# D3: Dynamic Directional Graph-Constrained Data Scheduling for LLM Training

arXiv: https://arxiv.org/abs/2605.31164 · HTML: https://mlsanity.com/paper/2605.31164/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 50 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 30 of 36)

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- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
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- [WPO: Enhancing RLHF with Weighted Preference Optimization](https://mlsanity.com/paper/2406.11827/) (2024)
- [Scaling Laws for Optimal Data Mixtures](https://mlsanity.com/paper/2507.09404/) (2025)
- [Strategic Data Ordering: Enhancing Large Language Model Performance through Curriculum Learning](https://mlsanity.com/paper/2405.07490/) (2024)
- [Dataset Decomposition: Faster LLM Training with Variable Sequence Length Curriculum](https://mlsanity.com/paper/2405.13226/) (2024)
- [Dynamic Loss-Based Sample Reweighting for Improved Large Language Model Pretraining](https://mlsanity.com/paper/2502.06733/) (2025)
- [Chameleon: A Flexible Data-mixing Framework for Language Model Pretraining and Finetuning](https://mlsanity.com/paper/2505.24844/) (2025)
- [Group-Level Data Selection for Efficient Pretraining](https://mlsanity.com/paper/2502.14709/) (2025)
- [Velocitune: A Velocity-based Dynamic Domain Reweighting Method for Continual Pre-training](https://mlsanity.com/paper/2411.14318/) (2024)

## Abstract (arXiv)

Training data plays a central role in large language models (LLMs) optimization, motivating extensive research on data scheduling strategies. Most existing approaches concentrate on adjusting the overall data distribution but neglect the underlying interactions between samples during training. However, we argue that such interactions cannot be overlooked, as real-world data samples frequently exhibit directional influences on each other, making the training order crucial. Intuitively, we can prioritize train-units with greater influence to improves learning efficiency. In this work, we propose D3, a Dynamic Directional graph-constrained Data scheduling framework. D3 formulates the complex interactions among train-units as a dynamic influence graph, where edges represent loss-based dependencies. It then solves a constrained optimization problem over this graph to derive the training order, which ensures that the data sequence respects the evolving information flow throughout training. Our approach is theoretically motivated and yields consistent improvements over existing data scheduling methods across both pre-training and post-training phases. Furthermore, for scalability, D3 also employs an efficient approximation algorithm that keeps the additional computational overhead within a manageable range. For future research, the code is available at https://github.com/xuyj233/D3.