Rethinking Expert Training for Model Merging with Prompt Learning

Multi-task model merging combines separately trained expert models into a single model that handles all tasks without co-training. Standard practice merges experts at their optimal validation loss. We challenge this convention by systematically studying how training duration of domain experts affects the quality of the merged model. We fine-tune experts on five domains (Math, Code, Instruction Following, Multilingual, and Safety) across three model sizes (Qwen 3.5 0.8B, 2B, and 4B), saving checkpoints from 25% to 500% of the optimal training steps and evaluating five merging methods at each duration. Our findings reveal a striking method-dependent pattern: simple averaging degrades sharply with overfitting, while sparsification-based methods achieve their best performance well past the validation optimum. We formalize this through bias-variance decomposition analysis, drawing a parallel to random forests where averaging benefits from high-variance individual learners. These results suggest that training duration and merging method should be chosen jointly rather than independently.

Multi-task model merging aims to consolidate several task-specific experts into a unified model, yet static merging consistently suffers from parameter interference. While dynamic merging models aim to bridge this gap, many works rely on the costly storage and loading of redundant expert components at inference. In this work, from the perspective of task expert, we view parameter interference as parameter perturbation introduced to each expert during merging process. We show that such parameter perturbations can be modeled as affine transformation, which can be approximated as additive offsets. Motivated by these, we propose Recover Task eXpert (ReTeX), a framework that predicts those offsets, in order to undo parameter interference and recover task-expert performance from a single merged checkpoint. To recover the appropriate expert when task identity is unknown, we introduce a router-free task identifier based on SVD subspace signatures computed offline before inference. At inference, the identifier selects the task whose subspace yields the smallest projection residual for a given input. As a result, ReTeX recovers over 95% of individual-expert performance in both vision and NLP domains, while significantly improving generalization to unseen tasks. Crucially, we also show that the parameter offset prediction leads to emergent adaptive interpolation of expert knowledge for out-of-distribution (OOD) tasks. ReTeX adaptively interpolates seen expert knowledge to handle unseen tasks. Our code is available at https://github.com/BAIKLAB/ReTeX

Model merging enables the reuse of fine-tuned models without joint training or access to original data. Dynamic merging further improves flexibility by selectively activating task-relevant parameters and efficiently composing experts across multiple tasks. However, existing dynamic methods either maintain a full shared model with tiny experts or allocate excessive capacity to experts, leading to suboptimal accuracy--efficiency trade-offs. To address this, we propose DiDi-Merging, a slim dynamic merging framework that leverages differentiable rank allocation to balance shared and expert parameters. By formulating parameter budgeting as differentiable rank optimization in low-rank modules and introducing a data-free refinement step to recover task fidelity, DiDi-Merging matches prior dynamic baselines at only 1.24x the parameters of a single fine-tuned model and surpasses them at 1.4x, substantially more compact than methods requiring > 2x storage. DiDi-Merging applies across vision, language, and multimodal tasks.