# CoSpaDi: Compressing LLMs via Calibration-Guided Sparse Dictionary Learning

arXiv: https://arxiv.org/abs/2509.22075 · HTML: https://mlsanity.com/paper/2509.22075/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 63 of its 97 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 30 of 63)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [AWQ: Activation-aware Weight Quantization for LLM Compression and Acceleration](https://mlsanity.com/paper/2306.00978/) (2023)
- [TinyBERT: Distilling BERT for Natural Language Understanding](https://mlsanity.com/paper/1909.10351/) (2019)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [LLM.int8(): 8-bit Matrix Multiplication for Transformers at Scale](https://mlsanity.com/paper/2208.07339/) (2022)

## Built on by (most cited first, 6 of 6)

- [A Practical Tensor-Network Compression Pipeline for Production-Scale Large Language Models](https://mlsanity.com/paper/2602.01613/) (2026)
- [ROCKET: Rapid Optimization via Calibration-guided Knapsack Enhanced Truncation for Efficient Model Compression](https://mlsanity.com/paper/2602.11008/) (2026)
- [COMPOT: Calibration-Optimized Matrix Procrustes Orthogonalization for Transformers Compression](https://mlsanity.com/paper/2602.15200/) (2026)
- [Motion-Compensated Weight Compression](https://mlsanity.com/paper/2605.24754/) (2026)
- [Output-Space Allocation Costs for Calibration-Guided LLM Compression: An Empirical Study](https://mlsanity.com/paper/2606.27785/) (2026)
- [GeoPair: Geometry-Preserving Cross-Layer Factorization for Training-Free Transformer Compression](https://mlsanity.com/paper/2609.25963/) (2026)

## Abstract (arXiv)

Post-training LLM compression often relies on low-rank approximations, which force all columns of a projection matrix to share a single low-dimensional subspace. We propose CoSpaDi, a training-free compression framework that replaces this single-subspace assumption with a union-of-subspaces model via sparse dictionary learning. CoSpaDi factorizes each weight matrix into a dense dictionary and column-sparse coefficients, allowing different columns to select different subsets of dictionary atoms at the same storage budget. To preserve model behavior, we use calibration activations to transform functional reconstruction into a standard dictionary learning problem. Across Llama and Qwen models, CoSpaDi improves accuracy--compression and perplexity--compression trade-offs over SVD-based and structured pruning baselines at 20--40% compression ratios, while naturally supporting sparse--dense computation and post-training quantization of sparse coefficients.