Why doesn't a dilated convolution lose information? In the example below (source), we see the difference between stride and dilation in CNNs. 
The explanation as quoted: "Using a dilated convolution increases the size of the receptive field relative to the kernel size. In my sketch, a 2x2 dilated convolution has the same receptive field as a 3x3 un-dilated convolution."
It is said that dilation covers more information, but isn't it also losing information since you're skipping over a lot of pixels at the same time (i.e the white crosses in the image)? How are dilated convolutions so useful with this being said?

It's more useful to think about it in terms of tradeoffs between these two options.

*

*Both of the convolutions you're comparing both cover 9 pixels, but they have different numbers of trainable parameters (9 for the ordinary convolution vs 4 for the dilated convolution).

*A convolutional layer applies the same filter to all patches of an image. In this case, the pixels that are omitted at one step does not omit them when the filter is shifted by one pixel. In other words, there is less overlap among pixels in the input.

*You're correct that the dilated convolution is not including 5 pixels' worth of information, but this information might not be too terribly valuable. If you think about a 3x3 patch of pixels in a natural image, there's a high probability that those values are all very similar in your image, so a dilated convolution is not discarding "too much" information. (On the other hand, if your task has high variation among pixels, then a dilated convolution might not be a good choice).

*It's cheaper to do a smaller number of operations. In very large neural networks, finding places to economize the computations can be very valuable (cloud compute time can be expensive!)

