// Beneath the Surface of Chains-of-Thought //

Impressive paper on whether reasoning steps have internal structure or only textual structure.

Researchers ask whether distinct reasoning operations, such as problem formulation, goal decomposition and deduction, are geometrically organized in hidden representations.

It turns out they are.

Operations are separable in held out representations, and separability peaks in middle layers.

The authors check that lexical and positional confounds do not explain it.

They find that identical surface tokens are represented differently depending on the operation of the surrounding chunk, so the geometry tracks function rather than wording.

And attention masking shows that operation aligned representations at the start of a chunk depend on preceding reasoning context, so the operation label is constructed from the trace rather than read off the current token.

Across layers, token wise operation alignment becomes more distributed over spans. If you want to steer or monitor reasoning by operation type, this study shows where the important signals might be.

Paper: https://arxiv.org/abs/2609.04753

Chat with Paper: https://academy.dair.ai/papers/beneath-the-surface-of-chains-of-thought-a-mechanistic-interpretation-of-reasoni-2609.04753