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In its most raw form, convolution is defined as: $(f*g)(t) = \int_{-\infty}^\infty f(\tau) \cdot g(t-\tau) d\tau$. Here, t doesn't represent the time domain. Infact, it represents the real valued argument the book is talking about. In this notion, at moment t, convolution can be thought of as a weighted average of the function $f(\tau)$ weighted by $g(–\tau)$...


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Statistical efficiency in this context essentially means that a CNN would require fewer training examples than a fully connected network to learn. Intuitively this seems reasonable: more parameters to learn should mean more samples needed. Of course it is always desirable to minimise the number of training samples needed, so that's a definite advantage of ...


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