Editing Neural Networks (section)

== <span style="color: #FFFFFF;">Analyzing</span> ==
{| class="wikitable"
|+ Neural Network Trade-offs
! Consideration !! Deeper Networks !! Shallower Networks
|-
| Representational power || Higher — can model complex functions || Lower — limited to simpler decision boundaries
|-
| Training difficulty || Harder — vanishing/exploding gradients || Easier — gradients flow cleanly
|-
| Overfitting risk || Higher — more parameters || Lower — fewer parameters
|-
| Training data needed || Much more (thousands to millions) || Less
|-
| Inference speed || Slower || Faster
|}

'''Common failure modes:'''
* '''Vanishing gradients''' — In deep networks, gradients shrink as they propagate backward, making early layers learn very slowly. Mitigated by ReLU, batch normalization, and residual connections.
* '''Exploding gradients''' — Gradients grow exponentially, causing weight updates to be catastrophically large. Mitigated by gradient clipping.
* '''Dead neurons''' — ReLU neurons that output zero for all inputs and receive no gradient, effectively becoming permanently inactive. Mitigated by Leaky ReLU or careful initialization.
* '''Data leakage''' — Accidentally allowing test-set information into training, leading to falsely optimistic evaluation metrics.
* '''Learning rate too high''' — The loss oscillates or diverges instead of converging. Use learning rate warmup and reduce on plateau.
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