Vanishing gradient problem

As explained in 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.

The vanishing gradient problem occurs when gradients become progressively smaller as they propagate backward through a deep neural network. Early layers then receive weak weight updates, making them difficult to train. Shortcut, skip, or residual connections create shorter gradient paths by adding an earlier layer’s output to a later layer’s output. section 4.4

Figure 4.12 A comparison between a deep neural network consisting of five layers without (left) and with shortcut connections (right). Shortcut connections involve adding the inputs of a layer to its outputs, effectively creating an alternate path that bypasses certain layers. The gradients denote the mean absolute gradient at each layer, which we compute in listing 4.5.

Compare five-layer networks with and without shortcut connections; the figure traces mean absolute gradients across layers. section 4.4

A small PyTorch experiment makes the training effect measurable:

• Build five Linear–GELU layers with three-value intermediate representations and a one-value output. section 4.4
• Compute mean absolute weight gradients after applying MSE loss and calling loss.backward(). section 4.4
• Compare models without and with shortcuts: the reported gradients rise from roughly 0.0001–0.0050 to 0.207–1.326. section 4.4

How Build a Large Language Model (From Scratch) covers it

How deep it goes

Traces backward gradient flow through a five-layer network and measures weight gradients, without deriving the underlying calculus.

Examples

Uses a five-layer Linear–GELU network, MSE loss, backward propagation, and printed mean absolute gradients.

What you can do after

Diagnose weak gradient flow with PyTorch and apply shortcut connections to improve gradient propagation.

How it connects

Connects vanishing gradients with shortcut connections, residual connections, layer normalization, transformer blocks, and GPT models.

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Also explained in

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  Sutskever's ListA vanishing gradient is an optimization failure in which derivatives become too small to support effective parameter updates during neural-network training.
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  Grokking Machine LearningA neural-network training problem in which gradients become extremely small as they are propagated through layers, slowing or preventing learning.
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  Math and Architectures of Deep LearningThe training difficulty in deep networks where repeated multiplication of small derivatives makes early-layer gradients nearly zero.
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  Deep Learning with R, Third EditionA vanishing gradient is a training condition in which gradients become extremely small as they propagate through a deep network, slowing or preventing parameter updates in earlier layers.
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  Deep Learning with Python, Third EditionA training problem in deep networks where gradient signals become too small to effectively update earlier layers.
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  Inside Deep Learning: Math, Algorithms, ModelsA training instability in which gradients become too small for effective learning updates.
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  Graph Neural Networks in ActionAn optimization problem in which gradients become progressively smaller as they are propagated through many computational steps, hindering learning of long-range dependencies.
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  Evolutionary Deep Learning: Genetic algorithms and neural networksA neural-network training failure in which backpropagated gradients become extremely small across successive layers, limiting effective parameter updates.
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  Grokking AI Algorithms, Second EditionThe vanishing gradient problem is a training difficulty in which derivatives become extremely small and cause neural-network parameter updates to become ineffective.
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  Deep Learning with PyTorch, Second EditionThe difficulty in training deep networks when gradients become too small as they propagate backward through many layers.
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  Learn Generative AI with PyTorchA training failure mode in deep networks where gradient signals become too small to effectively update early layers.
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  LLMs in ProductionA vanishing gradient is a training condition in which propagated derivatives become increasingly small and impede parameter updates.
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  Data Without LabelsThe vanishing gradient problem is an optimization difficulty in which gradients become extremely small during learning, hindering the retention of information across many sequence steps.

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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 Build a Large Language Model (From Scratch). The section links point to the parts of the book it draws on.