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Convolutional neural networks are capable of handling inputs of varying sizes. It is one of the key benefits of convolutional neural networks. But I am unsure about the cases when we should not utilize this advantage of the convolutional neural network.

Although the following example has been provided in the chapter named Convolutional Networks of the textbook titled Deep Learning by Ian Goodfellow et al.

Convolution does not make sense if the input has variable size because it can optionally include different kinds of observations. For example, if we are processing college applications, and our features consist of both grades and standardized test scores, but not every applicant took the standardized test, then it does not make sense to convolve the same weights over features corresponding to the grades as well as the features corresponding to the test scores.

It is not clear for me to understand the above example since I am habituated with images in the case of convolutional neural networks.

Can anyone provide a possible example of images where we cannot utilize the benefit of passing variable-size images to the convolutional neural network?

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Well, I think, this statement sounds somehow misleading.

The main statement is actually in the first passage of this statement:

Note that the use of convolution for processing variably sized inputs makes sense only for inputs that have variable size because they contain varying amounts of observation of the same kind of thing—different lengths of recordings over time, different widths of observations over space, and so forth.

Convolution is applicable only provided the input is the 1D, 2D, 3D array, graph, any collection of the data of the same kind. Each pixel is the feature vector of the same shape.

This statement means, that one cannot apply convolutions if the inputs are not-structured, like the data tables, which involve boolean, categorical, continuous features. There is no notion of locality and adjacency for this kind of data.

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