Explain how neural networks can help mitigate the curse of dimensionality in your product catalog system, and propose an architecture that leverages parameter sharing and feature sharing.

We will use a neural network with a shared embedding layer for all attributes. This way, we can share parameters across different attributes, reducing the number of trainable parameters and improving generalization. We will also leverage feature sharing by using a common set of hidden layers for all attributes. This will allow us to capture complex interactions between attributes while keeping the model compact.