The Geometry of Self-Verification in a Task-Specific Reasoning Model

How do reasoning models verify their own answers? We study this question by training a model using DeepSeek R1's recipe on the CountDown task. We leverage the fact that preference tuning leads to mode collapse, resulting in a model that always produces highly structured and easily parse-able chain-of-thought sequences. With this setup, we do a top-down and bottom-up analysis to reverse-engineer how the model verifies its outputs. Our top-down analysis reveals Gated Linear Unit (GLU) weights encoding verification-related tokens, such as ``success'' or ``incorrect'', which activate according to the correctness of the model's reasoning steps. Our bottom-up analysis reveals that ``previous-token heads'' are mainly responsible for model verification. Our analyses meet in the middle: drawing inspiration from inter-layer communication channels, we use the identified GLU vectors to localize as few as three attention heads that can disable model verification, pointing to a necessary component of a potentially larger verification circuit.