Abstract: As large language models (LLMs) become increasingly capable, their ability to exhibit *compositional generalization of skills*—i.e., utilizing combinations of skills in ways not encountered during training—has garnered significant attention. Such generalization, especially beyond training scenarios, is also of interest in study of AI safety and alignment. A recent study introduced the Skill-Mix evaluation, where models are tasked with composing a short paragraph demonstrating the use of a specified $k$-tuple of language skills. While small models struggled with composing even with $k=3$, larger models like GPT-4 showed reasonable performance with $k=5$ and $6$.In this paper, we employ a setup akin to Skill-Mix to evaluate the capacity of smaller models to learn compositional generalization from examples. Utilizing a diverse set of language skills—including rhetorical, literary, reasoning, theory of mind, and common sense—--GPT was used to generate text samples that exhibit random subsets of $k$ skills. Subsequent fine-tuning of 7B and 13B parameter models on these combined skill texts, for increasing values of $k$, revealed the following findings: (1) Training on combinations of $k=2$ and $3$ skills results in noticeable improvements in the ability to compose texts with $k=4$ and $5$ skills, despite models never having seen such examples during training. (2) When skill categories are split into training and held-out groups, models significantly improve at composing texts with held-out skills during testing despite having only seen training skills during fine-tuning, illustrating the efficacy of the training approach even with previously unseen skills.This study also suggests that incorporating skill-rich (potentially synthetic) text into training can substantially enhance the compositional capabilities of models.