Artificial Intelligence and Quantum Computing for Advanced Wireless Networks. Savo G. Glisic

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      One triplet of indexes (i^{l + 1}, j^{l + 1}, d^{l + 1}) specifies a row in S, while (i^l, j^l, d^l) specifies a column. These two triplets together pinpoint one element in (x^l). We set that element to 1 if d^{l + 1} = d^l and , are simultaneously satisfied, and 0 otherwise. One row of S(x^l) corresponds to one element in y, and one column corresponds to one element in x^l. By using this indicator matrix, we have vec(y) = S(x^l)vec(x^l) and

Figure 3.27 Illustration of preprocessing in a cooperative neural network (CoNN)‐based image classifier.

resulting in

      (3.104)

S(x^l) is very sparse since it has only one nonzero entry in every row. Thus, we do not need to use the entire matrix in the computation. Instead, we just need to record the locations of those nonzero entries – there are only H^{l + 1} W^{l + 1} D^{l + 1} such entries in S(x^l). Figure 3.27 illustrates preprocessing in a CoNN‐based image classifier.

      For further readings on CoNNs, the reader is referred to [30].

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