# Sparsity-Aware Low-Rank Representation for Efficient Fine-Tuning of Large Language Models

arXiv: https://arxiv.org/abs/2601.16991 · HTML: https://mlsanity.com/paper/2601.16991/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 17 references that are in the map.
- First posted on arXiv 8 Jan 2026.

## Builds on (most cited first, 7 of 7)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [LoRA-GA: Low-Rank Adaptation with Gradient Approximation](https://mlsanity.com/paper/2407.05000/) (2024)

## Abstract (arXiv)

Adapting large pre-trained language models to downstream tasks often entails fine-tuning millions of parameters or deploying costly dense weight updates, which hinders their use in resource-constrained environments. Low-rank Adaptation (LoRA) reduces trainable parameters by factorizing weight updates, yet the underlying dense weights still impose high storage and computation costs. Magnitude-based pruning can yield sparse models but typically degrades LoRA's performance when applied naively. In this paper, we introduce SALR (Sparsity-Aware Low-Rank Representation), a novel fine-tuning paradigm that unifies low-rank adaptation with sparse pruning under a rigorous mean-squared-error framework. We prove that statically pruning only the frozen base weights minimizes the pruning error bound, and we recover the discarded residual information via a truncated-SVD low-rank adapter, which provably reduces per-entry MSE by a factor of (1 - r/min(d,k)). To maximize hardware efficiency, we fuse multiple low-rank adapters into a single concatenated GEMM, and we adopt a bitmap-based encoding with a two-stage pipelined decoding + GEMM design to achieve true model compression and speedup. Empirically, SALR attains 50% sparsity on various LLMs while matching the performance of LoRA on GSM8K and MMLU, reduces model size by 2×, and delivers up to a 1.7× inference speedup.