  Pretrained Language Models (PLMs) have become the de facto starting point for
fine-tuning on downstream tasks. However, as model sizes continue to increase,
traditional fine-tuning of all the parameters becomes challenging. To address
this, parameter-efficient fine-tuning (PEFT) methods have gained popularity as
a means to adapt PLMs effectively. In parallel, recent studies have revealed
the presence of activation sparsity within the intermediate outputs of the
multilayer perceptron (MLP) blocks in transformers. Low activation density
enables efficient model inference on sparsity-aware hardware. Building upon
this insight, in this work, we propose a novel density loss that encourages
higher activation sparsity (equivalently, lower activation density) in the
pre-trained models. We demonstrate the effectiveness of our approach by
utilizing mainstream PEFT techniques, including QLoRA, LoRA, Adapter, and
Prompt/Prefix Tuning, to facilitate efficient model adaptation across diverse
downstream tasks. Experiments show that our proposed method, \textbf{DEFT}
(Density-Efficient Fine-Tuning), can consistently reduce activation density by
up to \textbf{44.94\%} on RoBERTa$_\mathrm{Large}$ and by \textbf{53.19\%}
(encoder density) and \textbf{90.60\%} (decoder density) on
Flan-T5$_\mathrm{XXL}$ (\textbf{11B}) compared to PEFT, using GLUE and QA
(SQuAD) benchmarks respectively. We also introduce \textbf{ADA-DEFT}, an
adaptive variant of our DEFT approach, which achieves significant memory and
runtime savings during inference. For instance, ADA-DEFT reduces runtime by
\textbf{8.79\%}and memory usage by \textbf{17.46\%} in Flan-T5$_\mathrm{XL}$,
and by \textbf{2.79\%} and \textbf{2.54\%} respectively in
Flan-T5$_\mathrm{XXL}$. Additionally, we showcase that DEFT works
complementarily with quantized and pruned models.
