Three Domains, One Direction: Reasoning-Calibration Steering Transfers Across Domains

Activation steering can reduce overthinking in reasoning language models by adding an extracted steering vector to the residual stream, shifting hidden states along a learned calibration direction (Chen et al., 2025). However, the steering vector is typically extracted from a single reasoning domain (Chen et al., 2025; Nguyen & Le, 2026), and this practice led us to ask whether effective calibration requires domain-specific vectors. We construct a general reasoning vector from three reasoning domains (mathematics, code, and logic) and investigate whether it achieves the same steering effect as domain-specific vectors without sacrificing accuracy or token efficiency. We take two approaches to constructing this general vector: a pooled vector, extracted from a dataset containing activations from all three domains, and a combined vector, obtained by averaging the three independently extracted domain vectors. Contrary to our initial intuition that each vector would perform best at home and degrade out of domain, no domain vector shows a measurable advantage on its home domain, and the results are uniform across the five vectors. On DeepSeek-R1-Distill-Qwen-1.5B, all pairwise McNemar comparisons among the five vectors are non-significant on MATH-500, APPS, and LogiQA2. Their geometry explains why: 87.0% of the domain vectors' squared variation lies along one singular direction, and the pooled and combined vectors have a cosine similarity of 0.981. On the same model, a random vector of the same magnitude instead lengthens responses and yields no accuracy benefit, showing that the effect depends on the learned direction. The finding replicates on the 7B model of the same family. These results suggest a shared, domain-general reasoning-calibration direction: a single axis in activation space modulating how much the model deliberates, common across mathematics, code, and logic. In practice, a single vector extracted once transfers across reasoning domains, potentially eliminating the need for per-domain extraction. Code, vectors, and per-problem outcomes are available at https://anonymous.4open.science/r/SEAL-EB7E/.