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Error Resilient Neural Networks on Low-Dimensional Manifolds

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Neural Advances in Processing Nonlinear Dynamic Signals (WIRN 2017 2017)

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Abstract

We introduce an algorithm that improves Neural Network classification/registration of corrupted data belonging to low-dimensional manifolds. The algorithm combines ideas of the Orthogonal Greedy Algorithm with the standard gradient back-propagation engine incorporated in Neural Networks. Therefore, we call it the Greedient algorithm.

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References

  1. Becker, S., Le Cun, Y.: Improving the convergence of backpropagation learning with second order methods. In: Proceedings of the 1988 Connectionist Models Summer School, pp. 29–37. Morgan Kaufmann, San Matteo (1988)

    Google Scholar 

  2. Candès, E.J., Tao, T.: Decoding by linear programming. IEEE Trans. Inf. Theory 51, 4203–4215 (2005)

    Article  MathSciNet  Google Scholar 

  3. Donoho, D.: Compressed sensing. IEEE Trans. Inf. Theory 52, 1289–1306 (2006)

    Article  MathSciNet  Google Scholar 

  4. Martens, J., Sutskever, I., Swersky, K.: Estimating the Hessian by back-propagating curvature (2012). arXiv:1206.6464

  5. Martens, J.: Second-order optimization for neural networks. Ph.D. thesis, University of Toronto (2016)

    Google Scholar 

  6. Mousavi, A., Baraniuk, R. G.: Learning to invert: signal recovery via deep convolutional networks (2017). arXiv:1701.03891v1 [stat.ML]

  7. Petukhov, A.: Fast implementation of orthogonal greedy algorithm for tight wavelet frames. Eur. J. Signal Process. 86, 471–479 (2006)

    Article  Google Scholar 

  8. Rudelson, M., Vershynin, R.: Geometric approach to error correcting codes and reconstruction of signals. Int. Math. Res. Not. 64, 4019–4041 (2005)

    Article  MathSciNet  Google Scholar 

  9. Simpson, A.: Deep Transform: Error Correction via Probabilistic Re-Synthesis (2015). arXiv:1502.04617 [cs.LG]

  10. Simpson, A.: Deep Transform: Time-Domain Audio Error Correction via Probabilistic Re-Synthesis (2015). arXiv:1503.05849 [cs.SD]

  11. Zhao, J., Mathieu, M., LeCun, Y.: Energy-Based Generative Adversarial Network (2017). arXiv:1609.03126 [cs.LG]

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Correspondence to Alexander Petukhov .

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Petukhov, A., Kozlov, I. (2019). Error Resilient Neural Networks on Low-Dimensional Manifolds. In: Esposito, A., Faundez-Zanuy, M., Morabito, F., Pasero, E. (eds) Neural Advances in Processing Nonlinear Dynamic Signals. WIRN 2017 2017. Smart Innovation, Systems and Technologies, vol 102. Springer, Cham. https://doi.org/10.1007/978-3-319-95098-3_5

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