Vanishing gradient problem

As explained in Grokking Machine Learning

A neural-network training problem in which gradients become extremely small as they are propagated through layers, slowing or preventing learning.

During backpropagation, gradients guide updates to a neural network’s weights. When sigmoid functions are composed across layers, their nearly flat regions can make derivatives—and therefore weight updates—extremely small. Learning may then take a very long time. section 10.2

Flat sigmoid, tiny updates

At large positive or negative inputs, the sigmoid curve is nearly flat. Its derivative is close to zero, so backpropagation can take tiny steps. ReLU is described as reducing this problem. section 10.2 section 10.6

Figure 10.17 The sigmoid function is flat at the ends, which means that for large positive and negative values, its derivative is very small, hampering the training.

The sigmoid plot highlights the flat ends associated with small derivatives. section 10.2

How Grokking Machine Learning covers it

How deep it goes

Explains how sigmoid derivatives shrink through backpropagation and points to activation changes without deriving gradients.

Examples

Uses sigmoid’s flat ends and contrasts its training effect with ReLU’s reduction of the problem.

What you can do after

Understand why sigmoid activations can slow training and how ReLU can reduce the problem.

How it connects

Links neural networks and backpropagation to sigmoid, activation functions, and ReLU.

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  Build a Large Language Model (From Scratch)A training difficulty in deep neural networks where gradients shrink as they propagate backward, hindering learning in early layers.

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Related concepts

• ReLUaddressed by · ReLU, or rectified linear unit, is an activation function that maps an input x to max(0, x).
• residual connectionaddressed by · A residual connection is a neural-network pathway that carries an earlier representation around one or more transformations to a later computation, where it can be combined with the transformed representation.
• LSTMaddressed by · An LSTM is a recurrent neural network architecture with gated memory mechanisms that control information flow and help retain or update information across sequences.
• ResNetaddressed by · ResNet is a family of deep neural-network architectures built from residual blocks with shortcut connections that facilitate information flow and optimization.
• GRUaddressed by · A gated recurrent unit (GRU) is a recurrent neural-network architecture that uses learned gates to regulate information flow and update a hidden state across sequence steps.
• normalizationaddressed by · Normalization is the process of transforming a value, representation, or data structure to satisfy a specified standard, scale, or structural constraint.

This explainer was generated by Manning's knowledge graph from the text of Grokking Machine Learning. The section links point to the parts of the book it draws on.