Prune Gradually, Adapt Sparsely: Efficient Pruning of Large Language Models at Extreme Sparsity

Weight pruning can reduce the storage and inference cost of large language models (LLMs), but preserving quality at high sparsity levels remains challenging. Existing methods face a quality-cost trade-off in this regime. One-shot pruning is cheap but degrades sharply as sparsity increases, even when followed by post-pruning recovery. A growing line of work instead optimizes the mask directly from the dense model under the end-to-end objective; among these methods, ELSA lee2026elsa, the recent state of the art at extreme sparsity, reaches high quality but at the cost of model-sized optimizer state and auxiliary variables. To address this gap, we propose ETAPS, which prunes gradually and adapts sparsely: it tightens a global sparsity constraint in progressive stages while training a sparse delta with a small, fixed budget. Our key observation is that gradual weight removal keeps each pruning step small enough for sparse adaptation to compensate, allowing the adapted model to provide end-to-end gradients that guide the next pruning decision without model-sized optimizer state. Across six models from 125M to 13B parameters, ETAPS achieves lower perplexity than ELSA at every evaluated sparsity from 50% to 90%, with perplexity reductions of up to 42%. ETAPS is also far cheaper: at 90% sparsity, it prunes LLaMA-2-7B on a single H200, where ELSA uses four, with $5.0\times$ smaller total persistent state and 49% fewer GPU-hours. Together, our findings point to a promising direction for achieving high quality in demanding regimes such as extreme sparsity at substantially lower cost.