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I'm reading the Wikipedia page for Convolutional Neural Networks along with some other papers and references. In the wiki article under the section called 'Building Blocks', subsection called 'Convolutional layer', there is the first mention of the input volume depth: "The layer's parameters consist of a set of learnable filters (or kernels), which have a small receptive field, but extend through the full depth of the input volume.".

Can someone please explain what is meant by this ? What is the length, breadth and depth of the input volume ? Is the length just the number of pixels in one dimension, the breadth the number of pixels in the other dimension and the volume simply the number of features for the image ?

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  • $\begingroup$ do you know what is a convolution in $2d$ ? it is $y(i,j) = \sum_{n,k} h(i-n,j-k) x(n,k)$ where $x$ is the input (2d) array, $y$ is the output array, and $h$ the filter, that usually is zero except for $|i|< L,|j| < L$ where $L$ is small. Here $x$ is the input of some layer of your RNN, $y$ its output, and $h$ are the weights you are learning for this layer (so they are the weights between the neurons, but those weights are constrained such that the layer $l+1$ is obtained by convolution of the layer $l$ with the weights $h$) $\endgroup$
    – reuns
    Oct 25, 2016 at 5:05
  • $\begingroup$ Yes I am aware of what a convolution is, I just really would like an explanation to the question I asked specifically. What is the length, breadth and depth of the input volume $\endgroup$
    – lara
    Oct 25, 2016 at 5:06
  • $\begingroup$ If you understand everything I wrote, then that's all, you know what is a convolutional layer (and how to implement the gradient descent / backpropagation for learning the weights of the filter) $\endgroup$
    – reuns
    Oct 25, 2016 at 5:07
  • $\begingroup$ Actually I'd really like to understand the language they use in the Wiki article. Thanks for the help though. $\endgroup$
    – lara
    Oct 25, 2016 at 5:10
  • $\begingroup$ Usually in the context of filters, "length" refers to the length of the filter : the $L$ I wrote (or possibly $L^2$ in 2d). $\endgroup$
    – reuns
    Oct 25, 2016 at 5:11

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