To mitigate catastrophic forgetting in downstream continual learning (CL) for large language models (LLMs), existing methods typically constrain parameter updates or introduce task-specific adaptation modules. However, these methods often rely on explicit task boundaries during training, limiting their applicability to realistic task-free scenarios.

In this paper, we propose a Fisher-guided unified (FiUni) framework for batch-level task detection and parameter-efficient continual adaptation. FiUni is motivated by a key observation about the Fisher information matrix (FIM) of pre-trained models: the orthogonality among the principal subspaces of its Kronecker-Factored Approximate Curvature (K-FAC) approximation, estimated from a small number of downstream task samples, can reflect the similarity between different tasks.

Based on this observation, FiUni constructs FIM-derived frozen subspaces to guide low-rank adaptation (LoRA), while matching the Fisher principal subspace of each incoming batch window with historical subspaces. This enables FiUni to adaptively determine whether to reuse existing knowledge, expand a related subspace, or create a new subspace, dynamically balancing knowledge sharing and task isolation.

Experiments show that FiUni can effectively infer latent batch-level task affiliations and achieve competitive performance against advanced task-aware CL methods with fewer trainable parameters.