EmbodiedTuring Machines

Stateful Code for Robot Recursive Self-Improvement

Code-Only-as-Policy

Kairui Hu1,2,*  Siyuan Hu1,*  Fangzhou Hong1,2  Zhaoxi Chen1,2  Ziwei Liu1,2 1Nanyang Technological University · 2Ropedia · *Equal contribution

Embodied Turing Machine & The Exploration of Code-Only-As-Policy (COAP)

How far can code-only policies go?

We view the embodied world as an Embodied Turing Machine, whose tape is the robot and environment state and rules are the policy. What if a robot policy didn't need a VLM or VLA in its runtime control loop?

We want to explore the limit of a different paradigm: Can code-only-as-policy go surprisingly far in embodied intelligence? Where does it work, and where does it break?

  • Data engine. Given offline time, coding agents iterate on a reusable code library. A working program then generates diverse trajectories efficiently and at scale for policy training.
  • Stable, fast execution. Decisions are explicit code, and no model is queried at run time, so execution is stable, fast and cheap. This suits industrial settings where the state can be measured reliably.
  • Generalization trade-off. Zero-shot generalization is difficult for code and generally calls for an agent in the loop. Code, however, is reusable: with offline development, it extends to new tasks and scenes.
FastNo model at runtime.
StableDecisions are code, not samples. Every decision is explicit.
Cross-episodeOne program for every episode. Fixes carry over.
ReusableShared library. Easy to extend, reuse and inherit.
Data engineEfficient trajectory generation for VLA, Agent-as-Policy and Harness VLA.

The rules are code. The tape is the state.

cover_blocks.py· pseudocoderunning

        
Recorded statestep 0
head camerastep 000
0 / 397

One benchmark, as an example.

success rate · RoboDojo, 42 bimanual tasks · 75.45 progress score
about 2.2× the best success rate on the public leaderboard (31.38%) · self-evaluated

White box and controllable.

Explicit state

Every step reads and writes explicit state, never hidden in a model.

Controllable
76%failures caught

Backtrack and reattempt another way.

Cheap
0.3 ms

per control step. No model calls.

Extendable

Easy to evolve new tasks.

Data engine

COAP evolves fast, runs fast and works across episodes, so it generates trajectories efficiently for VLA.

Developed offline by coding agents.

A coding agent tries several approaches in parallel and keeps the one that works.

current code
carry
hang it

Embodied Turing MachinesStateful Code for Robot Recursive Self-Improvement

Kairui Hu1,2,*  Siyuan Hu1,*  Fangzhou Hong1,2  Zhaoxi Chen1,2  Ziwei Liu1,2 1Nanyang Technological University · 2Ropedia · *Equal contribution

Nanyang Technological University Ropedia
@article{hu2026embodied,
  title   = {Embodied Turing Machines: Stateful Code
             for Robot Recursive Self-Improvement},
  author  = {Hu, Kairui and Hu, Siyuan and Hong, Fangzhou
             and Chen, Zhaoxi and Liu, Ziwei},
  journal = {arXiv preprint arXiv:2610.12369},
  year    = {2026}
}