Connectionists: e-print available: ReLU vs. sigmoidal activation

[Michael Biehl]

Dear Connectionists.
We have  compared the use of ReLU and sigmoidal
activations in layered neural networks, using
methods from the statistical physics of learning.
Our analysis reveals fundamental differences in
training and generalization behavior even in simple,
shallow systems. A corresponding e-print
is available at https://arxiv.org/abs/1910.07476:

*Hidden Unit Specialization in Layered Neural Networks: ReLU vs. Sigmoidal
Activation*
Elisa Oostwal, Michiel Straat, Michael Biehl

Abstract:
We study layered neural networks of rectified linear units (ReLU) in a
modelling framework for stochastic training processes. The comparison with
sigmoidal activation functions is in the center of interest. We compute
typical learning curves for shallow networks with K hidden units in
matching student teacher scenarios. The systems exhibit 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 networks
in the limit K to infinity.

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Prof. Dr. Michael Biehl
Bernoulli Institute for
Mathematics, Computer Science
and Artificial Intelligence
P.O. Box 407, 9700 AK Groningen
The Netherlands

Tel. +31 50 363 3997

www.cs.rug.nl/~biehl
m.biehl at rug.nl
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