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Hidden unit specialization in layered neural networks: ReLU vs. sigmoidal activation

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  • Oostwal, Elisa
  • Straat, Michiel
  • Biehl, Michael

Abstract

By applying concepts from the statistical physics of learning, we study layered neural networks of rectified linear units (ReLU). The comparison with conventional, sigmoidal activation functions is in the center of interest. We compute typical learning curves for large shallow networks with K hidden units in matching student teacher scenarios. The systems undergo phase transitions, i.e. sudden changes of the generalization performance via the process of hidden unit specialization at critical sizes of the training set. Surprisingly, our results show that the training behavior of ReLU networks is qualitatively different from that of networks with sigmoidal activations. In networks with K≥3 sigmoidal hidden units, the transition is discontinuous: Specialized network configurations co-exist and compete with states of poor performance even for very large training sets. On the contrary, the use of ReLU activations results in continuous transitions for all K. For large enough training sets, two competing, differently specialized states display similar generalization abilities, which coincide exactly for large hidden layers in the limit K→∞. Our findings are also confirmed in Monte Carlo simulations of the training processes.

Suggested Citation

  • Oostwal, Elisa & Straat, Michiel & Biehl, Michael, 2021. "Hidden unit specialization in layered neural networks: ReLU vs. sigmoidal activation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 564(C).
  • Handle: RePEc:eee:phsmap:v:564:y:2021:i:c:s0378437120308153
    DOI: 10.1016/j.physa.2020.125517
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    References listed on IDEAS

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    1. Richard H. R. Hahnloser & Rahul Sarpeshkar & Misha A. Mahowald & Rodney J. Douglas & H. Sebastian Seung, 2000. "Correction: Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit," Nature, Nature, vol. 408(6815), pages 1012-1012, December.
    2. Cocco, S. & Monasson, R. & Posani, L. & Rosay, S. & Tubiana, J., 2018. "Statistical physics and representations in real and artificial neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 504(C), pages 45-76.
    3. Richard H. R. Hahnloser & Rahul Sarpeshkar & Misha A. Mahowald & Rodney J. Douglas & H. Sebastian Seung, 2000. "Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit," Nature, Nature, vol. 405(6789), pages 947-951, June.
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    Cited by:

    1. Xiaoyu Li & Yuefeng Du & Lin Yao & Jun Wu & Lei Liu, 2021. "Design and Experiment of a Broken Corn Kernel Detection Device Based on the Yolov4-Tiny Algorithm," Agriculture, MDPI, vol. 11(12), pages 1-17, December.

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