Heads or Tails: A Simple Example of Causal Abstractive Simulation

This note illustrates how a variety of causal abstraction arXiv:1707.00819 arXiv:1812.03789, defined here as causal abstractive simulation, can be used to formalize a simple example of language model simulation. This note considers the case of simulating a fair coin toss with a language model. Examples are presented illustrating the ways language models can fail to simulate, and a success case is presented, illustrating how this formalism may be used to prove that a language model simulates some other system, given a causal description of the system. This note may be of interest to three groups. For practitioners in the growing field of language model simulation, causal abstractive simulation is a means to connect ad-hoc statistical benchmarking practices to the solid formal foundation of causality. Philosophers of AI and philosophers of mind may be interested as causal abstractive simulation gives a precise operationalization to the idea that language models are role-playing arXiv:2402.12422. Mathematicians and others working on causal abstraction may be interested to see a new application of the core ideas that yields a new variation of causal abstraction.