Trade-offs in Ensembling, Merging and Routing Among Parameter-Efficient Experts

Model merging combines the parameters of multiple neural networks into a single model without additional training. As fine-tuned large language models (LLMs) proliferate, merging offers a computationally efficient alternative to ensembles and full retraining, enabling practitioners to compose specialized capabilities at minimal cost. This survey examines model merging in the LLM era through the FUSE taxonomy, organized along Foundations, Unification Strategies, Scenarios, and Ecosystem. We first establish the theoretical underpinnings of merging, including loss landscape geometry and mode connectivity, then systematically review the algorithmic space spanning weight averaging, task vector arithmetic, sparsification-enhanced methods, mixture-of-experts architectures, and evolutionary optimization. We further examine downstream applications across multi-task learning, safety alignment, domain specialization, and federated learning, and survey the supporting ecosystem of tools and evaluation benchmarks. Finally, we identify key open challenges and future directions, aiming to equip researchers and practitioners with a structured foundation for advancing model 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.

Ever since the advent of foundation models and the pre-training-finetuning paradigm, there have been numerous efforts to merge multiple task-specific experts into a single multi-task model. Prior work largely focuses on finding a single merged model, but it often underperforms individual experts due to parameter interference. To resolve this, dynamic model merging employs routing to activate task-relevant parameters per input. However, existing routers typically require either additional training with abundant labeled datasets or assume the access to task IDs of each input at inference time. In this work, we aim to close the gap to expert performance without additional training or task-ID-access assumption. To this end, we formulate routing as training-free task classification for each test input. Using singular value decomposition (SVD)-based low-rank manifold approximations for each task, SiM scores tasks by the projection residual of the test input feature onto each task manifold and routes accordingly. The task manifolds are pre-computable offline from a pretrained backbone using a small per-task support set (e.g., 32 examples per task) prior to merging process, requiring no router training and no data during the merging process. Moreover, SiM integrates seamlessly with subspace-/mask-based merging that represents task-expert via lightweight compressed task vectors, avoiding the need to store full expert parameters. Experiments across computer vision and natural language processing benchmarks under task-unknown inference demonstrate that SiM substantially improves merged-model performance and consistently narrows the gap to individual task experts.