Statistical learning in high-dimensional spaces is challenging without a strong underlying data structure. Recent advances with foundational models suggest that text and image data contain such hidden structures, which help mitigate the curse of dimensionality. Inspired by results from nonparametric statistics, we hypothesize that this phenomenon can be partially explained in terms of decomposition of complex tasks into simpler subtasks. In this paper, we present a controlled experimental framework to test whether neural networks can indeed exploit such ``hidden factorial structures.'' We find that they do leverage these latent patterns to learn discrete distributions more efficiently, and derive scaling laws linking model sizes, hidden factorizations, and accuracy. We also study the interplay between our structural assumptions and the models' capacity for generalization.

Multimodal Retrieval Augmented Generation (MMRAG) is a powerful approach to questionanswering over multimodal documents. A key challenge with evaluating MMRAG is the paucity of high-quality datasets matching the question styles and modalities of interest. In light of this, we propose SMMQG, a synthetic data generation framework. SMMQG leverages interplay between a retriever, large language model (LLM) and large multimodal model (LMM) to generate question and answer pairs directly from multimodal documents, with the questions conforming to specified styles and modalities. We use SMMQG to generate an MMRAG dataset of 1024 questions Figure 1: An overview of SMMQG. Given userprovided over Wikipedia documents and evaluate stateof-the-art question style and modality requirements, SMmodels using it, revealing insights MQG selects question sources and produces questions into model performance that are attainable only and answers. The questions are grounded in the selected through style-and modality-specific evaluation question sources, and adhere to the question and modality data. Next, we measure the quality of data produced requirements.