Parameter Importance is Not Static: Evolving Parameter Isolation for Supervised Fine-Tuning

In real-world deployment, LLMs are often adapted continually across tasks to keep LLMs up-to-date in production, where new fine-tuning should preserve previously learned skills. However, indiscriminately mixing tasks can dilute task specialization, while sequential fine-tuning (full-parameter or low rank adaptation) often causes catastrophic forgetting due to destructive overwriting. Replay-based continual tuning and maintaining separate task-specific adapters can mitigate forgetting, but introduce additional compute, storage, and management overhead. Recognizing the redundancy of LLM parameters for any single task, we reframe continual task adaptation as task-specific parameter discovery via adaptation-aware probing: a short warm-start probe exposes a task's adaptation trace, enabling us to identify and isolate the small subset of parameters essential for each task to mitigate catastrophic forgetting. Building on this view, we introduce TRACE, a novel approach for discovering Task-specific paRameters via Adaptation-aware probing for Continual finE-tuning. We perform a short warm-start fine-tune to derive task-specific core parameters by comparing the warm-started and pre-trained models. Core parameters are identified via two strategies: importance scoring (L$_2$ norm and Fisher Information) and specificity analysis (cosine similarity of parameter updates). In continual fine-tuning settings, only the active task's core parameters are updated while others remain frozen, preserving prior knowledge. We conduct extensive experiments across multiple standard benchmarks to demonstrate the superior performance of our proposed method. Additionally, we validate the generalization of our method through a cross-model and scale transferability study, demonstrating a "small-to-large" paradigm that guides the fine-tuning of large-scale models under resource constraints.

Large Language Models (LLMs) have demonstrated excellent performance in general language understanding, generation and other tasks. However, when fine-tuning for specific domain tasks, the general knowledge accumulated in the pre-training phase is often partially overwritten or forgotten due to parameter updates, which severely limits the generalization ability and transferability of LLMs. Traditional fine-tuning strategies mostly train on the entire parameter space, ignoring the heterogeneity of model parameters, that is, some parameters are extremely important for general tasks, while other parameters are more sensitive to specific tasks. To alleviate the above problems, this paper innovatively proposes a parameter element importance evaluation method, which divides parameters into "core parameters" and "non-core parameters" by distinguishing the importance of parameters for general language ability tasks and specific domain tasks, and fixes the core parameters during fine-tuning, and only fine-tunes the non-core parameters. Extensive experiments on scientific, medical and physical tasks using GPT-J and LLaMA-3 show that our method can mitigate catastrophic forgetting while enhancing the adaptability of the model.

Parameter-efficient finetuning (PEFT) has become the standard approach for adapting large language models, yet evaluations largely emphasize downstream accuracy while overlooking the retention of pretrained capabilities. We argue that PEFT should be assessed through the stability-plasticity dilemma: the trade-off between target-task adaptation and resistance to forgetting. We introduce PEFT-Arena, a benchmark that jointly measures downstream performance and general capability retention. Across methods, we find distinct stability-plasticity profiles; under comparable parameter budgets, orthogonal finetuning achieves the most favorable Pareto frontier. To explain these differences, we analyze PEFT updates from two geometric perspectives. In weight space, spectral analysis reveals how parameterizations interact with the pretrained singular-value structure. In activation space, retention metrics show whether finetuning preserves or distorts general-capability representations, with forgetting linked to non-isometric representation distortion. Finally, an analysis shows that final SFT checkpoints often overshoot a better target-retention operating point. Inspired by this, we present case studies of a post-hoc improvement with path-wise rewinding.