# Influence-Preserving Proxies for Gradient-Based Data Selection in LLM Fine-tuning

arXiv: https://arxiv.org/abs/2602.17835 · HTML: https://mlsanity.com/paper/2602.17835/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 70 references that are in the map.
- First posted on arXiv 19 Feb 2026.

## Builds on (most cited first, 30 of 53)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [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)
- [TyDi QA: A Benchmark for Information-Seeking Question Answering in Typologically Diverse Languages](https://mlsanity.com/paper/2003.05002/) (2020)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [How Far Can Camels Go? Exploring the State of Instruction Tuning on Open Resources](https://mlsanity.com/paper/2306.04751/) (2023)
- [DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining](https://mlsanity.com/paper/2305.10429/) (2023)
- [ShortGPT: Layers in Large Language Models are More Redundant Than You Expect](https://mlsanity.com/paper/2403.03853/) (2024)
- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)
- [SVD-LLM: Truncation-aware Singular Value Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2403.07378/) (2024)
- [Language model compression with weighted low-rank factorization](https://mlsanity.com/paper/2207.00112/) (2022)
- [Large Language Models Are Latent Variable Models: Explaining and Finding Good Demonstrations for In-Context Learning](https://mlsanity.com/paper/2301.11916/) (2023)
- [A Kronecker-factored approximate Fisher matrix for convolution layers](https://mlsanity.com/paper/1602.01407/) (2016)
- [DataInf: Efficiently Estimating Data Influence in LoRA-tuned LLMs and Diffusion Models](https://mlsanity.com/paper/2310.00902/) (2023)
- [DsDm: Model-Aware Dataset Selection with Datamodels](https://mlsanity.com/paper/2401.12926/) (2024)
- [MATES: Model-Aware Data Selection for Efficient Pretraining with Data Influence Models](https://mlsanity.com/paper/2406.06046/) (2024)
- [Compressing Large-Scale Transformer-Based Models: A Case Study on BERT](https://mlsanity.com/paper/2002.11985/) (2020)
- [A Survey on Data Selection for LLM Instruction Tuning](https://mlsanity.com/paper/2402.05123/) (2024)
- [Latent Collaboration in Multi-Agent Systems](https://mlsanity.com/paper/2511.20639/) (2025)
- [Compressing Large Language Models using Low Rank and Low Precision Decomposition](https://mlsanity.com/paper/2405.18886/) (2024)
- [MoE-I2: Compressing Mixture of Experts Models through Inter-Expert Pruning and Intra-Expert Low-Rank Decomposition](https://mlsanity.com/paper/2411.01016/) (2024)

## Built on by (most cited first, 10 of 10)

- [Prune as You Generate: Online Rollout Pruning for Faster and Better RLVR](https://mlsanity.com/paper/2603.24840/) (2026)
- [GIST: Targeted Data Selection for Instruction Tuning via Coupled Optimization Geometry](https://mlsanity.com/paper/2602.18584/) (2026)
- [ReMix: Reinforcement routing for mixtures of LoRAs in LLM finetuning](https://mlsanity.com/paper/2603.10160/) (2026)
- [PRISM: Preference-Aware Influence Function Based Data Selection Method for Efficient Fine-Tuning](https://mlsanity.com/paper/2605.21422/) (2026)
- [AvAtar: Learning to Align via Active Optimal Transport](https://mlsanity.com/paper/2605.24395/) (2026)
- [One Algorithm, Two Goals: Dual Scoring for Parameter and Data Selection in LLM Fine-Tuning](https://mlsanity.com/paper/2605.06166/) (2026)
- [Let the Target Select for Itself: Data Selection via Target-Aligned Paths](https://mlsanity.com/paper/2605.09404/) (2026)
- [Refreshing Less, Selecting Better: Reusing Stale Gradient Features for Efficient Influence-Based Data Selection](https://mlsanity.com/paper/2609.32888/) (2026)
- [Scaling Influence Functions in LLMs through Eigenbasis-Corrected One-Bit Gradient Projection](https://mlsanity.com/paper/2609.37842/) (2026)
- [Two For The Price Of One: Curvature-Aware Pruning Preserves Influence Functions Too](https://mlsanity.com/paper/2610.18516/) (2026)

## Abstract (arXiv)

Supervised fine-tuning (SFT) relies critically on selecting training data that most benefits a model's downstream performance. Gradient-based data selection methods such as TracIn and Influence Functions leverage influence to identify useful samples, but their computational cost scales poorly, making them impractical for multi-billion-parameter large language models (LLMs). A common alternative is to use off-the-shelf smaller models as proxies, but they remain suboptimal since their learning dynamics are unclear, their sizes cannot be flexibly adjusted, and they cannot be further aligned with the target model in terms of gradient-based influence estimation. To address these challenges, we introduce Iprox, a two-stage framework that derives influence-preserving proxies directly from the target model. It first applies a low-rank compression stage to preserve influence information of the target model, and then an aligning stage to align both model gradients and logits, thereby constructing proxies that flexibly control computational cost while retaining the target model's influence. Experimental results across diverse LLM families and evaluation tasks show that Iprox consistently outperforms off-the-shelf proxies and baseline methods. On Qwen3-4B, a 1.5B proxy constructed with Iprox achieves stronger performance than the larger 1.7B off-the-shelf proxy. Notably, on Llama3.2, Iprox achieves better performance than baselines while reducing computational cost by more than half relative to the full 3B model. These results show that Iprox provides effective influence-preserving proxies, making gradient-based data selection more scalable for LLMs.