Modeling LLM Unlearning as an Asymmetric Two-Task Learning Problem

Abstract

Machine unlearning for large language models (LLMs) aims to remove targeted knowledge while preserving general capability. In this paper, we recast LLM unlearning as an asymmetric two-task problem: retention is the primary objective and forgetting is an auxiliary. From this perspective, we propose a retention-prioritized gradient synthesis framework that decouples task-specific gradient extraction from conflict-aware combination. Instantiating the framework, we adapt established PCGrad to resolve gradient conflicts, and introduce SAGO, a novel retention-prioritized gradient synthesis method. Theoretically, both variants ensure non-negative cosine similarity with the retain gradient, while SAGO achieves strictly tighter alignment through constructive sign-constrained synthesis. Empirically, on WMDP Bio/Cyber and RWKU benchmarks, SAGO consistently pushes the Pareto frontier: e.g., on WMDP Bio (SimNPO+GD), recovery of target model MMLU performance progresses from 44.6% (naive) to 94.0% (+PCGrad) and further to 96.0% (+SAGO), while maintaining comparable forgetting strength. Our results show that re-shaping gradient geometry, rather than re-balancing losses, is the key to mitigating unlearning-retention trade-offs.