Compress Then Adapt? No, Do It Together via Task-aware Union of Subspaces

Adapting large pretrained models to diverse tasks is now routine, yet the two dominant strategies of parameter-efficient fine-tuning (PEFT) and low-rank compression are typically composed in sequence. This decoupled practice first compresses and then fine-tunes adapters, potentially misaligning the compressed subspace with downstream objectives and squandering a global parameter budget. To overcome this limitation, we introduce JACTUS (Joint Adaptation and Compression with a Task-aware Union of Subspaces), a single framework that unifies compression and adaptation. From a small calibration set, JACTUS estimates input and pre-activation gradient covariances, forms their orthogonal union with the pretrained weight subspace, performs a projected low-rank approximation inside this union, allocates rank globally by marginal gain per parameter, and trains only a compact core matrix. This explicitly mitigates the potential misalignment between the compressed subspace and downstream objectives by coupling the directions preserved for compression with those required for adaptation, yielding a deployable low-rank model that avoids retaining full frozen weights while enabling fast and robust tuning. On vision, JACTUS attains an average 89.2% accuracy on ViT-Base across eight datasets at 80% retained parameters, surpassing strong 100% PEFT baselines (e.g., DoRA 87.9%). On language, JACTUS achieves an 80.9% average on Llama2-7B commonsense QA at the same 80% retained-parameter budget, outperforming 100% PEFT (e.g., DoRA 79.7%) and exceeding prior compress-then-finetune pipelines under the same ratained-parameter budget. We will release code.