ Smoothed: true = 1-ε, others = ε/(V-1)</text>

Figure: Three cross-entropy variants. Standard is hardest; label smoothing prevents overfitting; weighted handles class imbalance.

6. From RT-1 to RT-2 to Native VLA

RT-1’s importance is not “state-of-the-art performance” but proof that VLA can be engineered:

Turn images into tokens;
Turn actions into tokens;
Train a decoder-only Transformer with causal masks and cross-entropy end-to-end.

RT-2 later scaled this by attaching a vision-language model (VLM) directly to action outputs, letting robots leverage internet-scale vision-language knowledge. Then π0, OpenVLA, and Xiaomi pushed toward native VLA + continuous generation, improving precision and smoothness.

So RT-1 is not the destination; it is the starting point of “reframing control as language.” Understanding TokenLearner, causal masks, and cross-entropy means understanding the shared DNA of nearly every VLA that followed.

Investment angle: the embodied-AI model stack is converging quickly. The discrete route (RT-1/RT-2/OpenVLA) and the continuous route (π0/Xiaomi) are not mutually exclusive — they will coexist across different latency/accuracy/cost scenarios. Watch teams that can run both routes and have a real data flywheel.