# Influential Language Data Selection via Gradient Trajectory Pursuit

arXiv: https://arxiv.org/abs/2410.16710 · HTML: https://mlsanity.com/paper/2410.16710/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 60 references that are in the map.
- First posted on arXiv 22 Oct 2024.

## Builds on (most cited first, 30 of 46)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [ALFWorld: Aligning Text and Embodied Environments for Interactive Learning](https://mlsanity.com/paper/2010.03768/) (2020)
- [Gemma: Open Models Based on Gemini Research and Technology](https://mlsanity.com/paper/2403.08295/) (2024)
- [The Flan Collection: Designing Data and Methods for Effective Instruction Tuning](https://mlsanity.com/paper/2301.13688/) (2023)
- [OpenAssistant Conversations -- Democratizing Large Language Model Alignment](https://mlsanity.com/paper/2304.07327/) (2023)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [Dataset Condensation with Gradient Matching](https://mlsanity.com/paper/2006.05929/) (2020)
- [TyDi QA: A Benchmark for Information-Seeking Question Answering in Typologically Diverse Languages](https://mlsanity.com/paper/2003.05002/) (2020)
- [Dataset Distillation by Matching Training Trajectories](https://mlsanity.com/paper/2203.11932/) (2022)
- [How Far Can Camels Go? Exploring the State of Instruction Tuning on Open Resources](https://mlsanity.com/paper/2306.04751/) (2023)
- [Data Selection for Language Models via Importance Resampling](https://mlsanity.com/paper/2302.03169/) (2023)
- [TextWorld: A Learning Environment for Text-based Games](https://mlsanity.com/paper/1806.11532/) (2018)
- [Stochastic Gradient Descent as Approximate Bayesian Inference](https://mlsanity.com/paper/1704.04289/) (2017)
- [GRAD-MATCH: Gradient Matching based Data Subset Selection for Efficient Deep Model Training](https://mlsanity.com/paper/2103.00123/) (2021)
- [Convergence of denoising diffusion models under the manifold hypothesis](https://mlsanity.com/paper/2208.05314/) (2022)
- [Prioritized Training on Points that are Learnable, Worth Learning, and Not Yet Learnt](https://mlsanity.com/paper/2206.07137/) (2022)

## Built on by (most cited first, 7 of 7)

- [ICONS: Influence Consensus for Vision-Language Data Selection](https://mlsanity.com/paper/2501.00654/) (2024)
- [Synthetic Data Generation for Training Diversified Commonsense Reasoning Models](https://mlsanity.com/paper/2603.18361/) (2026)
- [Filter-then-Weight: Online Data Selection and Reweighting for LLM Fine-Tuning](https://mlsanity.com/paper/2604.00001/) (2026)
- [GRACE: A Dynamic Coreset Selection Framework for Large Language Model Optimization](https://mlsanity.com/paper/2604.11810/) (2026)
- [Let the Target Select for Itself: Data Selection via Target-Aligned Paths](https://mlsanity.com/paper/2605.09404/) (2026)
- [MAGIC: Multimodal Alignment & Grounding-aware Instruction Coreset for Vision-Language Models](https://mlsanity.com/paper/2605.26004/) (2026)
- [Every Batch Is Its Own Validation Set: Leave-One-Out Gradient Matching for Online Data Selection in LLM Fine-Tuning](https://mlsanity.com/paper/2610.00436/) (2026)

## Abstract (arXiv)

Curating a desirable dataset for training has been the core of building highly capable large language models (Touvron et al., 2023; Achiam et al., 2023; Team et al.,2024). Gradient influence scores (Pruthi et al., 2020; Xia et al., 2024) are shown to be correlated with model performance and are commonly used as the criterion for data selection. However, existing methods are built upon either individual sample rankings or inefficient matching process, leading to suboptimal performance or scaling up issues.In this paper, we propose Gradient Trajectory Pursuit (GTP), an algorithm that performs pursuit of gradient trajectories via jointly selecting data points under an L0-norm regularized objective. The proposed algorithm highlights: (1) joint selection instead of independent top-k selection, which automatically de-duplicates samples; (2) higher efficiency with compressive sampling processes, which can be further sped up using a distributed framework. In the experiments, we demonstrate the algorithm in both in-domain and target-domain selection benchmarks and show that it outperforms top-k selection and competitive algorithms consistently, for example, our algorithm chooses as low as 0.5% data to achieve full performance on the targeted instruction tuning tasks