# Refreshing Less, Selecting Better: Reusing Stale Gradient Features for Efficient Influence-Based Data Selection

arXiv: https://arxiv.org/abs/2609.32888 · HTML: https://mlsanity.com/paper/2609.32888/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 34 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 29 of 29)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [The Flan Collection: Designing Data and Methods for Effective Instruction Tuning](https://mlsanity.com/paper/2301.13688/) (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)
- [What Makes Good Data for Alignment? A Comprehensive Study of Automatic Data Selection in Instruction Tuning](https://mlsanity.com/paper/2312.15685/) (2023)
- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [GRAD-MATCH: Gradient Matching based Data Subset Selection for Efficient Deep Model Training](https://mlsanity.com/paper/2103.00123/) (2021)
- [A Survey on Data Selection for Language Models](https://mlsanity.com/paper/2402.16827/) (2024)
- [DataInf: Efficiently Estimating Data Influence in LoRA-tuned LLMs and Diffusion Models](https://mlsanity.com/paper/2310.00902/) (2023)
- [#InsTag: Instruction Tagging for Analyzing Supervised Fine-tuning of Large Language Models](https://mlsanity.com/paper/2308.07074/) (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)
- [What is Your Data Worth to GPT? LLM-Scale Data Valuation with Influence Functions](https://mlsanity.com/paper/2405.13954/) (2024)
- [Data Diversity Matters for Robust Instruction Tuning](https://mlsanity.com/paper/2311.14736/) (2023)
- [Capturing the Temporal Dependence of Training Data Influence](https://mlsanity.com/paper/2412.09538/) (2024)
- [G-DIG: Towards Gradient-based Diverse and High-quality Instruction Data Selection for Machine Translation](https://mlsanity.com/paper/2405.12915/) (2024)
- [TAGCOS: Task-agnostic Gradient Clustered Coreset Selection for Instruction Tuning Data](https://mlsanity.com/paper/2407.15235/) (2024)
- [Improving Influence-based Instruction Tuning Data Selection for Balanced Learning of Diverse Capabilities](https://mlsanity.com/paper/2501.12147/) (2025)
- [Rethinking Data Selection at Scale: Random Selection is Almost All You Need](https://mlsanity.com/paper/2410.09335/) (2024)
- [D3: Diversity, Difficulty, and Dependability-Aware Data Selection for Sample-Efficient LLM Instruction Tuning](https://mlsanity.com/paper/2503.11441/) (2025)
- [Influence-Preserving Proxies for Gradient-Based Data Selection in LLM Fine-tuning](https://mlsanity.com/paper/2602.17835/) (2026)

## Abstract (arXiv)

Gradient-based data selection methods such as LESS score each candidate by the alignment between its gradient and a target validation gradient, and recomputing per-example gradient features at every new checkpoint dominates their cost. Across three selection seeds, two model families, two candidate pools, and two target tasks, features cached at a post-warmup checkpoint and paired with fresh validation gradients preserve the ranking 40 optimizer steps later with Spearman correlation from 0.952 to 0.991, while the top-10% subset they induce misses 10 to 22% of the examples that full recomputation selects. We therefore propose Cached Diverse Influence Selection (CDIS), which recomputes gradient features for the top-ranked fraction p of candidates under the stale scores, fits an affine calibration on the recomputed examples, and selects the final subset under source and length quotas. A refresh fraction at or above the selection fraction recovers the exact top-k subset whenever the calibrated stale scores have bounded error, and the budget curves follow this rule: at p=0.3 the recovered top-k subset coincides with full recomputation in every setting, allocating the same budget per stratum recovers the stratified subset at 0.92 to 1.00, and gradient-stage wall-clock drops 3.5 to 3.6 times. Iterating the cache over four checkpoints keeps top-k overlap at 0.98 or higher at 1.9 gradient features per example against 4 for full recomputation, and stale-to-recomputed agreement on the refreshed examples provides a free check for unsafe reuse. Downstream, unconstrained top-k selection collapses to a single data source and scores 13 points below random selection on GSM8K. CDIS scores 12 points above random selection with paired confidence intervals that exclude zero and trails full recomputation by 4.3 points, one training-run standard deviation, at 3.4 times lower selection cost.