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Depth vs width — which do you scale first?

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Answer

  • Depth compounds representational capacity exponentially in the number of piecewise-linear regions for ReLU networks, while width only grows it polynomially.
  • So depth is usually the better initial investment for representation.
  • However, very deep networks are harder to optimize — need normalization, residual connections, and careful init.
  • Modern architectures (transformers, ConvNeXt) balance both via 'compound scaling'.
Check yourself — multiple choice
  • Width is exponentially more powerful than depth
  • Depth compounds capacity exponentially but needs residuals + normalization to train
  • Depth and width are equivalent
  • Only width matters for CNNs

Depth grows expressiveness exponentially — invest there first, then balance.

#fundamentals#architectures

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