Drift-Constrained Optimization: set a behavioral drift budget before fine-tuning, then only pick the direction

arXiv·medium signalXBlueskyLinkedInCopy link

arXiv 2609.13680 (submitted 12 Sep) reframes instruct-model fine-tuning by declaring a behavioral drift budget up front rather than treating drift from the reference model as an uncontrolled side effect. The authors show drift induces a shared local geometry anchored at the reference model where the budget defines a boundary and distance is fixed, leaving update direction as the only remaining degree of freedom — so fine-tuning becomes direction selection and methods can be compared on directional efficiency. They test the resulting prediction in a stringent QA-only setting where strong instruct models are fine-tuned on final answers alone but must still produce multi-step reasoning at inference, which is exactly the regime where naive SFT quietly destroys capability.