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You might be interested in this method of weighting neural networks in 2 different spaces to get layer-wise fully connected networks with only a few weights per neuron and potentially some other benefits.
http://randomprojectionai.blogspot.com/2017/11/double-weighting-for-neural-networks.html
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I haven't read through your blog since it's not available by visiting the link submitted, but I think that weighting ANN in 2 different spaces is not efficient or not really possible. Thanks.
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