neural networksnormalization
I have just heard, that it's a good idea to choose initial weights of a neural network from the range $(\frac{-1}{\sqrt d} , \frac{1}{\sqrt d})$, where $d$ is the number of inputs to a given neuron. It is assumed, that the sets are normalized – mean 0, variance 1 (don't know if this matters).
Why is this a good idea?
This is expected. Weights in a CNN form feature detectors, so that a certain pattern in an image is connected to strong weights, but the rest of the image pixels should not cause any activations in the next layer neurons.
Only a small fraction of neurons in a layer is activated every time an image is shown, and a small fraction of weights is needed to be large to activate (or suppress) any particular neuron. Moreover, the number of patterns a network needs to detect is fairly small, especially in the early layers. Therefore, overall connectivity for the network is usually very sparse.
The same reasoning applies to regulatization methods, such as L2/L1 - forcing the weights to be small makes the network more robust to noise in the data, and forces the network to learn only the features present in many images.
I think its about saturation of the neurons. Think about you have an activation function like sigmoid.
If your weight val gets value >= 2 or <=-2 your neuron will not learn. So, if you truncate your normal distribution you will not have this issue(at least from the initialization) based on your variance. I think thats why, its better to use truncated normal in general.
Best Answer
I assume you are using logistic neurons, and that you are training by gradient descent/back-propagation.
The logistic function is close to flat for large positive or negative inputs. The derivative at an input of $2$ is about $1/10$, but at $10$ the derivative is about $1/22000$ . This means that if the input of a logistic neuron is $10$ then, for a given training signal, the neuron will learn about $2200$ times slower that if the input was $2$.
If you want the neuron to learn quickly, you either need to produce a huge training signal (such as with a cross-entropy loss function) or you want the derivative to be large. To make the derivative large, you set the initial weights so that you often get inputs in the range $[-4,4]$.
The initial weights you give might or might not work. It depends on how the inputs are normalized. If the inputs are normalized to have mean $0$ and standard deviation $1$, then a random sum of $d$ terms with weights uniform on $(\frac{-1}{\sqrt{d}},\frac{1}{\sqrt{d}})$ will have mean $0$ and variance $\frac{1}{3}$, independent of $d$. The probability that you get a sum outside of $[-4,4]$ is small. That means as you increase $d$, you are not causing the neurons to start out saturated so that they don't learn.
With inputs which are not normalized, those weights may not be effective at avoiding saturation.