Model merging offers an effective way to integrate the capabilities of multiple fine-tuned models. However, the performance degradation of the merged model remains a challenge, particularly when none or few data are available. This paper first highlights the necessity of domain-specific data for model merging by proving that data-agnostic algorithms can have arbitrarily bad worst-case performances. Building on this theoretical insight, we explore the relationship between model merging and distillation, introducing a novel few-shot merging algorithm, ProDistill (Progressive Layer-wise Distillation). Unlike common belief that layer-wise training hurts performance, we show that layer-wise teacher-student distillation not only enhances the scalability but also improves model merging performance. We conduct extensive experiments to show that compared to existing few-shot merging methods,ProDistill achieves state-of-the-art performance, with up to 6.14\% and 6.61\% improvements in vision and NLU tasks. Furthermore, we extend the experiments to models with over 10B parameters, showcasing the exceptional scalability of ProDistill.

Large Language Models (LLMs) are typically trained on data mixtures: most data come from web scrapes, while a small portion is curated from high-quality sources with dense domain-specific knowledge. In this paper, we show that when training LLMs on such data mixtures, knowledge acquisition from knowledge-dense datasets—unlike training exclusively on knowledge-dense data—does not always follow a smooth scaling law but can exhibit phase transitions with respect to the mixing ratio and model size. Through controlled experiments on a synthetic biography dataset mixed with web-scraped data, we demonstrate that: (1) as we increase the model size to a critical value, the model suddenly transitions from memorizing very few to most of the biographies; (2) below a critical mixing ratio, the model memorizes almost nothing even with extensive training, but beyond this threshold, it rapidly memorizes more biographies. We attribute these phase transitions to a capacity allocation phenomenon: a model with bounded capacity must act like a knapsack problem solver to minimize the overall test loss, and the optimal allocation across datasets can change discontinuously as the model size or mixing ratio varies. We formalize this intuition in an information-theoretic framework and reveal that these phase transitions are predictable, with the critical mixing ratio following a power-law relationship with the model size. Our findings highlight a concrete case where a good mixing recipe for large models may not be optimal for small models, and vice versa.