Recent research demonstrates that pretrained large language models (LLMs) require minimal but carefully curated data for instruction-tuning. Building on LLMs, multi-modal models further contend with far larger data volumes, heterogeneous sources, and cross-modal alignment, amplifying both the necessity and the complexity of data selection. However, existing methods rely on deeply extracted embeddings, gradients or narrow quality scores that are time-consuming to compute and limited in expressiveness, frequently failing to surpass a simple random-sampling baseline. To overcome these limitations, we step back from complex embedding spaces and target the fundamental objective of instruction tuning: how and what knowledge should be elicited from the pretrained model and exposed to users. We leverage interaction Styles as a proxy for structural diversity, and decompose data quality into capability-specific Scores, yielding an explicit yet Rich (SSR) profile for each sample. We further cast the selection as submodular coverage maximization over the capability-style grid, providing an approximation guarantee. SSR consistently delivers superior performance across two distinct architecture stacks, LLaVA-1.5 (Vicuna + CLIP) and LLaVA-OneVision (Qwen2 + SigLIP), two large-scale data pools, six data budget settings, and 14 multi-modal benchmarks. To our knowledge, SSR is the first data selection method validated at million-scale, achieving 99.1% of full-data performance using only 30% of a 2.6M pool. Furthermore, the SSR profile models and selected subsets transfer training-free across data pools and model architectures with capability extensibility.

Pre-training on large, high-quality datasets is essential for improving the reasoning abilities of Large Language Models (LLMs), particularly in specialized fields like mathematics. However, the field of Multimodal LLMs (MLLMs) lacks a comprehensive, open-source dataset for mathematical reasoning. To fill this gap, we present InfiMM-WebMath-40B, a high-quality dataset of interleaved image-text documents. It consists of 24 million web pages, 85 million image URLs, and 40 billion text tokens, all carefully extracted and filtered from CommonCrawl. We outline our data collection and processing pipeline in detail. Models trained on InfiMM-WebMath-40B demonstrate strong performance in both text-only and multimodal settings, setting a new state-of-the-art on multimodal math benchmarks such as MathVerse and We-Math.