Quantifying the Necessity of Chain of Thought through Opaque Serial Depth

ArXi:2603.09786v1 Announce Type: new Large language models (LLMs) tend to externalize their reasoning in their chain of thought, making the chain of thought a good target for monitoring. This is partially an inherent feature of the Transformer architecture: sufficiently long serial cognition must pass through the chain of thought (Korbak, 2025). We formalize this argument through the notion of opaque serial depth, given by the length of the longest computation that can be done without the use of interpretable intermediate steps like chain of thought.