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Quantization Error-Based Regularization in Neural Networks

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Artificial Intelligence XXXIV (SGAI 2017)

Abstract

Deep neural network is a state-of-the-art technology for achieving high accuracy in various machine learning tasks. Since the available computing power and memory footprint are restricted in embedded computing, precision quantization of numerical representations, such as fixed-point, binary, and logarithmic, are commonly used for higher computing efficiency. The main problem of quantization is accuracy degradation due to its lower numerical representation. There is generally a trade-off between numerical precision and accuracy. In this paper, we propose a quantization-error-aware training method to attain higher accuracy in quantized neural networks. Our approach appends an additional regularization term that is based on quantization errors of weights to the loss function. We evaluate the accuracy by using MNIST and CIFAR-10. The evaluation results show that the proposed approach achieves higher accuracy than the standard approach with quantized forwarding.

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References

  1. Ando, K., Orimo, K., Ueyoshi, K., Yonekawa, H., Sato, S., Nakahara, H., Ikebe, M., Asai, T., Takamaeda-Yamazaki, S., Kuroda, T., Motomura, M.: BRein memory: a 13-layer 4.2 K neuron/0.8 M synapse binary/ternary reconfigurable in-memory deep neural network accelerator in 65 nm CMOS. In: 2017 IEEE Symposium on VLSI Circuits (VLSI-Circuits), pp. C24–C25, Kyoto, Japan (2017)

    Google Scholar 

  2. Courbariaux, M., Hubara, I., Soudry, D., El-Yaniv, R., Bengio, Y.: Binarized neural networks: training deep neural networks with weights and activations constrained to +1 or \(-1\). ArXiv e-prints arXiv:1602.02830, February 2016

  3. Gysel, P., Motamedi, M., Ghiasi, S.: Hardware-oriented approximation of convolutional neural networks. CoRR abs/1604.03168 (2016). http://arxiv.org/abs/1604.03168

  4. Hou, L., Yao, Q., Kwok, J.T.: Loss-aware binarization of deep networks. CoRR abs/1611.01600 (2016). http://arxiv.org/abs/1611.01600

  5. Janocha, K., Czarnecki, W.M.: On loss functions for deep neural networks in classification. CoRR abs/1702.05659 (2017). http://arxiv.org/abs/1702.05659

  6. Johnson, M., Schuster, M., Le, Q.V., Krikun, M., Wu, Y., Chen, Z., Thorat, N., Viégas, F., Wattenberg, M., Corrado, G., Hughes, M., Dean, J.: Google’s multilingual neural machine translation system: enabling zero-shot translation. ArXiv e-prints, Nov 2016

    Google Scholar 

  7. Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. CoRR abs/1412.6980 (2014). http://arxiv.org/abs/1412.6980

  8. Krizhevsky, A., Nair, V., Hinton, G.: Cifar-10 (Canadian institute for advanced research). http://www.cs.toronto.edu/ kriz/cifar.html

  9. LeCun, Y., Bengio, Y., Hinton, G.: Artificial intelligence: deep neural reasoning. Nature 538, 467–468 (2016)

    Article  Google Scholar 

  10. LeCun, Y., Cortes, C.: MNIST handwritten digit database (2010). http://yann.lecun.com/exdb/mnist/

  11. Lin, D.D., Talathi, S.S., Annapureddy, V.S.: Fixed point quantization of deep convolutional networks. CoRR abs/1511.06393 (2015). http://arxiv.org/abs/1511.06393

  12. Miyashita, D., Lee, E.H., Murmann, B.: Convolutional neural networks using logarithmic data representation. CoRR abs/1603.01025 (2016). http://arxiv.org/abs/1603.01025

  13. Shin, D., Lee, J., Lee, J., Yoo, H.J.: 14.2 DNPU: an 8.1TOPS/W reconfigurable CNN-RNN processor for general-purpose deep neural networks. In: 2017 IEEE International Solid-State Circuits Conference (ISSCC), pp. 240–241, February 2017

    Google Scholar 

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Acknowledgment

This work is supported in part by JST ACCEL and Technova.

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Correspondence to Kazutoshi Hirose .

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Hirose, K. et al. (2017). Quantization Error-Based Regularization in Neural Networks. In: Bramer, M., Petridis, M. (eds) Artificial Intelligence XXXIV. SGAI 2017. Lecture Notes in Computer Science(), vol 10630. Springer, Cham. https://doi.org/10.1007/978-3-319-71078-5_11

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  • DOI: https://doi.org/10.1007/978-3-319-71078-5_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71077-8

  • Online ISBN: 978-3-319-71078-5

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