Looped Transformers as Programmable Computers

We present a framework for using transformer networks as universal computers by programming them with specific weights and placing them in a loop. Our input sequence acts as a punchcard, consisting of instructions and memory for data read/writes. We demonstrate that a constant number of encoder layers can emulate basic computing blocks, including lexicographic operations, non-linear functions, function calls, program counters, and conditional branches. Using this framework, we emulate a computer using a simple instruction-set architecture, which allows us to map iterative algorithms to programs that can be executed by a constant depth looped transformer network. We show how a single frozen transformer, instructed by its input, can emulate a basic calculator, a basic linear algebra library, and even a full backpropagation, in-context learning algorithm. Our findings reveal the potential of transformer networks as programmable compute units and offer insight into the mechanics of attention.