Unlocking the Potential of Continual Model Merging: An ODE Perspective

Model merging provides a compelling paradigm for integrating specialized expertise into a unified multi-task model, a goal that aligns naturally with the sequential knowledge acquisition in continual learning (CL). However, the requirement for preserving diverse forms of previous knowledge conflicts with the storage limitations inherent to CL. In this paper, we systematically analyze existing model merging methods under the constraints of CL. We find that current methods prioritize global alignment, which often leads to the accumulation and amplification of task-specific errors within the continuous data stream; and the vanishing gradients at the onset of subsequent tasks frequently cause optimization to stagnate. These leave the merged model in a suboptimal state at the beginning of the next training phase. To address these challenges, we propose Trajectory Regularized Merging (TRM), a framework that reformulates the merging phase as an optimization process within an augmented trajectory subspace. Our framework integrates three synergistic objectives including task alignment, prediction consistency, and gradient responsiveness to concurrently preserve merged model's historical stability and re-activate optimization dynamics. Extensive experimental results demonstrate that our method achieves state-of-the-art performance across multiple benchmarks.

Data-free continual model merging must incorporate a stream of specialized models while retaining both pretrained general knowledge and previously acquired tasks, without access to task data. Existing methods mainly merge task updates by suppressing interference among downstream tasks; while this protects previously acquired tasks, it overlooks the safety of the pretrained knowledge itself, whose erosion degrades generalization to held-out distributions and weakens the foundation for future task acquisition. We propose SAFE-Merge, a simple data-free continual-merging framework that first decides which parameter updates are safe to retain, and then recovers the task information lost through masking. Specifically, to ensure safety, risk-aware sparse masking selects parameter updates that carry task-specific information while posing low risk to general knowledge. Masked low-rank recovery then compensates for the lost task information using only the same retained parameter updates, while leaving all masked-out parameters strictly unchanged. Finally, the combined update is fused into the backbone, incurring no additional inference cost. Across vision and language benchmarks, SAFE-Merge consistently achieves the best H-score. On longer CLIP task sequences, it substantially improves H-score over NUFILT while also achieving the highest accuracy.

Continual learning (CL) aims to train models sequentially on multiple tasks while mitigating catastrophic forgetting of previously learned knowledge. Recent advances in large pre-trained models (LPMs) and model merging techniques, such as MAGMAX, have demonstrated effective CL performance by combining task-specific parameters. However, existing methods primarily focus on average performance across all tasks and do not adequately address how to construct models accommodating different deployment environments or varying user preferences. This paper proposes a model merging framework, termed Tunable MAGMAX, which enables preference-aware control of task-specific performance in CL. Our method introduces a preference vector that controls the number of elements selected from each task vector during model merging, allowing us to adjust the merged model performance according to their deployment needs. We further propose a method for automatically constructing appropriate preference vectors by leveraging small amounts of target environment data and datasets from model training tasks, thereby eliminating the need for manual specification. The experimental result on CL benchmark tasks demonstrates that Tunable MAGMAX effectively controls task-wise performance and successfully adapts merged models to various target environments. The proposed Tunable MAGMAX achieves superior or comparable performance to baseline methods, making it a practical solution for deploying CL models to various environments where the preferences of each task performance differ.