Signature-Guided Capacity Occupancy for Dense Expert Merging

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.

Model merging offers a training-free way to combine multiple post-trained expert models, but merging experts obtained through reinforcement learning (RL) remains challenging. Existing spectral merging methods often assume that leading singular directions contain the main task signal, while lower-energy residual components can be compressed, selected, or attenuated to reduce interference. We find that this assumption does not hold for RL task vectors: after decomposing each task vector into a leading spectral head and a residual component, both parts can independently recover substantial behavior knowledge, while exhibiting different merging properties. The head is highly concentrated and informative but more prone to sharp cross-expert conflicts, whereas the residual component is more dispersed and provides a more stable basis for aggregation. Based on this observation, we propose ResMerge, a residual-based spectral merging framework for RL experts. ResMerge first constructs a stable residual backbone with Spherical Residual Consensus Adaptation, which estimates a reliability-weighted consensus direction on the Frobenius sphere. It then reintroduces leading-head information through a Lightweight Head Correction module gated by positive cross-expert agreement. Experiments across multiple RL expert groups and capability domains show that ResMerge better preserves expert capabilities than representative task-vector and spectral merging baselines. The implementation of ResMerge is publicly available at https://github.com/sunyd0303-cpu/ResMerge-release.

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.