# Compression Trinity: Exploring Sparsity, Quantization, and Low-Rank Approximations for LLM Compression

arXiv: https://arxiv.org/abs/2608.24070 · HTML: https://mlsanity.com/paper/2608.24070/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 43 of its 170 references that are in the map.
- First posted on arXiv 25 Aug 2026.

## Builds on (most cited first, 30 of 43)

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- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [The State of Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1902.09574/) (2019)
- [Sparse Networks from Scratch: Faster Training without Losing Performance](https://mlsanity.com/paper/1907.04840/) (2019)
- [FP8 Formats for Deep Learning](https://mlsanity.com/paper/2209.05433/) (2022)
- [Learning N:M Fine-grained Structured Sparse Neural Networks From Scratch](https://mlsanity.com/paper/2102.04010/) (2021)
- [Scatterbrain: Unifying Sparse and Low-rank Attention Approximation](https://mlsanity.com/paper/2110.15343/) (2021)
- [Layer-adaptive sparsity for the Magnitude-based Pruning](https://mlsanity.com/paper/2010.07611/) (2020)
- [LUT-GEMM: Quantized Matrix Multiplication based on LUTs for Efficient Inference in Large-Scale Generative Language Models](https://mlsanity.com/paper/2206.09557/) (2022)
- [On the Effect of Pretraining Corpora on In-context Learning by a Large-scale Language Model](https://mlsanity.com/paper/2204.13509/) (2022)
- [AffineQuant: Affine Transformation Quantization for Large Language Models](https://mlsanity.com/paper/2403.12544/) (2024)
- [MARLIN: Mixed-Precision Auto-Regressive Parallel Inference on Large Language Models](https://mlsanity.com/paper/2408.11743/) (2024)
- [BESA: Pruning Large Language Models with Blockwise Parameter-Efficient Sparsity Allocation](https://mlsanity.com/paper/2402.16880/) (2024)
- [LQER: Low-Rank Quantization Error Reconstruction for LLMs](https://mlsanity.com/paper/2402.02446/) (2024)
- [Efficient Subsampled Gauss-Newton and Natural Gradient Methods for Training Neural Networks](https://mlsanity.com/paper/1906.02353/) (2019)
- [SPDF: Sparse Pre-training and Dense Fine-tuning for Large Language Models](https://mlsanity.com/paper/2303.10464/) (2023)
- [STEP: Learning N:M Structured Sparsity Masks from Scratch with Precondition](https://mlsanity.com/paper/2302.01172/) (2023)
- [Rethinking the Value of Transformer Components](https://mlsanity.com/paper/2011.03803/) (2020)
- [Scalable Second Order Optimization for Deep Learning](https://mlsanity.com/paper/2002.09018/) (2020)

## Abstract (arXiv)

Prohibitive computational and environmental costs impede the scalable deployment of Large Language Models (LLMs). Traditional compression techniques (sparsity, quantization, low-rank approximations) are typically applied in isolation, and each hits an accuracy-efficiency wall. This thesis proposes the "Compression Trinity," a unified framework that applies the three pillars jointly: sparsity to reduce computation, quantization to minimize memory bandwidth, and low-rank approximations to recover accuracy. To accelerate pretraining, we apply the Trinity to the optimizer and model architecture. MKOR approximates curvature via block-diagonal sparsity and low-rank inversion, maintaining numerical stability for quantized states; it reduces curvature update complexity from O(d3) to O(d2) and accelerates convergence by up to 1.85x over KFAC. SLoPe accelerates training by up to 1.25x via a double-pruned backward pass for N:M sparsity, using low-rank "lazy" adapters in the final 1% of training to recover accuracy. For post-training compression, OPTIMA stabilizes static masks in a zero-training regime by formulating weight reconstruction as globally optimal column-wise quadratic programs, improving zero-shot accuracy by up to 3.97%. Given a fine-tuning budget, PATCH breaks the ceiling of static masks by learning a dynamic hybrid sparsity ratio between 0% and 50%, yielding up to 1.38x speedups. Finally, SLiM realizes the full Compression Trinity in one shot, using mathematically derived low-rank adapters to recover information lost to quantization and sparsity, improving accuracy by up to 5.66% over state-of-the-art methods and outperforming uncompressed dense models at equal parameter budgets by 0.6%. Together, these results show that jointly applying the Compression Trinity is essential for efficient, scalable, high-performance LLMs.