Sigmoid of x is 1

Question

I just read "Make your own neural network" book. Now I am trying to create NeuralNetwork class in Python. I use sigmoid activation function. I wrote basic code and tried to test it. But my implementation didn't work properly at all. After long debugging and comparation to code from book I found out that sigmoid of very big number is 1 because Python rounds it. I use numpy.random.rand() to generate weights and this function returns only values from 0 to 1. After summing all products of weights and inputs I get very big number. I fixed this problem with numpy.random.normal() function that generates random numbers from range, (-1, 1) for example. But I have some questions.

• Is sigmoid good activation function?
• What to do if output of node is still so big and Python rounds result to 1, which is impossible for sigmoid?
• How can I prevent Python to rounding floats that are very close to integer
• Any advices for me as beginner in neural networks (books, techniques, etc).

Answer 1

1. The answer to this question obviously depends on context. What it means by "good". The sigmoid activation function will result in outputs that are between 0 and 1. As such, they are standard output activations for binary classification where you want your neural network to output a number between 0 and 1 - with the output being interpreted as the probability of your input being in the specified class. However, if you are using sigmoid activation functions throughout your neural network (i.e. in intermediate layers as well), you might consider switching to RELU activation function. Historically, the sigmoid activation function was used throughout neural networks as a way to introduce non-linearity so that a neural network could do more than approximate linear functions. However, it was found that sigmoid activations suffer heavily from the vanishing gradients problem because the function is so flat far from 0. As such, nowadays, most intermediate layers will use RELU activation functions (or something even more fancy - e.g. SELU/Leaky RELU/etc.) The RELU activation function is 0 for inputs less than 0 and equals the input for inputs greater than 0. Its been found to be sufficient for introducing non-linearity into a neural network.

2. Generally you don't want to be in a regime where your outputs are so huge or so small that it becomes computationally unstable. One way to help fix this issue, as mentioned earlier, is to use a different activation function (e.g. RELU). Another way, and perhaps even better way, to help with this issue is by initializing the weights better with e.g. the Xavior-Glorot initialization scheme or simply initializing them to smaller values e.g. within the range [-.01,.01]. Basically, you scale the random initializations so that your outputs are in a good range of values and not some gigantic or miniscule number. You can certainly also do both.

3. You can use higher precision floats to make python keep more decimals around. E.g. you can use np.float64 instead of np.float32...however, this increases the computational complexity and probably isn't necessary. Most neural networks today use 32-bit floats and they work just fine. See points 1 and 2 for better alternatives to solving your problem.

4. This question is overly broad. I would say that the coursera course and specialization by Prof. Andrew Ng is my strongest recommendation in terms of learning neural networks.