Look Within or Beyond? A Theoretical Comparison Between Parameter-Efficient and Full Fine-Tuning

Parameter-Efficient Fine-Tuning (PEFT) has become a popular alternative to Full-Parameter Fine-Tuning (FFT), achieving similar performance on many benchmarks with far lower computational and memory costs. Yet, its effectiveness on complex tasks such as reasoning and instruction-following remains unclear. In this work, we provide a theoretical and empirical comparison of PEFT and FFT in terms of representational capacity and robustness. We show that PEFT's solution space is a strict subset of FFT's and derive upper bounds revealing how its restricted parameterization limits expressiveness and increases vulnerability to perturbations. Experiments on 20 datasets and 11 adversarial test sets support these findings, indicating that while PEFT performs well on standard tasks, its weaknesses on complex and adversarial settings call for new directions beyond current PEFT paradigms. The source code is in the GitHub repository 1 .