Learning Task Mixtures from Task Affinities: A Probabilistic Graphical Model for Supervised Fine-Tuning

Supervised fine-tuning performance for large language models depends strongly on how training budget is distributed across a heterogeneous set of tasks. In practice, mixtures are often fixed using simple heuristics (e.g., uniform or size-proportional sampling) that ignore task interactions, which can hurt transfer and waste budget on redundant sources. We introduce TaskPGM, a framework for learning continuous task mixtures via an energy-based model over tasks. Tasks form the nodes of a Markov random field: unary potentials capture per-task utility, and pairwise potentials encode inter-task relationships using behavioral divergences computed from predictive distributions of single-task fine-tuned models (e.g., Jensen--Shannon divergence and pointwise mutual information). Optimizing this objective yields mixtures that balance coverage against redundancy. We show that the resulting set function is weakly submodular under budget constraints, enabling approximation guarantees for discrete selection variants. Empirically, a fixed benchmark-independent TaskPGM--PMI mixture improves over heuristic mixing across two 7B model families (Qwen2-7B, Llama2-7B) and two budgets (25K/50K), while TaskPGM--JSD provides complementary gains on instruction-following and science QA. TaskPGM additionally yields interpretable structure over task interactions.