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I have made an RNN from scratch in Tensorflow.js. In order to update my weights (without needing to calculate the derivatives), I thought of using the normal equation to find the optimal values for my RNN's weights. Would you recommend this approach and if not why?

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Unfortunately, this is not possible. The normal equation can only directly optimise a single layer that connects input and output. There is no equivalent for multiple layers such as those in any neural network architecture.

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