Darwin Family: MRI-Trust-Weighted Evolutionary Merging for Training-Free Scaling of Language-Model Reasoning

Model merging has emerged as a lightweight paradigm for enhancing Large Language Models (LLMs), yet its underlying mechanisms remain poorly understood. In this work, we analyze late-stage pre-training trajectories and uncover a \textbf{Rank-1 Subspace} phenomenon: while raw optimization steps oscillate violently, consecutive \emph{merged} checkpoints collapse onto a stable, approximately one-dimensional linear manifold. We theoretically ground this observation in a \emph{river-valley} landscape analysis: averaging acts as a geometric low-pass filter that dampens high-curvature noise to reveal the optimal descent direction. Capitalizing on this insight, we propose \textbf{Extra-Merge}, a training-free strategy that extrapolates along this subspace to minimize loss without additional gradient updates. Extensive experiments across GPT-2 and LLaMA families (124M to 2B) demonstrate that Extra-Merge consistently outperforms standard merging baselines. Notably, it yields consistent zero-shot accuracy gains on Pythia-12B downstream tasks and generalizes effectively to the Muon optimizer \citep{jordan2024muon}.

Evolutionary model merging provides a powerful framework for the automated, training-free composition of LLMs through parameter-space search. However, existing methods predominantly rely on stochastic, hand-crafted operators that overlook the underlying performance landscape of the coefficient space. We propose Evolutionary Generative Merging (EvoGM), a framework that transcends manual heuristics by employing learnable generative modeling to optimize merging coefficients. Specifically, EvoGM features a dual-generator architecture with cycle-consistent learning to adaptively sample and refine promising merging candidates. By constructing winner-loser pairs from historical search trajectories, our framework effectively captures high-performance parameter distributions and maximizes data efficiency. This generative process is seamlessly integrated into a multi-round evolutionary pipeline, where elite merged models iteratively serve as new expert foundations. Extensive experiments across diverse benchmarks demonstrate that EvoGM significantly outperforms state-of-the-art baselines, exhibiting robust performance on both seen and unseen tasks. Code and data are available at https://github.com/JiangTao97/evogm.

Model merging has emerged as a cost-effective alternative to training large language models (LLMs) from scratch, enabling researchers to combine pre-trained models into more capable systems without full retraining. Evolutionary approaches to model merging have shown particular promise, automatically searching for optimal merging configurations across both parameter space (PS) and data flow space (DFS). However, the optimization challenges underlying these approaches -- particularly in DFS merging -- remain poorly understood and formally underspecified in the literature. This paper makes two contributions. First, we provide a structured survey of evolutionary model merging techniques, organizing them into three categories: parameter-space merging, data flow space merging, and hybrid approaches. Second, we formally characterize the DFS merging problem as a black-box optimization problem involving mixed binary-continuous variables, high-dimensional search spaces, and conditional dependencies between variable types -- challenges that standard optimization methods such as CMA-ES are not designed to handle. We provide preliminary empirical validation using real pre-trained language models, demonstrating that a structured approach respecting the binary-continuous conditional dependency outperforms an unstructured approach by 6.7% accuracy while reducing the effective search space by 51.4%. By connecting the model merging community with the broader evolutionary computation and black-box optimization literature, we identify concrete open problems and propose research directions to address them.