Vanishing and Exploding Gradients

In a deep or recurrent network the backward gradient is a product of many per-layer Jacobians, so its magnitude compounds: factors mostly below one shrink it toward zero (early layers stop learning) and factors above one blow it up (training diverges into NaNs). The root cause is the repeated multiplication, and the standard fixes target it directly: residual connections to give gradient a shortcut, normalization to keep activations in scale, gating to preserve signal across time, gradient clipping to cap the blow-up, and careful initialization. Applied-AI interviews probe it because it is the mechanism behind most deep-net training failures you have to diagnose.