# Hierarchical Data Selection via Manifold Coverage and Sparse Feature Coverage in LLM Post-training

arXiv: https://arxiv.org/abs/2608.16927 · HTML: https://mlsanity.com/paper/2608.16927/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 50 references that are in the map.
- First posted on arXiv 5 Aug 2026.

## Builds on (most cited first, 30 of 33)

- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Improved Baselines with Visual Instruction Tuning](https://mlsanity.com/paper/2310.03744/) (2023)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [MMBench: Is Your Multi-modal Model an All-around Player?](https://mlsanity.com/paper/2307.06281/) (2023)
- [Towards VQA Models That Can Read](https://mlsanity.com/paper/1904.08920/) (2019)
- [ChartQA: A Benchmark for Question Answering about Charts with Visual and Logical Reasoning](https://mlsanity.com/paper/2203.10244/) (2022)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [DocVQA: A Dataset for VQA on Document Images](https://mlsanity.com/paper/2007.00398/) (2020)
- [VizWiz Grand Challenge: Answering Visual Questions from Blind People](https://mlsanity.com/paper/1802.08218/) (2018)
- [A Diagram Is Worth A Dozen Images](https://mlsanity.com/paper/1603.07396/) (2016)
- [Deep Learning on a Data Diet: Finding Important Examples Early in Training](https://mlsanity.com/paper/2107.07075/) (2021)
- [Measuring Multimodal Mathematical Reasoning with MATH-Vision Dataset](https://mlsanity.com/paper/2402.14804/) (2024)
- [LLaVA-CoT: Let Vision Language Models Reason Step-by-Step](https://mlsanity.com/paper/2411.10440/) (2024)
- [We-Math: Does Your Large Multimodal Model Achieve Human-like Mathematical Reasoning?](https://mlsanity.com/paper/2407.01284/) (2024)
- [LogicVista: Multimodal LLM Logical Reasoning Benchmark in Visual Contexts](https://mlsanity.com/paper/2407.04973/) (2024)
- [LLaVA-OneVision-1.5: Fully Open Framework for Democratized Multimodal Training](https://mlsanity.com/paper/2509.23661/) (2025)
- [Qwen3-VL-Embedding and Qwen3-VL-Reranker: A Unified Framework for State-of-the-Art Multimodal Retrieval and Ranking](https://mlsanity.com/paper/2601.04720/) (2026)
- [k-Sparse Autoencoders](https://mlsanity.com/paper/1312.5663/) (2013)
- [GME: Improving Universal Multimodal Retrieval by Multimodal LLMs](https://mlsanity.com/paper/2412.16855/) (2024)
- [Vision-Flan: Scaling Human-Labeled Tasks in Visual Instruction Tuning](https://mlsanity.com/paper/2402.11690/) (2024)
- [D2 Pruning: Message Passing for Balancing Diversity and Difficulty in Data Pruning](https://mlsanity.com/paper/2310.07931/) (2023)
- [PRISM: Self-Pruning Intrinsic Selection Method for Training-Free Multimodal Data Selection](https://mlsanity.com/paper/2502.12119/) (2025)
- [Large-Scale Data Selection for Instruction Tuning](https://mlsanity.com/paper/2503.01807/) (2025)
- [ICONS: Influence Consensus for Vision-Language Data Selection](https://mlsanity.com/paper/2501.00654/) (2024)
- [OPUS: Towards Efficient and Principled Data Selection in Large Language Model Pre-training in Every Iteration](https://mlsanity.com/paper/2602.05400/) (2026)
- [FisherSFT: Data-Efficient Supervised Fine-Tuning of Language Models Using Information Gain](https://mlsanity.com/paper/2505.14826/) (2025)
- [MIG: Automatic Data Selection for Instruction Tuning by Maximizing Information Gain in Semantic Space](https://mlsanity.com/paper/2504.13835/) (2025)
- [CoIDO: Efficient Data Selection for Visual Instruction Tuning via Coupled Importance-Diversity Optimization](https://mlsanity.com/paper/2510.17847/) (2025)

## Abstract (arXiv)

As supervised fine-tuning data continues to scale, selecting high-value subsets from large candidate pools is crucial for reducing training cost and improving model performance. Existing methods often measure diversity directly in the original embedding space, where geometric metrics entangle dominant semantic directions, fine-grained supervision differences, and local noise. We address this limitation by formulating data selection as a coarse-to-fine hierarchical coverage problem and propose MASS. MASS learns low-dimensional principal manifold coordinates with a dense autoencoder for coarse semantic grouping, and then performs quality-aware sparse feature coverage within each group using a TopK sparse autoencoder. Experiments on Vision Flan and LLaVA-CoT show that MASS consistently outperforms strong data selection baselines across multiple budgets, and in several settings matches or surpasses full data training with only a small subset of data.