How deeply does Deep Learning with R, Third Edition cover sigmoid?

Defines sigmoid as a squashing function, explains its probability interpretation, and contrasts its bounded range with linear regression outputs.

Sigmoid

As explained in Deep Learning with R, Third Edition

A sigmoid activation function maps arbitrary real-valued inputs to values in the interval from zero to one.

A sigmoid activation function squashes arbitrary real-valued inputs into the interval [0, 1]. In binary classification, this scalar output can be interpreted as the probability of the positive class. section 4.1.3

Binary classification output

A model for sentiment classification can use sigmoid only in its final one-unit Dense layer: layer_dense(1, activation = "sigmoid"). The intermediate layers use ReLU, while the sigmoid output supplies a score between zero and one. With this output, binary_crossentropy is the matching loss. section 4.1.3 section 4.1.7

Activation functions add nonlinearity; without one, stacked Dense layers would still represent only linear transformations. Sigmoid is therefore useful for bounded classification outputs, but it constrains regression predictions to values between zero and one. section 4.1.3 section 4.3.3

Listing 4.4 Model definition

model <- keras_model_sequential() |>
  layer_dense(16, activation = "relu") |>
  layer_dense(16, activation = "relu") |>
  layer_dense(1, activation = "sigmoid")

Inspect the complete three-layer model definition and its final sigmoid-enabled Dense layer. section 4.1.3

How Deep Learning with R, Third Edition covers it

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Also explained in

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Grokking Machine LearningA function that maps a real-valued input to a value between zero and one, commonly interpreted as a binary class probability.
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Inside Deep Learning: Math, Algorithms, ModelsA nonlinear activation function that maps real-valued inputs to a bounded interval.
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Statistics Every Programmer NeedsA sigmoid function is a function with an S-shaped curve that transitions smoothly between lower and upper limiting values.
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Grokking StatisticsAn S-curve is a sigmoid-shaped relationship in which growth is initially rapid, then slows toward a plateau.
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Grokking AI Algorithms, Second EditionA sigmoid function is a bounded S-shaped mathematical function that maps real-valued inputs to values between two limits, commonly zero and one.
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Data Without LabelsA sigmoid function is a differentiable S-shaped function that maps real-valued inputs to bounded output values and is commonly used to produce binary-classification scores.
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Natural Language Processing in Action, Second EditionA logistic function is an S-shaped mathematical function that maps an input to a bounded continuous value and provides a soft threshold.
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Knowledge Graphs and LLMs in ActionA sigmoid activation maps a real-valued score to a value between zero and one, commonly interpreted as a probability for a binary outcome.
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Machine Learning for Tabular Data: XGBoost, Deep Learning, and AIA sigmoid is a smooth mathematical function that maps real-valued inputs to values between zero and one.
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How Large Language Models WorkAn S-curve is a growth pattern in which progress accelerates, reaches a transition region, and then approaches a plateau.
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Learn Generative AI with PyTorchAn activation function that maps outputs into the range 0 to 1, used here to interpret the discriminator output as a probability.
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Machine Learning Algorithms in DepthA sigmoid function is a continuous S-shaped function that maps real-valued inputs to values between zero and one.
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Deep Learning with Python, Third EditionA statistical classification method that models class probabilities with a linear predictor passed through a logistic function.
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Math and Architectures of Deep LearningAn S-shaped nonlinear activation function whose steepness and horizontal position can be adjusted with parameters.
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Reinforcement Learning from Human FeedbackThe sigmoid function maps a real-valued input to a number between zero and one using the function 1/(1+e^-x).

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Related concepts

activation functionkind of · An activation function maps a neural-network unit’s or layer’s input to an output, often introducing nonlinearity into the network’s computation.
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probability theoryproduces · Probability theory is the branch of mathematics that formalizes uncertainty and analyzes random events and outcomes using probability measures.
cross entropy lossused by · Cross-entropy loss measures the expected negative log probability that a predicted distribution assigns to outcomes drawn from a target distribution.

This explainer was generated by Manning's knowledge graph from the text of Deep Learning with R, Third Edition. The section links point to the parts of the book it draws on.