Is a single neuron in a Neural Network a GLM? I was thinking about count data, and saw some research that said that some of the best functions to use for count data were GLMs rather than transforming the data. 
I'm training a neural network, and the question I had was if a single neuron in a neural network was a GLM. 
GLM's have the form $y = e^{\theta^T * x}$. A neuron is just $z = \theta^T*x$, and then via sigmoidal activation is $y = \frac{1}{(1+e^{-z})}$. 
It's not quite the same form though. 
I'm trying to figure out how to handle count data being input into my neural network. 
 A: GLM (generalized linear model) are "general" in the sense, that they can use any kind of transformation on the results of the linear combination. So GLMs don't necessary have the form $y=e^{\theta^T*x}$. They just have the form $y=f(\theta^T*x)$ where $f$ is almost any monotonous and differentiable function (link function). $f$ transforms the result of the linear combination to the mean of a distribution from the exponential family. This family also contains the Bernoulli distribution and for this distribution, the link function is $f(z)=\frac{1}{1+e^{-z}}$ (inverse logistic function). So, the sigmoid function sometimes used in neurons of artificial networks does in fact turn that neuron into a GLM.
About your question on how to handle count data (I assume as input) in an artificial neural network: First try to just input the data as is. The link function transforms the output, no the input. You are correct, that GLMs can be used to analyze count data (usually via Poisson based link function), but in that case, the count data is the output to be fitted by the GLM.
Only if your networks does not learn well, you could think about other methods of transforming your input data. NNs usually handle transforming input data quite well. They are universal function approximators after all. But in some cases they can use some help to find the correct transformation, and they may learn faster if given suitably transformed data.
