I was looking at the original implementation of LeNet-5 and I noticed a disparity in different sources. Wikipedia suggests that the non linearity used is the same sigmoid in each layer, some blog posts use a combination of Tanh and sigmoid while Andrew NG said it used some crude non linearity which no one uses today without naming it. I looked at the original paper but it's like 50 pages long and the diagram does not mention the activation functions used explicitly. I searched a bit and the sigmoid function was there and mentioned in context of activations while the tanh function is taken as a squashing function. I'm not sure if that is the same or different as then it used other terms when referring to the sigmoid ones. Anyone knows what's up with this?


1 Answer 1


In the original paper there are some clarifying statements:

The four inputs to a unit in S2 are added, then multiplied by a trainable coefficient, and added to a trainable bias. The result is passed through a sigmoidal function. (p.7, col.1)

Here, sigmoidal function is generic.

As in classical neural networks, units in layers up to F6 compute.. This weighted sum .. is then passed through a sigmoid squashing function .. The squashing function is a scaled hyperbolic tangent. (p.8, col.1 - but see also Appendix A for details)

Here, "sigmoid squashing function" is used to indicate a scaled "tanh" (remember that tanh is a rescaled logistic sigmoid function).

Therefore, I think Wikipedia's suggestion to use the same "sigmoidal function" is correct. For the sake of precision, the tanh should be used.


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