Compressing Large Language Models using Low Rank and Low Precision Decomposition

• URL: http://arxiv.org/abs/2405.18886v2
• Date: Sun, 03 Nov 2024 20:25:29 GMT
• Title: Compressing Large Language Models using Low Rank and Low Precision Decomposition
• Authors: Rajarshi Saha, Naomi Sagan, Varun Srivastava, Andrea J. Goldsmith, Mert Pilanci,
• Abstract summary: This work introduces $rm CALDERA$ -- a new post-training LLM compression algorithm. It harnesses the inherent low-rank structure of a weight matrix $mathbfW$ by approximating it via a low-rank, low-precision decomposition. Results show that compressing LlaMa-$2$ $7$B/$13B$/$70$B and LlaMa-$3$ $8$B models using $rm CALDERA$ outperforms existing post-training compression techniques.
• Score: 46.30918750022739
• License:
• Abstract: 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.

Related papers

• Locality Regularized Reconstruction: Structured Sparsity and Delaunay Triangulations [7.148312060227714]
  Linear representation learning is widely studied due to its conceptual simplicity and empirical utility in tasks such as compression, classification, and feature extraction. In this work we seek $mathbfw$ that forms a local reconstruction of $mathbfy$ by solving a regularized least squares regression problem. We prove that, for all levels of regularization and under a mild condition that the columns of $mathbfX$ have a unique Delaunay triangulation, the optimal coefficients' number of non-zero entries is upper bounded by $d+1$.
  arXiv  Detail & Related papers  (2024-05-01T19:56:52Z)
• Provably learning a multi-head attention layer [55.2904547651831]
  Multi-head attention layer is one of the key components of the transformer architecture that sets it apart from traditional feed-forward models. In this work, we initiate the study of provably learning a multi-head attention layer from random examples. We prove computational lower bounds showing that in the worst case, exponential dependence on $m$ is unavoidable.
  arXiv  Detail & Related papers  (2024-02-06T15:39:09Z)
• SQ Lower Bounds for Learning Mixtures of Linear Classifiers [43.63696593768504]
  We show that known algorithms for this problem are essentially best possible, even for the special case of uniform mixtures. The key technical ingredient is a new construction of spherical designs that may be of independent interest.
  arXiv  Detail & Related papers  (2023-10-18T10:56:57Z)
• Matrix Compression via Randomized Low Rank and Low Precision Factorization [47.902465710511485]
  Modern matrices can involve billions of elements, making their storage and processing quite demanding in terms of computational resources and memory usage. We propose an algorithm that exploits this structure to obtain a low rank decomposition of any matrix $mathbfA$ as $mathbfLmathbfR$. We empirically demonstrate the efficacy of our algorithm in image compression, nearest neighbor classification of image and text embeddings, and compressing the layers of LlaMa-$7$b.
  arXiv  Detail & Related papers  (2023-10-17T06:56:57Z)
• Learning a Single Neuron with Adversarial Label Noise via Gradient Descent [50.659479930171585]
  We study a function of the form $mathbfxmapstosigma(mathbfwcdotmathbfx)$ for monotone activations. The goal of the learner is to output a hypothesis vector $mathbfw$ that $F(mathbbw)=C, epsilon$ with high probability.
  arXiv  Detail & Related papers  (2022-06-17T17:55:43Z)
• Fast Graph Sampling for Short Video Summarization using Gershgorin Disc Alignment [52.577757919003844]
  We study the problem of efficiently summarizing a short video into several paragraphs, leveraging recent progress in fast graph sampling. Experimental results show that our algorithm achieves comparable video summarization as state-of-the-art methods, at a substantially reduced complexity.
  arXiv  Detail & Related papers  (2021-10-21T18:43:00Z)
• Threshold Phenomena in Learning Halfspaces with Massart Noise [56.01192577666607]
  We study the problem of PAC learning halfspaces on $mathbbRd$ with Massart noise under Gaussian marginals. Our results qualitatively characterize the complexity of learning halfspaces in the Massart model.
  arXiv  Detail & Related papers  (2021-08-19T16:16:48Z)
• Minimax Optimal Regression over Sobolev Spaces via Laplacian Regularization on Neighborhood Graphs [25.597646488273558]
  We study the statistical properties of Laplacian smoothing, a graph-based approach to nonparametric regression. We prove that Laplacian smoothing is manifold-adaptive.
  arXiv  Detail & Related papers  (2021-06-03T01:20:41Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.