The Vanishing Gradient Problem
Deep networks in the 2000s simply refused to learn: the learning signal is born at the last layer and shrinks a little more at every layer it passes back through, until early layers get nothing. This topic shows why that happens (gradients are multiplied, not added) and the toolkit that fixed it — ReLU, good init, normalization, residual connections, and gates.
01.The Problem: You Added Layers and the Model Got Worse
It's 2010.
You train a 3-layer neural network. It works.
A colleague says go deeper.
So you build one with 20 layers. And something embarrassing happens.
The training error got worse. Not the test error — the training error.
A small model could memorize the data. The big one can't.
What is going wrong?
Nothing mystical. The learning signal dies before it reaches the first layer. That is the vanishing gradient problem — and it kept deep learning stuck at a handful of layers for roughly 15 years.
Quick background, in one plain sentence each. A gradient (Topic 3) is a list of slopes: one number per knob, telling you which way to turn that knob to lower the loss. Backprop (Topic 12) is the bookkeeping trick that computes all those slopes.
Here's the part beginners never see coming.
The loss is measured at the last layer.
So the gradient signal is born at the end of the network...
...and it has to travel backwards, layer by layer, to reach layer 1.
That journey is where it dies.
Multiplicative Decay and Its Fixes
Multiplicative Decay and Its Fixes
Backprop multiplies per-layer derivatives; sigmoid caps that factor at 0.25. Five independent 2010s inventions each restore unit-gain gradient flow.
Unlock Topic #85: The Vanishing Gradient Problem
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