How deeply does Machine Learning Algorithms in Depth cover momentum?

Explains exponential averaging, gradient alignment, parameter choice, and Nesterov’s evaluation difference, but does not provide a full derivation.

Momentum

As explained in Machine Learning Algorithms in Depth

Momentum is an optimization technique that incorporates an exponentially weighted moving average of past gradients into parameter updates.

Momentum is an optimization technique that accumulates an exponentially decaying moving average of past gradients. Updates continue in directions supported by recent gradients, so their size reflects gradient magnitude and alignment. section 10.4

Momentum is characterized by these practical points:

Use the momentum parameter α to control the moving average; common values are 0.5 and 0.9. section 10.4
Interpret aligned gradients as reinforcing movement, while the resulting step size depends on the magnitude and alignment of the gradient sequence. section 10.4
Distinguish Nesterov momentum by evaluating the gradient after applying the current velocity, which adds a correction factor. section 10.4

Optimizer comparison

Compare momentum with stochastic gradient descent, Nesterov momentum, AdaGrad, RMSProp, and Adam when training a LeNet model on CIFAR-100, using cross-entropy loss and validation accuracy. section 10.4

How Machine Learning Algorithms in Depth covers it

Cover of Machine Learning Algorithms in Depth

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Also explained in

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Inside Deep Learning: Math, Algorithms, ModelsA stochastic gradient-based optimization method that uses an accumulated velocity term for parameter updates.
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Sutskever's ListMomentum is an optimization technique that incorporates a running history of parameter updates to smooth and accelerate training.
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Math and Architectures of Deep LearningAn optimization strategy that accelerates parameter updates using accumulated past gradients or a lookahead variant to smooth descent on the loss surface.
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Natural Language Processing in Action, Second EditionMomentum is an optimization hyperparameter that incorporates prior update direction to accelerate or damp parameter movement during gradient-based optimization.
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Deep Learning with R, Third EditionMomentum is an optimization technique that incorporates previous parameter updates into the current update to improve movement through the optimization landscape.

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Related concepts

adamused by · Adam is an adaptive stochastic-gradient optimization algorithm that updates model parameters using moving estimates of the first and second moments of gradients.
inner productuses · An inner product is a scalar-valued operation on two vectors that combines their corresponding components, summing their products and, for complex vectors, using conjugation.
stochastic gradient descentconfigures · Stochastic gradient descent is an iterative optimization method that updates parameters using gradients estimated from individual examples or randomly selected small batches.
partial derivativeequivalent to · A partial derivative is the derivative of a multivariable function with respect to one variable while holding the other variables constant.
batch sizeuses · Batch size is the number of items grouped together for processing or computation as a single batch.
Nesterov momentumincludes · Nesterov momentum is an optimization method that evaluates the gradient at a momentum-based lookahead position before updating model parameters.

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