Learning an Anchored Prompt Space for Continual Adaptation of Large Language Models

Continual learning remains challenging for large language models, which must enable models to acquire new skills and knowledge without degrading existing capabilities. Existing approaches typically address this challenge by carefully designing how model parameters are updated. In contrast, prompt optimization avoids costly parameter updates while achieving competitive or even superior performance to reinforcement learning methods such as GRPO on individual knowledge-intensive and reasoning tasks. This raises a natural question: Can prompt optimization, as an efficient adaptation approach, be directly applied to continual learning? Our analysis shows that, under sequential task adaptation, it suffers from catastrophic forgetting, while optimized prompts accumulate rules that overfit to local task distributions. To address these limitations, we propose Evolving Functional REpertoires (EFRE), which replaces a single prompt with a repertoire of functions that evolves as new tasks arrive: compatible updates refine existing functions, while conflicting updates trigger the emergence of new ones. On a three-task continual-learning stream, EFRE achieves a final average performance 7.50 percentage points higher than GRPO. Moreover, after adaptation to the Bio task, its performance on FinQA decreases by only 1.56 percentage points, compared with 25.10 percentage points for the base prompt optimization method. We further instantiate EFRE in a minimal agent system and observe consistent improvements across different backbone models. Overall, these results demonstrate EFRE's strong performance in continual learning for large language models and highlight its substantial potential for continual learning in advanced agent systems.

Automatic prompt optimization is a promising approach for adapting large language models (LLMs) to downstream tasks, yet existing methods typically search for a specific prompt specialized to a fixed task. This paradigm limits generalization across heterogeneous queries and prevents models from accumulating reusable prompting knowledge over time. In this paper, we propose MemAPO, a memory-driven framework that reconceptualizes prompt optimization as generalizable and self-evolving experience accumulation. MemAPO maintains a dual-memory mechanism that distills successful reasoning trajectories into reusable strategy templates while organizing incorrect generations into structured error patterns that capture recurrent failure modes. Given a new prompt, the framework retrieves both relevant strategies and failure patterns to compose prompts that promote effective reasoning while discouraging known mistakes. Through iterative self-reflection and memory editing, MemAPO continuously updates its memory, enabling prompt optimization to improve over time rather than restarting from scratch for each task. Experiments on diverse benchmarks show that MemAPO consistently outperforms representative prompt optimization baselines while substantially reducing optimization cost.

While prompt engineering is instrumental in maximizing the capabilities of Large Language Models (LLMs) during inference, the role of prompts during training remains critically underexplored. Prevailing fine-tuning paradigms typically treat training prompts as mere surface forms, assuming that semantically equivalent instructions yield identical learning outcomes. However, we reveal that this equivalence is deceptive: while paraphrased prompts often lead to comparable in-task performance, they induce drastically different cross-task impacts regarding catastrophic forgetting and generalization. Crucially, these impacts are positively correlated across tasks, indicating the existence of superior prompts that consistently yield better performance. Furthermore, we discover that these superior prompts can be robustly identified by task loss prior to learning. Leveraging these insights, we introduce State-Adaptive Prompt Optimization (SAPO), a lightweight yet effective training strategy that shifts task formulation from a static input to a dynamic, state-adaptive variable. Comprehensive experiments on diverse benchmarks confirm its effectiveness, which significantly mitigates forgetting while improving generalization, achieving substantial performance gains over state-of-the-art methods. These results provide insights into how training prompts shape learning dynamics and offer a practical recipe for robust fine-tuning. Our code is available at https://github.com/Eric8932/SAPO.