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Full-stack recurrence

Looped Transformers as Programmable Computers

Looped Transformers as Programmable Computers

Angeliki Giannou, Shashank Rajput, Jy-yong Sohn, Kangwook Lee, Jason D. Lee, Dimitris Papailiopoulos

Programs a fixed-weight transformer and places it in a loop so the input sequence acts as a punchcard of instructions and memory, emulating a small instruction-set computer with a 13-layer looped encoder.

Inside the method

Punchcard input → [ 13-layer programmed transformer ] × steps

Simplified conceptual schematic. Consult the paper for the complete architecture.

Recurrence family
Full-stack recurrence
Depth control
Loop until the program halts
KV / state strategy
Not applicable (constructive encoder)

Reading note

A constructive theory result: the looped transformer emulates a calculator, a basic linear-algebra library and in-context learning via backpropagation. Weights are hand-constructed, not trained.

Sources checked 2026-10-28. This catalog does not imply independent reproduction.

Related works

Cite this work

@misc{programmablecomputers2023,
  title = {Looped Transformers as Programmable Computers},
  author = {Angeliki Giannou and Shashank Rajput and Jy-yong Sohn and Kangwook Lee and Jason D. Lee and Dimitris Papailiopoulos},
  year = {2023},
  eprint = {2301.13196},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2301.13196}
}

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