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Compression Image Dataset Based on Multiple Matrix Product States

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Advances in Information and Communication (FICC 2024)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 920))

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Abstract

Large-scale datasets have made impressive progress in deep learning. However, storing datasets and training neural network models on large datasets have become increasingly expensive. In this paper, we present an effective dataset compression approach based on the matrix product states (short as MPS) and knowledge distillation. MPS can decompose image samples into a sequential product of tensors to achieve task-agnostic image compression by preserving the low-rank information of the images. Based on this property, we use multiple MPS to represent the image datasets samples. Meanwhile, we also designed a task-related component based on knowledge distillation to enhance the generality of the compressed dataset. Extensive experiments have demonstrated the effectiveness of the proposed approach in image datasets compression, especially obtaining better model performance (2.26\(\%\) on average) than the best baseline method on the same compression ratio.

Z.F. Gao and P. Liu–Authors contributed equally.

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Notes

  1. 1.

    Available at https://www.cs.toronto.edu/~kriz/cifar.html.

  2. 2.

    Available at https://www.worldlink.com.cn/en/osdir/fashion-mnist.html.

References

  1. Agarwal, P.K., Har-Peled, S., Varadarajan, K.R.: Approximating extent measures of points. J. ACM 51(4), 606–635 (2004)

    Article  MathSciNet  Google Scholar 

  2. Aljundi, R., Lin, M., Goujaud, B., Bengio, Y.: Gradient based sample selection for online continual learning. In: Hanna, M., et al. (eds.), Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurIPS 2019, 8-14 December 2019, Vancouver, BC, Canada, pp. 11816–11825 (2019)

    Google Scholar 

  3. Ba, J., Caruana, R.: Do deep nets really need to be deep? In: Zoubin, G., Max, W., Corinna, C., Neil, D.L., Kilian, Q.W. (eds.), Advances in Neural Information Processing Systems 27: Annual Conference on Neural Information Processing Systems 2014, December 8-13 2014, Montreal, Quebec, Canada, pp. 2654–2662 (2014)

    Google Scholar 

  4. Bengua, J.A., Phien, H.N., Tuan, H.D.: Optimal feature extraction and classification of tensors via matrix product state decomposition. In: 2015 IEEE International Congress on Big Data, pp. 669–672. IEEE (2015)

    Google Scholar 

  5. Bucilua, C., Caruana, R., Niculescu-Mizil, A.: Model compression. In: Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 535–541 (2006)

    Google Scholar 

  6. Castro, F.M., Marín-Jiménez, M.J., Guil, N., Schmid, C., Alahari, K.: End-to-end incremental learning. In: Ferrari, V., Hebert, M., Sminchisescu, C., Weiss, Y. (eds.) ECCV 2018. LNCS, vol. 11216, pp. 241–257. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-01258-8_15

    Chapter  Google Scholar 

  7. Devlin, J., Chang, M.W., Lee, K., Toutanova, K.: BERT: pre-training of deep bidirectional transformers for language understanding. In: Burstein, J., Doran, C., Solorio, T. (eds.), Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, NAACL-HLT 2019, Minneapolis, MN, USA, 2-7 June 2019, Volume 1 (Long and Short Papers), pp. 4171–4186. Association for Computational Linguistics (2019)

    Google Scholar 

  8. Fannes, M., Nachtergaele, B., Werner, R.F.: Finitely correlated states on quantum spin chains. Commun. Math. Phys. 144(3), 443–490 (1992)

    Article  MathSciNet  Google Scholar 

  9. Gao, Z.F., et al.: Compressing deep neural networks by matrix product operators. Phys. Rev. Res. 2, 023300 (2020)

    Article  Google Scholar 

  10. Gao, Z.F., Liu, P., Zhao, W.X., Lu, Z.Y., Wen, J.R.: Parameter-efficient mixture-of-experts architecture for pre-trained language models. In: Proceedings of the 29th International Conference on Computational Linguistics, pp. 3263–3273 (2022)

    Google Scholar 

  11. Gao, Z.F., Sun, X., Gao, L., Li, J., Lu, Z.Y.: Compressing LSTM networks by matrix product operators. arXiv preprintarXiv:2012.11943 (2020)

  12. Gao, Z.F., Zhou, K., Liu, P., Zhao, W.X., Wen, J.R.: Small pre-trained language models can be fine-tuned as large models via over-parameterization. In: Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pp. 3819–3834 (2023)

    Google Scholar 

  13. Har-Peled, S., Mazumdar, S.: On coresets for k-means and k-median clustering. In: Proceedings of the Thirty-Sixth Annual ACM Symposium on Theory of Computing, pp. 291–300 (2004)

    Google Scholar 

  14. He, K., Gkioxari, G., Dollár, P., Girshick, R.: Mask R-CNN. In: IEEE International Conference on Computer Vision, ICCV 2017, Venice, Italy, 22–29 October 2017, pp. 2980–2988. IEEE Computer Society (2017)

    Google Scholar 

  15. Henry, E.R., Hofrichter, J.: [8] singular value decomposition: application to analysis of experimental data. Methods Enzymol. 210, 129–192 (1992)

    Article  Google Scholar 

  16. Hinton, G.E., Osindero, S., Teh, Y.W.: A fast learning algorithm for deep belief nets. Neural Comput. 18, 1527–1554 (2006)

    Article  MathSciNet  Google Scholar 

  17. Hinton, G., Vinyals, O., Dean, J.: Distilling the knowledge in a neural network. CoRR, abs/1503.02531 (2015)

    Google Scholar 

  18. Hitchcock, F.L.: The expression of a tensor or a polyadic as a sum of products. J. Math. Phys. 6(1–4), 164–189 (1927)

    Article  Google Scholar 

  19. Kim, T., Oh, J., Kim, N., Cho, S., Yun, S.Y.: Comparing kullback-leibler divergence and mean squared error loss in knowledge distillation. In: Zhou, Z.-H. (ed.), Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence, IJCAI 2021, Virtual Event/Montreal, Canada, 19-27 August 2021, pp. 2628–2635. ijcai.org (2021)

    Google Scholar 

  20. Kim, W., Son, B., Kim, I.: Vilt: vision-and-language transformer without convolution or region supervision. In: Meila, M., Zhang, T. (eds.), Proceedings of the 38th International Conference on Machine Learning, ICML 2021, 18–24 July 2021, Virtual Event, volume 139 of Proceedings of Machine Learning Research, pp. 5583–5594. PMLR (2021)

    Google Scholar 

  21. Krizhevsky, A., Hinton, G., et al.: Learning multiple layers of features from tiny images (2009)

    Google Scholar 

  22. Latorre, J.I.: Image compression and entanglement. CoRR, abs/quant-ph/0510031 (2005)

    Google Scholar 

  23. LeCun, Y.: Mnist handwritten digit database, yann lecun, corinna cortes and chris burges. http://yannlecun.com/exdb/mnist

  24. Liu, P., Gao, Z.F., Zhao, W.X., Wen, J.R.: Scaling pre-trained language models to deeper via parameter-efficient architecture. arXiv preprint arXiv:2303.16753 (2023)

  25. Liu, P., Gao, Z.F., Zhao, W.X., Xie, Z.Y., Lu, Z.Y., Wen, J.R.: Enabling lightweight fine-tuning for pre-trained language model compression based on matrix product operators. In: Zong, C., Xia, F., Li, W., Navigli, R. (eds.), Proceedings of the 59th Annual Meeting of the Association for Computational Linguistics and the 11th International Joint Conference on Natural Language Processing, ACL/IJCNLP 2021, (Volume 1: Long Papers), Virtual Event, 1–6 August 2021, pp. 5388–5398. Association for Computational Linguistics (2021)

    Google Scholar 

  26. Neifeld, M.A., Ashok, A., Baheti, P.K.: Task-specific information for imaging system analysis. J. Opt. Soc. Am. A 24(12), B25–B41 (2007)

    Google Scholar 

  27. Nene, S.A., Nayar, S.K., Murase, H., et al.: Columbia object image library (coil-100) (1996)

    Google Scholar 

  28. Perez-Garcia, D., Verstraete, F., Wolf, M.M., Cirac, J.I.: Matrix product state representations. Quantum Inf. Comput. 7(5–6), 401–430 (2007)

    MathSciNet  Google Scholar 

  29. Rebuffi, S.A., Kolesnikov, A., Sperl, G., Lampert, C.H.: ICARL: incremental classifier and representation learning. In: 2017 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2017, Honolulu, HI, USA, 21–26 July 2017, pp. 5533–5542. IEEE Computer Society (2017)

    Google Scholar 

  30. Romero, A., et al.: Fitnets: hints for thin deep nets. In: Bengio, Y., LeCun, Y. (eds.), 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, 7-9 May 2015, Conference Track Proceedings (2015)

    Google Scholar 

  31. Russakovsky, O., et al.: ImageNet large scale visual recognition challenge. Int. J. Comput. Vis. (IJCV) 115(3), 211–252 (2015)

    Article  MathSciNet  Google Scholar 

  32. Russakovsky, O., et al.: ImageNet large scale visual recognition challenge. Int. J. Comput. Vis. 115(3), 211–252 (2015)

    Article  MathSciNet  Google Scholar 

  33. SainathTN, M.,, et al.: Deep convolutional neural networks for LVCSR. IEEE Int. Conf. Acoust. Speech and Sig. Process. 8614, 8618 (2013)

    Google Scholar 

  34. Sandler, M., Howard, A., Zhu, M., Zhmoginov, A. and Chen, L.C.: Mobilenetv2: inverted residuals and linear bottlenecks. In: 2018 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2018, Salt Lake City, UT, USA, 18–22 June 2018, pp. 4510–4520. Computer Vision Foundation / IEEE Computer Society (2018)

    Google Scholar 

  35. Sener, O., Savarese, S.: Active learning for convolutional neural networks: a core-set approach. In: 6th International Conference on Learning Representations, ICLR 2018, Vancouver, BC, Canada, April 30 - May 3, 2018, Conference Track Proceedings, OpenReview.net (2018)

    Google Scholar 

  36. Simonyan, K., Zisserman, A.: Very deep convolutional networks for large-scale image recognition. In: Bengio, Y., LeCun, Y. (eds.), 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, 7-9 May 2015, Conference Track Proceedings (2015)

    Google Scholar 

  37. Sun, X., Gao, Z.F., Lu, Z.Y., Li, J., Yan, Y.: Yonghong: a model compression method with matrix product operators for speech enhancement. IEEE/ACM Trans. Audio Speech Lang. Process. 28, 2837–2847 (2020)

    Google Scholar 

  38. Sun, X., Gao, Z.F., Lu, Z.Y., Li, J., Yan, Y.: A model compression method with matrix product operators for speech enhancement. IEEE/ACM Trans. Audio Speech Lang. Process. 28, 2837–2847 (2020)

    Article  Google Scholar 

  39. Toneva, M., Sordoni, A., Combes, R.T.D., Trischler, A., Bengio, Y., Gordon, G.J.: An empirical study of example forgetting during deep neural network learning. In: 7th International Conference on Learning Representations, ICLR 2019, New Orleans, LA, USA, 6-9 May 2019. OpenReview.net (2019)

    Google Scholar 

  40. Wang, L., Shi, J., Song, G., Shen, I.: Object detection combining recognition and segmentation. In: Yagi, Y., Kang, S.B., Kweon, I.S., Zha, H. (eds.) ACCV 2007. LNCS, vol. 4843, pp. 189–199. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-76386-4_17

    Chapter  Google Scholar 

  41. Wang, T., Zhu, J.Y., Torralba, A., Efros, A.A.: Dataset distillation. CoRR, abs/1811.10959 (2018)

    Google Scholar 

  42. Wolf, G.W.: Facility location: concepts, models, algorithms and case studies. series: Contributions to management science. Int. J. Geogr. Inf. Sci. 25(2), 331–333 (2011)

    Google Scholar 

  43. Xie, H.D., et al.: Reorthonormalization of chebyshev matrix product states for dynamical correlation functions. Phys. Rev. B 97(7), 075111 (2018)

    Article  Google Scholar 

  44. Zhao, B., Mopuri, K.R., Bilen, H.: Dataset condensation with gradient matching. In: 9th International Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, 3-7 May 2021. OpenReview.net (2021)

    Google Scholar 

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Acknowledgments

This work was partially supported by National Natural Science Foundation of China under Grants No. 62206299 and 62222215, Beijing Outstanding Young Scientist Program under Grant No. BJJWZYJH012019100020098 and CCF-Zhipu AI Large Model Fund.

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Authors and Affiliations

  1. Gaoling School of Artificial Intelligence, Renmin University of China, Beijing, China

    Ze-Feng Gao, Peiyu Liu, Wayne Xin Zhao & Ji-Rong Wen

  2. Department of Physics, Renmin University of China, Beijing, China

    Ze-Feng Gao, Zhi-Yuan Xie & Zhong-Yi Lu

  3. Beijing Key Laboratory of Big Data Management and Analysis Methods, Beijing, China

    Peiyu Liu, Wayne Xin Zhao & Ji-Rong Wen

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  1. Ze-Feng Gao
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  4. Zhi-Yuan Xie
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  6. Zhong-Yi Lu
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Correspondence to Wayne Xin Zhao or Zhi-Yuan Xie .

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  1. Saga University, Saga, Japan

    Kohei Arai

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Gao, ZF., Liu, P., Zhao, W.X., Xie, ZY., Wen, JR., Lu, ZY. (2024). Compression Image Dataset Based on Multiple Matrix Product States. In: Arai, K. (eds) Advances in Information and Communication. FICC 2024. Lecture Notes in Networks and Systems, vol 920. Springer, Cham. https://doi.org/10.1007/978-3-031-53963-3_43

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