Treating chain-of-thought faithfulness as an information-flow problem
A structural approach: reasoning is faithful when answer-relevant information actually routes through the mediated path from prompt to chain-of-thought to answer. It replaces judging whether an explanation sounds right with tracing whether it carried the information.
The trouble with faithfulness research has been circularity — most methods assess whether an explanation looks like it explains the answer, which is a judgement about plausibility. An information-flow framing sidesteps that by asking a structural question with a structural answer.
The criterion is precise. If the chain-of-thought is doing real work, information needed for the answer should pass through it: prompt to reasoning to answer, mediated. If the answer can be produced without the trace carrying that information, the trace is commentary regardless of how sensible it reads.
Why it matters practically: chain-of-thought monitoring is one of the more promising oversight mechanisms available, and it is worth exactly as much as the trace's fidelity to the computation. A structural test tells you when monitoring is load-bearing and when it is theatre.
The complication is that faithfulness turns out to be measurement-dependent — classifier choice materially changes the result. A structural criterion is more robust to that than a judged one, which is a good argument for preferring it.
arXiv — Faithfulness as Information Flow: Evaluating and Training Faithful Chain-of-Thought Reasoning → · arXiv — Measuring Chain-of-Thought Monitorability Through Faithfulness and Verbosity →