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Singular Value Decomposition and Neural Networks

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Artificial Neural Networks and Machine Learning – ICANN 2019: Deep Learning (ICANN 2019)

Abstract

Singular Value Decomposition (SVD) constitutes a bridge between the linear algebra concepts and multi-layer neural networks—it is their linear analogy. Besides of this insight, it can be used as a good initial guess for the network parameters, leading to substantially better optimization results.

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Notes

  1. 1.

    Since we use TensorFlow as Keras’ backend execution engine, the resulting computation graph would have been cut into two different executions for each optimization step which causes a too high computational overhead.

References

  1. Chollet, F., et al.: Keras (2015). https://keras.io

  2. Jones, E., Oliphant, T., Peterson, P., et al.: SciPy: open source scientific tools for Python (2001). http://www.scipy.org/

  3. Kohonen, T.: Self-Organization and Associative Memory. SSINF, vol. 8, 3rd edn. Springer, Heidelberg (1989). https://doi.org/10.1007/978-3-642-88163-3. https://www.springer.com/de/book/9783540513872

    Book  MATH  Google Scholar 

  4. McLoone, S., Brown, M.D., Irwin, G., Lightbody, A.: A hybrid linear/nonlinear training algorithm for feedforward neural networks. IEEE Trans. Neural Networks 9(4), 669–684 (1998). https://doi.org/10/dwvsrs

    Article  Google Scholar 

  5. Saxe, A.M., McClelland, J.L., Ganguli, S.: Exact solutions to the nonlinear dynamics of learning in deep linear neural networks. arXiv 1312.6120 (2013). http://arxiv.org/abs/1312.6120

  6. Simonyan, K., Zisserman, A.: Very deep convolutional networks for large-scale image recognition. arXiv 1409.1556, September 2014. http://arxiv.org/abs/1409.1556

  7. Trefethen, L.N., Bau III, D.: Numerical Linear Algebra, vol. 50. SIAM (1997). ISBN 978-0-898713-61-9

    Google Scholar 

  8. Xue, J., Li, J., Gong, Y.: Restructuring of deep neural network acoustic models with singular value decomposition. In: Bimbot, F., et al. (eds.) INTERSPEECH 2013, 14th Annual Conference of the International Speech Communication Association, Lyon, France, 25–29 August 2013, pp. 2365–2369. ISCA (2013). https://isca-speech.org/archive/interspeech_2013/i13_2365.html

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Correspondence to Bernhard Bermeitinger .

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Bermeitinger, B., Hrycej, T., Handschuh, S. (2019). Singular Value Decomposition and Neural Networks. In: Tetko, I., Kůrková, V., Karpov, P., Theis, F. (eds) Artificial Neural Networks and Machine Learning – ICANN 2019: Deep Learning. ICANN 2019. Lecture Notes in Computer Science(), vol 11728. Springer, Cham. https://doi.org/10.1007/978-3-030-30484-3_13

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  • DOI: https://doi.org/10.1007/978-3-030-30484-3_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-30483-6

  • Online ISBN: 978-3-030-30484-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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