Abstract
We are focused on the theoretical background of convolutional neural networks. In particular, we examine the problem whether semantic meaning can be assigned to convolutional kernels in the first layers and how this fact can simplify the learning procedure. In this respect, we prove the suitability and efficiency of the F-transform kernels. We describe various experiments that support our claim.
Supported by University of Ostrava.
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Notes
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The text of this and the following subsection is a free version of a certain part of [6] where the theory of a higher degree F-transform was introduced.
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We performed several independent training runs.
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Hyperparameters values were left at their respective default values - as they are set in the Caffe framework example.
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ImageNet dataset differs, depending on the year of ILSVRC competition.
References
LeCun, Y., Bengio, Y., Hinton, G.: Deep learning. Nature 521(7553), 436–444 (2015)
LeCun, Y., Bottou, L., Bengio, Y., Haffner, P.: Gradient-based learning applied to document recognition. Proc. IEEE 86(11), 2278–2324 (1998)
Molek, V., Perfilieva, I.: Convolutional neural networks with the F-transform kernels. In: Rojas, I., Joya, G., Catala, A. (eds.) IWANN 2017. LNCS, vol. 10305, pp. 396–407. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59153-7_35
Perfilieva, I., Holčapek, M., Kreinovich, V.: A new reconstruction from the F-transform components. Fuzzy Sets Syst. 288, 3–25 (2016)
Perfilieva, I.: Fuzzy transforms: theory and applications. Fuzzy Sets Syst. 157(8), 993–1023 (2006)
Perfilieva, I., Danková, M., Bede, B.: Towards F-transform of a higher degree. In: IFSA/EUSFLAT Conference, pp. 585–588 (2009)
Perfilieva, I., Kreinovich, V.: Fuzzy transforms of higher order approximate derivatives: a theorem. Fuzzy Sets Syst. 180(1), 55–68 (2011)
Russakovsky, O., et al.: ImageNet large scale visual recognition challenge. Int. J. Comput. Vision 115(3), 211–252 (2015)
Schmidhuber, J.: Deep learning in neural networks: an overview. Neural Netw. 61, 85–117 (2015)
Szegedy, C., Ioffe, S., Vanhoucke, V.: Inception-V4, inception-ResNet and the impact of residual connections on learning. CoRR abs/1602.07261 (2016). http://arxiv.org/abs/1602.07261
Acknowledgment
The work was supported from ERDF/ESF “Centre for the development of Artificial Intelligence Methods for the Automotive Industry of the region” (No. CZ.02.1.01/0.0/0.0/17_049/0008414).
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Molek, V., Perfilieva, I. (2019). Convolutional Neural Networks with Interpretable Kernels. In: Seki, H., Nguyen, C., Huynh, VN., Inuiguchi, M. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2019. Lecture Notes in Computer Science(), vol 11471. Springer, Cham. https://doi.org/10.1007/978-3-030-14815-7_27
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DOI: https://doi.org/10.1007/978-3-030-14815-7_27
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