Gradient Routing Generalizes to Unrouted Hack Types

TLDR: I lightly extend Ward, Hu et al (2026) to measure how well gradient routing generalizes. I route gradients on one type of reward hack (e.g. ones that reason in English) and check whether this suppresses other types at test time (e.g. ones that reason in French), despite the model being trained on those too. This models a realistic monitor that catches some types of hack during training but not others, rather than catching each at the same rate. I find encouraging evidence of generalization...