# GRIP: Geometric Refinement and Adaptive Information Potential for Data Efficiency

arXiv: https://arxiv.org/abs/2603.00031 · HTML: https://mlsanity.com/paper/2603.00031/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in MoE large language models, one of 12 directions in Mixture-of-experts.
- Builds on 34 of its 40 references that are in the map.
- First posted on arXiv 4 Feb 2026.

## Placed in

- Mixture-of-experts / [MoE large language models](https://mlsanity.com/moe/moe-large-language-models/)

## Builds on (most cited first, 30 of 34)

- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [SimCSE: Simple Contrastive Learning of Sentence Embeddings](https://mlsanity.com/paper/2104.08821/) (2021)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [CodeBERT: A Pre-Trained Model for Programming and Natural Languages](https://mlsanity.com/paper/2002.08155/) (2020)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [StarCoder: may the source be with you!](https://mlsanity.com/paper/2305.06161/) (2023)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [GraphCodeBERT: Pre-training Code Representations with Data Flow](https://mlsanity.com/paper/2009.08366/) (2020)
- [Textbooks Are All You Need](https://mlsanity.com/paper/2306.11644/) (2023)
- [Beyond neural scaling laws: beating power law scaling via data pruning](https://mlsanity.com/paper/2206.14486/) (2022)
- [StarCoder 2 and The Stack v2: The Next Generation](https://mlsanity.com/paper/2402.19173/) (2024)
- [DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining](https://mlsanity.com/paper/2305.10429/) (2023)
- [Data Selection for Language Models via Importance Resampling](https://mlsanity.com/paper/2302.03169/) (2023)
- [SemDeDup: Data-efficient learning at web-scale through semantic deduplication](https://mlsanity.com/paper/2303.09540/) (2023)
- [CRUXEval: A Benchmark for Code Reasoning, Understanding and Execution](https://mlsanity.com/paper/2401.03065/) (2024)
- [Understanding Dataset Difficulty with V-Usable Information](https://mlsanity.com/paper/2110.08420/) (2021)
- [A Theory of Usable Information Under Computational Constraints](https://mlsanity.com/paper/2002.10689/) (2020)
- [D4: Improving LLM Pretraining via Document De-Duplication and Diversification](https://mlsanity.com/paper/2308.12284/) (2023)
- [Language models scale reliably with over-training and on downstream tasks](https://mlsanity.com/paper/2403.08540/) (2024)
- [LongAlign: A Recipe for Long Context Alignment of Large Language Models](https://mlsanity.com/paper/2401.18058/) (2024)
- [InfoBatch: Lossless Training Speed Up by Unbiased Dynamic Data Pruning](https://mlsanity.com/paper/2303.04947/) (2023)
- [Scaling Laws for Data Filtering -- Data Curation cannot be Compute Agnostic](https://mlsanity.com/paper/2404.07177/) (2024)
- [Capturing the Temporal Dependence of Training Data Influence](https://mlsanity.com/paper/2412.09538/) (2024)
- [Harnessing Diversity for Important Data Selection in Pretraining Large Language Models](https://mlsanity.com/paper/2409.16986/) (2024)

## Abstract (arXiv)

The performance of Large Language Models (LLMs) is increasingly governed by data efficiency rather than raw scaling volume. However, existing selection methods often decouple global distribution balancing from local instance selection, compromising the hierarchical integrity of the training set. We introduce GRIP (Geometric Refinement and Adaptive Information Potential), a framework that unifies these dimensions by modeling the corpus as an information-dense geometric space. GRIP employs a Rapid Adaptation Probe (RAP) to quantify the information potential of semantic clusters, dynamically re-allocating the sampling budget to regions with the highest representation deficits. Subsequently, we perform Intra-Cluster Selection using a length-rectified geometric prior to counteract embedding density artifacts and preserve long-tail logical sequences. Extensive evaluations on Mixture-of-Experts (MoE) models up to 300B tokens demonstrate that GRIP consistently outperforms state-of-the-art baselines, surpassing the performance of models trained on 3× larger uncurated datasets. Our work establishes a robust geometric foundation for adaptive data curation in large-scale pre-training.