# GIST: Targeted Data Selection for Instruction Tuning via Coupled Optimization Geometry

arXiv: https://arxiv.org/abs/2602.18584 · HTML: https://mlsanity.com/paper/2602.18584/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 51 references that are in the map.
- First posted on arXiv 20 Feb 2026.

## Builds on (most cited first, 30 of 35)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (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)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [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)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (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)
- [GaLore: Memory-Efficient LLM Training by Gradient Low-Rank Projection](https://mlsanity.com/paper/2403.03507/) (2024)
- [Large Dual Encoders Are Generalizable Retrievers](https://mlsanity.com/paper/2112.07899/) (2021)
- [Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability](https://mlsanity.com/paper/2103.00065/) (2021)
- [How Far Can Camels Go? Exploring the State of Instruction Tuning on Open Resources](https://mlsanity.com/paper/2306.04751/) (2023)
- [Measuring the Intrinsic Dimension of Objective Landscapes](https://mlsanity.com/paper/1804.08838/) (2018)
- [What Makes Good Data for Alignment? A Comprehensive Study of Automatic Data Selection in Instruction Tuning](https://mlsanity.com/paper/2312.15685/) (2023)
- [Don't Decay the Learning Rate, Increase the Batch Size](https://mlsanity.com/paper/1711.00489/) (2017)
- [From Quantity to Quality: Boosting LLM Performance with Self-Guided Data Selection for Instruction Tuning](https://mlsanity.com/paper/2308.12032/) (2023)
- [An Investigation into Neural Net Optimization via Hessian Eigenvalue Density](https://mlsanity.com/paper/1901.10159/) (2019)
- [Eigenvalues of the Hessian in Deep Learning: Singularity and Beyond](https://mlsanity.com/paper/1611.07476/) (2016)
- [Traces of Class/Cross-Class Structure Pervade Deep Learning Spectra](https://mlsanity.com/paper/2008.11865/) (2020)
- [Long Is More for Alignment: A Simple but Tough-to-Beat Baseline for Instruction Fine-Tuning](https://mlsanity.com/paper/2402.04833/) (2024)
- [Perplexed by Perplexity: Perplexity-Based Data Pruning With Small Reference Models](https://mlsanity.com/paper/2405.20541/) (2024)
- [A Survey on Data Selection for LLM Instruction Tuning](https://mlsanity.com/paper/2402.05123/) (2024)
- [Large-Scale Data Selection for Instruction Tuning](https://mlsanity.com/paper/2503.01807/) (2025)

## Built on by (most cited first, 8 of 8)

- [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)
- [Two to Tango: Coupled Task-Reference Selection for Safe LLM Fine-tuning](https://mlsanity.com/paper/2606.09866/) (2026)
- [How Output Format Confounds Data Quality and Capability in Instruction Tuning](https://mlsanity.com/paper/2609.02015/) (2026)
- [Token Utility Is Selection-Conditioned: Coupled Selection of Prompt Context and Response Supervision for Instruction Tuning](https://mlsanity.com/paper/2609.22943/) (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)
- [Scalable, Transferable Meta-network for Data Selection Requires a Different Loss (and Why the Obvious Choice is Problematic)](https://mlsanity.com/paper/2610.02092/) (2026)
- [LESSER: Post-Training Data Selection with Output-Layer Gradients](https://mlsanity.com/paper/2610.03702/) (2026)

## Abstract (arXiv)

Targeted data selection has emerged as a crucial paradigm for efficient instruction tuning, aiming to identify a small yet influential subset of training examples for a specific target task. In practice, influence is often measured through the effect of an example on parameter updates. To make selection scalable, many approaches leverage optimizer statistics (e.g., Adam states) as an axis-aligned surrogate for update geometry (i.e., diagonal precondition), implicitly treating parameters as coordinate-wise independent. We show that this assumption breaks down in parameter-efficient fine-tuning (PEFT) methods such as LoRA. In this setting, the induced optimization geometry exhibits strong cross-parameter coupling with non-trivial off-diagonal interactions, while the task-relevant update directions are confined to a low-dimensional subspace. Motivated by this mismatch, we propose GIST (Gradient Isometric Subspace Transformation), a simple yet principled alternative that replaces axis-aligned scaling with robust subspace alignment. GIST recovers a task-specific subspace from validation gradients via singular value decomposition (SVD), projects training gradients into this coupled subspace, and scores examples by their alignment with target directions. Extensive experiments have demonstrated that GIST matches or outperforms the state-of-the-art baseline with only 0.29% of the storage and 25% of the computational time under the same selection budget.