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It isn't too surprising to see behaviour like this, since you're using $\mathrm{ReLU}$ activation. Here is a simple result which explains the phenomenon for a single-layer neural network. I don't have much time so I haven't checked whether this would extend reasonably to multiple layers; I believe it probably will. Proposition. In a single-layer neural ...

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Check the documentation for Dense layer: Note: If the input to the layer has a rank greater than 2, then Dense computes the dot product between the inputs and the kernel along the last axis of the inputs and axis 1 of the kernel (using tf.tensordot). For example, if input has dimensions (batch_size, d0, d1), then we create a kernel with shape (d1, units), ...

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It looks like your network is overfitting, because the training loss carries on decreasing to zero even though validation loss levels off, and then starts to increase again. I would guess that your network is essentially "memorising" the training examples because you're getting a near zero loss in training. You could try: applying some form of ...

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Short answer: Yes. Consider a non-linear regression on that dataset. Using a model of degree two, it would fit a quadratic exactly to your perfect data here. But I suppose you're asking about neural networks. You can have neural networks set up that are exactly equivalent to this kind of regression, so even with neural networks, yes you can get this non-...

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