AI4AI in unlearning: improving unlearning algorithm autodesign with UDSL

Machine unlearning requires removing the influence of selected data while preserving utility on retained data. Existing unlearning methods are typically implemented as monolithic trainers, where choices about what signal to optimize, how to update the model, where to apply the update, and what behavior to protect are intertwined in code. This representation makes it difficult to systematically explore alternative combinations of unlearning mechanisms. We introduce UDSL, a domain-specific language that factorizes an unlearning procedure into four composable dimensions—Signal, Update, Scope, and Protect—and compiles each program onto a shared training stack. This representation enables LLM-guided evolutionary search to explore algorithmic structure rather than implementation details. On TOFU-forget10 with Llama-3.2-1B-Instruct, UDSL-guided search discovers unlearning procedures that outperform several established unlearning methods under a small evaluation budget. Ablations show that the gains stem from exploring new compositions of unlearning mechanisms rather than merely tuning or recombining existing methods. Across forget ratios and datasets, UDSL provides a common representation in which new procedures can be re-searched without redesigning the underlying training infrastructure. These results suggest that, for LLM-guided unlearning design, the representation of the algorithmic search space can be as important as the search procedure itself.