Accelerate Scaling of LLM Finetuning via Quantifying the Coverage and Depth of Instruction Set

Scaling the amount of data used for supervied fine-tuning(SFT) does not guarantee the proportional gains in model performance, highlighting a critical need to understand what makes training samples effective. This work identifies two fundamental dataset properties that govern SFT scalability: $\mathbf{\text{semantic}}\mathbf{\text{coverage}}$, or the breadth of task domains, and $\mathbf{\text{information}}\mathbf{\text{depth}}$, or the richness of individual examples. We demonstrate that simple proxies for these properties explain the majority of validation loss variance in our experiments. In this work, we further propose the $\mathbf{\text{Information}}\mathbf{\text{Landscape}}\mathbf{\text{Approximation}}\mathbf{\text{(ILA)}}$, a model-agnostic data selection framework that jointly optimizes for these two factors. ILA constructs compact subsets that approximate the informational value of large datasets. Empirical results show that models tuned on ILA-selected data achieve faster and more sustained performance improvements across diverse tasks and model sizes compared to existing methods, a phenomenon we term $\mathbf{\text{accelerated}}\mathbf{\text{scaling}}$.