Activation function

Q: How deeply does Optimization Algorithms: AI techniques for design, planning, and control problems cover activation function?

Defines the role, lists major forms, and demonstrates tanh in code without deriving activation-function formulas.

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

An activation function is a function applied to a neural-network unit’s pre-activation value to produce its output and introduce nonlinear behavior.

An activation function transforms a neuron's weighted input, bias, and threshold into its output, allowing neural-network units to fire nonlinearly. section 9.7

Common activation-function choices include:

Sign, step, tanh, arctan, logistic sigmoid, softmax, radial basis function, and ReLU. section 9.7
The chosen function operates within a forward pass whose parameters are optimized against a loss or cost function. section 9.7

Tanh in a neural-network forward pass

A NumPy implementation computes the hidden pre-activation as z1 = X.dot(W1) + b1, then applies a1 = np.tanh(z1) before producing output logits.

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

Cover of Optimization Algorithms: AI techniques for design, planning, and control problems

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Also explained in

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Grokking Machine LearningA function that transforms a model's score into an output or prediction.
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Grokking AI Algorithms, Second EditionAn activation function is a nonlinear or linear mathematical function that transforms a neuron's weighted input before passing the result onward.
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Natural Language Processing in Action, Second EditionAn activation function is a nonlinear function applied to a neural-network signal to transform its value before further processing.
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Classic Computer Science Problems in Swift: Essential techniques for practicing programmersAn activation function is a function applied to a neuron's output to introduce nonlinearity and constrain the output range in a neural network.
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Inside Deep Learning: Math, Algorithms, ModelsA nonlinear function applied in a neural network to transform layer outputs and increase representational power.
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Deep Learning with PyTorch, Second EditionA nonlinear function applied within a neural network to transform signals so the whole model can represent more complex mappings than a purely linear model.
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Data Without LabelsAn activation function is a mathematical function applied to a neuron's combined input to determine its output, typically introducing nonlinearity.
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Deep Learning with R, Third EditionAn activation function transforms a neural-network unit's pre-activation value into its output, often element by element.
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Sutskever's ListAn activation function transforms a neuron's weighted input before passing its output to subsequent layers.
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Deep Learning with JAXA nonlinear function applied inside a neural network to let stacked layers represent more than a single linear transformation.
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Graph Neural Networks in ActionAn activation function is a nonlinear or otherwise specified function applied to a layer's transformed values.
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Machine Learning Algorithms in DepthAn activation function is a nonlinear function applied to a neural-network layer output to increase the model's expressive capacity.
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Deep Learning with Python, Third EditionA nonlinear function applied to a layer’s output to reshape it and increase model expressiveness.

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Related concepts

sigmoidincludes · A sigmoid is a smooth, bounded, S-shaped function that maps real-valued inputs between two limiting values, commonly zero and one.
ReLUincludes · ReLU, or rectified linear unit, is an activation function that maps an input x to max(0, x).
nonlinear mappingproduces · A nonlinear mapping is a function that does not preserve linear combinations of its inputs.
step functionincludes · A step function is a piecewise-constant function that changes abruptly between discrete output values when its input crosses one or more specified thresholds.
GELUincludes · GELU, or Gaussian error linear unit, is a smooth neural-network activation function that scales an input by the cumulative distribution function of the standard normal distribution at that input.
Swishincludes · Swish, also called SiLU, is a smooth neural-network activation function defined as x multiplied by the sigmoid of βx.

This explainer was generated by Manning's knowledge graph from the text of Optimization Algorithms: AI techniques for design, planning, and control problems. The section links point to the parts of the book it draws on.