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Let $\mathcal{S}$ be the training input data set where each input $u^i \in \mathcal{S}$ has $d$ features. I want to design a ANN so that the cost function below is minimized (the sum of square of pairwise differences between model outputs) and the given constraint is satisfied, where $w$ is ANN model parameter vector.

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Question: what kind of ANN is suitable for this purpose?[

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A Siamese network (a network with multiple outputs) will work for such a case.

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  • $\begingroup$ Why multiple outputs, could you please explain the reason? and What will be the number of outputs? $\endgroup$
    – data_science_learner
    May 2 '21 at 21:51
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    $\begingroup$ Look at Triplet loss. Your question's has the same formulation like that. You would need three outputs. Then, you can reduce that loss. Or look at metric learning. There you get your embeddings for a batch and then try to reduce or increase distances between them. In case of metric learning you just need one output but a larger batch size will be needed. $\endgroup$
    – Abhishek Verma
    May 3 '21 at 20:23

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