Compressing Large Language Models using Low Rank and Low Precision Decomposition
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2024
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| _version_ | 1866916465433640960 |
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| author | Saha, Rajarshi Sagan, Naomi Srivastava, Varun Goldsmith, Andrea J. Pilanci, Mert |
| author_facet | Saha, Rajarshi Sagan, Naomi Srivastava, Varun Goldsmith, Andrea J. Pilanci, Mert |
| contents | The prohibitive sizes of Large Language Models (LLMs) today make it difficult to deploy them on memory-constrained edge devices. This work introduces $\rm CALDERA$ -- a new post-training LLM compression algorithm that harnesses the inherent low-rank structure of a weight matrix $\mathbf{W}$ by approximating it via a low-rank, low-precision decomposition as $\mathbf{W} \approx \mathbf{Q} + \mathbf{L}\mathbf{R}$. Here, $\mathbf{L}$ and $\mathbf{R}$ are low rank factors, and the entries of $\mathbf{Q}$, $\mathbf{L}$ and $\mathbf{R}$ are quantized. The model is compressed by substituting each layer with its $\mathbf{Q} + \mathbf{L}\mathbf{R}$ decomposition, and the zero-shot performance of the compressed model is evaluated. Additionally, $\mathbf{L}$ and $\mathbf{R}$ are readily amenable to low-rank adaptation, consequently enhancing the zero-shot performance. $\rm CALDERA$ obtains this decomposition by formulating it as an optimization problem $\min_{\mathbf{Q},\mathbf{L},\mathbf{R}}\lVert(\mathbf{Q} + \mathbf{L}\mathbf{R} - \mathbf{W})\mathbf{X}^\top\rVert_{\rm F}^2$, where $\mathbf{X}$ is the calibration data, and $\mathbf{Q}, \mathbf{L}, \mathbf{R}$ are constrained to be representable using low-precision formats. Theoretical upper bounds on the approximation error of $\rm CALDERA$ are established using a rank-constrained regression framework, and the tradeoff between compression ratio and model performance is studied by analyzing the impact of target rank and quantization bit budget. Results illustrate that compressing LlaMa-$2$ $7$B/$13B$/$70$B and LlaMa-$3$ $8$B models using $\rm CALDERA$ outperforms existing post-training LLM compression techniques in the regime of less than $2.5$ bits per parameter. The implementation is available at: https://github.com/pilancilab/caldera. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_18886 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compressing Large Language Models using Low Rank and Low Precision Decomposition Saha, Rajarshi Sagan, Naomi Srivastava, Varun Goldsmith, Andrea J. Pilanci, Mert Machine Learning Artificial Intelligence Optimization and Control The prohibitive sizes of Large Language Models (LLMs) today make it difficult to deploy them on memory-constrained edge devices. This work introduces $\rm CALDERA$ -- a new post-training LLM compression algorithm that harnesses the inherent low-rank structure of a weight matrix $\mathbf{W}$ by approximating it via a low-rank, low-precision decomposition as $\mathbf{W} \approx \mathbf{Q} + \mathbf{L}\mathbf{R}$. Here, $\mathbf{L}$ and $\mathbf{R}$ are low rank factors, and the entries of $\mathbf{Q}$, $\mathbf{L}$ and $\mathbf{R}$ are quantized. The model is compressed by substituting each layer with its $\mathbf{Q} + \mathbf{L}\mathbf{R}$ decomposition, and the zero-shot performance of the compressed model is evaluated. Additionally, $\mathbf{L}$ and $\mathbf{R}$ are readily amenable to low-rank adaptation, consequently enhancing the zero-shot performance. $\rm CALDERA$ obtains this decomposition by formulating it as an optimization problem $\min_{\mathbf{Q},\mathbf{L},\mathbf{R}}\lVert(\mathbf{Q} + \mathbf{L}\mathbf{R} - \mathbf{W})\mathbf{X}^\top\rVert_{\rm F}^2$, where $\mathbf{X}$ is the calibration data, and $\mathbf{Q}, \mathbf{L}, \mathbf{R}$ are constrained to be representable using low-precision formats. Theoretical upper bounds on the approximation error of $\rm CALDERA$ are established using a rank-constrained regression framework, and the tradeoff between compression ratio and model performance is studied by analyzing the impact of target rank and quantization bit budget. Results illustrate that compressing LlaMa-$2$ $7$B/$13B$/$70$B and LlaMa-$3$ $8$B models using $\rm CALDERA$ outperforms existing post-training LLM compression techniques in the regime of less than $2.5$ bits per parameter. The implementation is available at: https://github.com/pilancilab/caldera. |
| title | Compressing Large Language Models using Low Rank and Low Precision Decomposition |
| topic | Machine Learning Artificial Intelligence Optimization and Control |
| url | https://arxiv.org/abs/2405.18886 |