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From this article, I read that "to accurately classify data with neural networks, wide layers are sometimes necessary."

However, I have seen many implementations and discussions on deep-learning, such as this, mention the concept of depth.

What is the difference in the context of neural networks? How does width vs depth impact a neural network's performance?

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The width refers to the number of neurons in a layer. The depth refers to the number of layers.

Have a look at the following question regarding the impact of these hyper-parameters on the performance of the neural network: https://stats.stackexchange.com/q/214360/82135.

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