Organizations: Yokohama National University, Yokohama Kanagawa 240-8501, Japan
Abstract
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.
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.
Continual Model Merging (CMM) enables rapid customization of foundation models by sequentially incorporating task-adapted models without repeated retraining. However, existing merging rules usually update the deployed model through fixed algebraic or projection-based operations, providing limited control over how much previously accumulated knowledge should be retained relative to the incoming task model. This limitation leads to unstable retention and performance degradation in long task streams, and becomes more pronounced when tasks have heterogeneous utilities. We propose ODE-driven Merging (ODE-M), a controllable framework that formulates each continual merge as a trajectory in parameter space rather than a one-step endpoint update. Motivated by mode connectivity, ODE-M constructs a barrier-aware trajectory using a rectified time-dependent velocity field, where lightweight first-order feedback from a small calibration set suppresses loss-increasing motion while preserving progress toward the incoming model. The next merged model is then obtained by selecting an operating point along this trajectory through a utility-aware time schedule, providing an explicit mechanism for balancing retained historical knowledge and incoming task expertise. Extensive experiments on standard CMM benchmarks show that ODE-M consistently improves over strong continual merging baselines across CLIP ViT backbones, stream lengths, and heterogeneous task-utility settings.
In the literature, many continual learning (CL) algorithms have been proposed to address the issue of catastrophic forgetting in ML models (i.e., learning new tasks leads to the loss of performance on previously learned tasks). Although all CL approaches use some form of memory to retain information about past tasks, a grounded understanding of what information needs to be stored to minimize catastrophic forgetting remains elusive. Recently, it has been recognized that under the strong assumption of the existence of a common global minimizer over all tasks, catastrophic forgetting can be completely avoided. However, in practice, tasks rarely have a common global minimizer, and a certain amount of forgetting is inevitable. In this paper, we propose a foundational framework for principled and systematic CL of conflicting tasks using a multi-task learning (MTL) perspective. The approach is based on finding Pareto-optimal solutions, i.e., the solutions which, by definition, minimally forget the previous tasks in the Pareto sense. We derive Pareto-minimal-forgetting CL algorithms for linear and basis-function regression, and general loss functions which have a quadratic upper bound, e.g., logistic regression. For quadratic problems, PMF-CL uses memory-efficient iterative updates with a static memory footage of O(d2) for models with d parameters.