# Scaling Sparse Fine-Tuning to Large Language Models

arXiv: https://arxiv.org/abs/2401.16405 · HTML: https://mlsanity.com/paper/2401.16405/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 34 references that are in the map.
- First posted on arXiv 29 Jan 2024.

## Builds on (most cited first, 19 of 19)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [The Flan Collection: Designing Data and Methods for Effective Instruction Tuning](https://mlsanity.com/paper/2301.13688/) (2023)
- [Instruction Tuning with GPT-4](https://mlsanity.com/paper/2304.03277/) (2023)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [Rigging the Lottery: Making All Tickets Winners](https://mlsanity.com/paper/1911.11134/) (2019)
- [TyDi QA: A Benchmark for Information-Seeking Question Answering in Typologically Diverse Languages](https://mlsanity.com/paper/2003.05002/) (2020)
- [How Far Can Camels Go? Exploring the State of Instruction Tuning on Open Resources](https://mlsanity.com/paper/2306.04751/) (2023)
- [Camels in a Changing Climate: Enhancing LM Adaptation with Tulu 2](https://mlsanity.com/paper/2311.10702/) (2023)
- [Training Neural Networks with Fixed Sparse Masks](https://mlsanity.com/paper/2111.09839/) (2021)
- [Scaling Down to Scale Up: A Guide to Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.15647/) (2023)

## Built on by (most cited first, 26 of 26)

- [Programming Refusal with Conditional Activation Steering](https://mlsanity.com/paper/2409.05907/) (2024)
- [On-Device Language Models: A Comprehensive Review](https://mlsanity.com/paper/2409.00088/) (2024)
- [SLTrain: a sparse plus low-rank approach for parameter and memory efficient pretraining](https://mlsanity.com/paper/2406.02214/) (2024)
- [Unlocking Continual Learning Abilities in Language Models](https://mlsanity.com/paper/2406.17245/) (2024)
- [Layer Swapping for Zero-Shot Cross-Lingual Transfer in Large Language Models](https://mlsanity.com/paper/2410.01335/) (2024)
- [Sparse High Rank Adapters](https://mlsanity.com/paper/2406.13175/) (2024)
- [Efficient Model Editing with Task-Localized Sparse Fine-tuning](https://mlsanity.com/paper/2504.02620/) (2025)
- [MoE-CAP: Benchmarking Cost, Accuracy and Performance of Sparse Mixture-of-Experts Systems](https://mlsanity.com/paper/2505.11415/) (2025)
- [S2FT: Efficient, Scalable and Generalizable LLM Fine-tuning by Structured Sparsity](https://mlsanity.com/paper/2412.06289/) (2024)
- [Exploring Sparsity for Parameter Efficient Fine Tuning Using Wavelets for Vision](https://mlsanity.com/paper/2505.12532/) (2025)
- [LoLDU: Low-Rank Adaptation via Lower-Diag-Upper Decomposition for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2410.13618/) (2024)
- [SaRA: High-Efficient Diffusion Model Fine-tuning with Progressive Sparse Low-Rank Adaptation](https://mlsanity.com/paper/2409.06633/) (2024)
- [Sketch to Adapt: Fine-Tunable Sketches for Efficient LLM Adaptation](https://mlsanity.com/paper/2410.06364/) (2024)
- [The Multiple Ticket Hypothesis: Random Sparse Subnetworks Suffice for RLVR](https://mlsanity.com/paper/2602.01599/) (2026)
- [MoEGen: Mixture-of-Experts for Instance-Adaptive LoRA Generation](https://mlsanity.com/paper/2608.03275/) (2026)
- [Leave it to the Specialist: Repair Sparse LLMs with Sparse Fine-Tuning via Sparsity Evolution](https://mlsanity.com/paper/2505.24037/) (2025)
- [SliceFine: The Universal Winning-Slice Hypothesis for Pretrained Networks](https://mlsanity.com/paper/2510.08513/) (2025)
- [When Data Is Scarce: Scaling Sparse Language Models with Repeated Training](https://mlsanity.com/paper/2606.01155/) (2026)
- [GaLLoP: Gradient-based Sparse Learning on Low-Magnitude Parameters](https://mlsanity.com/paper/2510.19778/) (2025)
- [Super-Tuning: From Activation-Aware Pruning to Sparse Fine-Tuning](https://mlsanity.com/paper/2607.09287/) (2026)
- [S2A: A Unified Framework for Parameter and Memory Efficient Transfer Learning](https://mlsanity.com/paper/2503.08154/) (2025)
- [Exploring Sparse Adapters for Scalable Merging of Parameter Efficient Experts](https://mlsanity.com/paper/2507.07140/) (2025)
- [Random Initialization of Gated Sparse Adapters](https://mlsanity.com/paper/2511.01794/) (2025)
- [TokenSeek: Memory Efficient Fine Tuning via Instance-Aware Token Ditching](https://mlsanity.com/paper/2601.19739/) (2026)
- [One Algorithm, Two Goals: Dual Scoring for Parameter and Data Selection in LLM Fine-Tuning](https://mlsanity.com/paper/2605.06166/) (2026)
- [On-Policy Parameter Update Direction Underlies Generalization in LLM Post-Training](https://mlsanity.com/paper/2609.36659/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) are difficult to fully fine-tune (e.g., with instructions or human feedback) due to their sheer number of parameters. A family of parameter-efficient sparse fine-tuning methods have proven promising in terms of performance but their memory requirements increase proportionally to the size of the LLMs. In this work, we scale sparse fine-tuning to state-of-the-art LLMs like LLaMA 2 7B and 13B. We propose SpIEL, a novel sparse fine-tuning method which, for a desired density level, maintains an array of parameter indices and the deltas of these parameters relative to their pretrained values. It iterates over: (a) updating the active deltas, (b) pruning indices (based on the change of magnitude of their deltas) and (c) regrowth of indices. For regrowth, we explore two criteria based on either the accumulated gradients of a few candidate parameters or their approximate momenta estimated using the efficient SM3 optimizer. We experiment with instruction-tuning of LLMs on standard dataset mixtures, finding that SpIEL is often superior to popular parameter-efficient fine-tuning methods like LoRA (low-rank adaptation) in terms of performance and comparable in terms of run time. We additionally show that SpIEL is compatible with both quantization and efficient optimizers, to facilitate scaling to ever-larger model sizes. We release the code for SpIEL at https://github.com/AlanAnsell/peft and for the instruction-tuning experiments at https://github.com/ducdauge/sft-llm.