# GradientSpace: Unsupervised Data Clustering for Improved Instruction Tuning

arXiv: https://arxiv.org/abs/2512.06678 · HTML: https://mlsanity.com/paper/2512.06678/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 33 references that are in the map.
- First posted on arXiv 7 Dec 2025.

## Builds on (most cited first, 24 of 24)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [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)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Instruction Tuning for Large Language Models: A Survey](https://mlsanity.com/paper/2308.10792/) (2023)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [Conflict-Averse Gradient Descent for Multi-task Learning](https://mlsanity.com/paper/2110.14048/) (2021)
- [Mixture of LoRA Experts](https://mlsanity.com/paper/2404.13628/) (2024)
- [DataInf: Efficiently Estimating Data Influence in LoRA-tuned LLMs and Diffusion Models](https://mlsanity.com/paper/2310.00902/) (2023)
- [A Closer Look at the Limitations of Instruction Tuning](https://mlsanity.com/paper/2402.05119/) (2024)
- [Data Diversity Matters for Robust Instruction Tuning](https://mlsanity.com/paper/2311.14736/) (2023)
- [Clustering and Ranking: Diversity-preserved Instruction Selection through Expert-aligned Quality Estimation](https://mlsanity.com/paper/2402.18191/) (2024)
- [TAGCOS: Task-agnostic Gradient Clustered Coreset Selection for Instruction Tuning Data](https://mlsanity.com/paper/2407.15235/) (2024)
- [Mixture-of-Skills: Learning to Optimize Data Usage for Fine-Tuning Large Language Models](https://mlsanity.com/paper/2406.08811/) (2024)
- [CommonIT: Commonality-Aware Instruction Tuning for Large Language Models via Data Partitions](https://mlsanity.com/paper/2410.03077/) (2024)
- [Solving Token Gradient Conflict in Mixture-of-Experts for Large Vision-Language Model](https://mlsanity.com/paper/2406.19905/) (2024)
- [Ensembles of Low-Rank Expert Adapters](https://mlsanity.com/paper/2502.00089/) (2025)
- [MoRE: A Mixture of Low-Rank Experts for Adaptive Multi-Task Learning](https://mlsanity.com/paper/2505.22694/) (2025)
- [Towards Alignment-Centric Paradigm: A Survey of Instruction Tuning in Large Language Models](https://mlsanity.com/paper/2508.17184/) (2025)
- [Scalable Multi-Domain Adaptation of Language Models using Modular Experts](https://mlsanity.com/paper/2410.10181/) (2024)
- [Coresets from Trajectories: Selecting Data via Correlation of Loss Differences](https://mlsanity.com/paper/2508.20230/) (2025)
- [ClusterUCB: Efficient Gradient-Based Data Selection for Targeted Fine-Tuning of LLMs](https://mlsanity.com/paper/2506.10288/) (2025)

## Built on by (most cited first, 2 of 2)

- [On Representation Redundancy in Large-Scale Instruction Tuning Data Selection](https://mlsanity.com/paper/2602.13773/) (2026)
- [Gradient Atoms: Unsupervised Discovery, Attribution and Steering of Model Behaviors via Sparse Decomposition of Training Gradients](https://mlsanity.com/paper/2603.14665/) (2026)

## Abstract (arXiv)

Instruction tuning is one of the key steps required for adapting large language models (LLMs) to a broad spectrum of downstream applications. However, this procedure is difficult because real-world datasets are rarely homogeneous; they consist of a mixture of diverse information, causing gradient interference, where conflicting gradients pull the model in opposing directions, degrading performance. A common strategy to mitigate this issue is to group data based on semantic or embedding similarity. However, this fails to capture how data influences model parameters during learning. While recent works have attempted to cluster gradients directly, they randomly project gradients into lower dimensions to manage memory, which leads to accuracy loss. Moreover, these methods rely on expert ensembles which necessitates multiple inference passes and expensive on-the-fly gradient computations during inference. To address these limitations, we propose GradientSpace, a framework that clusters samples directly in full-dimensional gradient space. We introduce an online SVD-based algorithm that operates on LoRA gradients to identify latent skills without the infeasible cost of storing all sample gradients. Each cluster is used to train a specialized LoRA expert along with a lightweight router trained to select the best expert during inference. We show that routing to a single, appropriate expert outperforms expert ensembles used in prior work, while significantly reducing inference latency. Our experiments across mathematical reasoning, code generation, finance, and creative writing tasks demonstrate that GradientSpace leads to coherent expert specialization and consistent accuracy gains over state-of-the-art clustering methods and finetuning techniques.