Vanishing Gradient Problem

Definition:
During backpropagation, gradients are repeatedly multiplied as they move through network layers. When these values are small (< 1), they shrink exponentially, eventually approaching zero.

Effect:
Earlier layers receive negligible gradient updates and stop learning effectively, even while later layers continue to train.

Common Causes:

  • Deep neural networks
  • Sigmoid activations
  • Tanh activations
  • Poor weight initialization

Symptoms:

  • Slow convergence
  • Training stagnation
  • Lower layers learn little or nothing

Example:

A gradient of 0.5 becomes nearly zero after passing through 20 layers.

Solutions:

  • ReLU and variants (Leaky ReLU, GELU)
  • Xavier/He initialization
  • Batch normalization
  • Residual connections (ResNets)
  • LSTM/GRU architectures for sequence models

Mental Model:
Backpropagation is like passing a message backward through many layers. If each layer weakens the message slightly, eventually the earliest layers receive almost no signal and cannot learn.


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