CARGO: Carrying Curvature Across Tasks for Continual Pruning of Large Language Models

Continual pruning has recently emerged as a promising direction that progressively updates pruned LLMs as new tasks arrive, while retaining knowledge from previously encountered tasks. Existing methods focus primarily on which weights to prune, leaving unexplored whether the remaining weights can be actively adapted to compensate for the information lost through continual pruning. We find that combining accumulated-importance-based weight pruning with existing single-task weight reconstruction strategies can improve final performance but leads to larger forgetting, calling for a dedicated design for continual pruning. To this end, we first formulate a progressive weight reconstruction problem for continual pruning to jointly minimize the layer-wise pruning error of the pruned model over all tasks seen so far. Under fixed layer inputs and an invertible sum of task Hessians, we show that optimal compensation for a single-weight deletion depends on historical tasks only through their accumulated Hessian, enabling efficient bluereconstruction without retaining past calibration data. Building on this insight, we next propose CARGO (**C**urvature **A**ccumulation and **R**egime-**G**ated C**o**nsolidation), a training-free continual pruning framework that carries curvature information across tasks to guide both weight selection and reconstruction. To robustly consolidate curvature over time, CARGO further incorporates spectral cleaning to suppress noisy low-energy curvature components and a task-correlation-aware directional gate to selectively retain historical curvature. Experiments across three model families and two task streams show that CARGO substantially improves continual pruning performance over the strongest baselines.