Abstract
Modern Convolutional Neural Networks (CNNs) are typically based on floating point linear algebra based implementations. Recently, reduced precision Neural Networks (NNs) have been gaining popularity as they require significantly less memory and computational resources compared to floating point. This is particularly important in power constrained compute environments. However, in many cases a reduction in precision comes at a small cost to the accuracy of the resultant network. In this work, we investigate the accuracy-throughput trade-off for various parameter precision applied to different types of NN models. We firstly propose a quantization training strategy that allows reduced precision NN inference with a lower memory footprint and competitive model accuracy. Then, we quantitatively formulate the relationship between data representation and hardware efficiency. Our experiments finally provide insightful observation. For example, one of our tests show 32-bit floating point is more hardware efficient than 1-bit parameters to achieve 99% MNIST accuracy. In general, 2-bit and 4-bit fixed point parameters show better hardware trade-off on small-scale datasets like MNIST and CIFAR-10 while 4-bit provide the best trade-off in large-scale tasks like AlexNet on ImageNet dataset within our tested problem domain.
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Notes
- 1.
This assumes that both networks have the same memory footprint for their parameters.
- 2.
The reason that the particular 784–1000 \(\times \) 3–10 structure is selected in Table 2 is that it is the only structure that is reported in all mentioned works. We compare different methods on the same structure in the same classification task for fair comparisons on memory and accuracy.
References
Umuroglu, Y., Fraser, N.J., Gambardella, G., Blott, M., Leong, P.H.W., Jahre, M., Vissers, K.A.: FINN: a framework for fast, scalable binarized neural network inference, CoRR (2016)
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, CoRR abs/1602.02830 (2016)
Rastegari, M., Ordonez, V., Redmon, J., Farhadi, A.: XNOR-Net: imagenet classification using binary convolutional neural networks. In: ECCV (2016)
Sung, W., Shin, S., Hwang, K.: Resiliency of deep neural networks under quantization, CoRR abs/1511.06488 (2015)
Zhou, S., Ni, Z., Zhou, X., Wen, H., Wu, Y., Zou, Y.: DoReFa-Net: training low bitwidth convolutional neural networks with low bitwidth gradients, CoRR abs/1606.06160 (2016)
Denil, M., Shakibi, B., Dinh, L., Ranzato, M., de Freitas, N.: Predicting parameters in deep learning, CoRR abs/1306.0543 (2013)
Hwang, K., Sung, W.: Fixed-point feedforward deep neural network design using weights +1, 0, and \(-\)1. In: Proceedings of IEEE ICASSP, pp. 1–6. IEEE (2014)
Wu, J., Leng, C., Wang, Y., Hu, Q., Cheng, J.: Quantized convolutional neural networks for mobile devices, CoRR abs/1512.06473 (2015)
Courbariaux, M., Bengio, Y., David, J.: Low precision arithmetic for deep learning, CoRR abs/1412.7024 (2014)
Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization, CoRR abs/1412.6980 (2014)
Glorot, X., Bengio, Y.: Understanding the difficulty of training deep feedforward neural networks. In: Proceedings of AISTATS 2010 (2010)
Fraser, N.J., et al.: Scaling binarized neural networks on reconfigurable logic, CoRR abs/1701.03400 (2017)
Krizhevsky, A., Hinton, G.: Learning multiple layers of features from tiny images, Technical report (2009)
Krizhevsky, A., Sutskever, I., Hinton, G.E.: Imagenet classification with deep convolutional neural networks. In: Proceedings of NIPS, pp. 1097–1105 (2012)
Simonyan, K., Zisserman, A.: Very deep convolutional networks for large-scale image recognition, CoRR abs/1409.1556 (2014)
Ciresan, D.C., Meier, U., Masci, J., Gambardella, L.M., Schmidhuber, J.: High-performance neural networks for visual object classification, CoRR abs/1102.0183 (2011)
Hinton, G., Vinyals, O., Dean, J.: Distilling the knowledge in a neural network abs/1503.02531 (2015)
Chen, W., Wilson, J.T., Tyree, S., Weinberger, K.Q., Chen, Y.: Compressing neural networks with the hashing trick, CoRR abs/1504.04788 (2015)
Cai, Z., He, X., Sun, J., Vasconcelos, N.: Deep learning with low precision by half-wave Gaussian quantization, CoRR abs/1702.00953 (2017)
Acknowledgments
The authors from Imperial College London would like to acknowledge the support of UK’s research council (RCUK) with the following grants: EP/K034448, P010040 and N031768. The authors from The University of Sydney acknowledge support from the Australian Research Council Linkage Project LP130101034.
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Su, J. et al. (2018). Accuracy to Throughput Trade-Offs for Reduced Precision Neural Networks on Reconfigurable Logic. In: Voros, N., Huebner, M., Keramidas, G., Goehringer, D., Antonopoulos, C., Diniz, P. (eds) Applied Reconfigurable Computing. Architectures, Tools, and Applications. ARC 2018. Lecture Notes in Computer Science(), vol 10824. Springer, Cham. https://doi.org/10.1007/978-3-319-78890-6_3
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