How deeply does Machine Learning Algorithms in Depth cover gradient?

Explains gradient-based update directions, learning rates, momentum, Nesterov momentum, and adaptive optimization methods.

Gradient

As explained in Machine Learning Algorithms in Depth

A gradient is a vector of partial derivatives that indicates how a scalar function changes with respect to its variables.

A gradient is a vector of partial derivatives describing how a scalar loss changes with respect to model parameters. For minimization, optimization moves parameters in the gradient’s negative direction. section 10.4

Neural-network optimization uses the gradient to determine parameter updates:

Stochastic gradient descent computes the loss gradient on a mini-batch and updates parameters using a learning rate. section 10.4
Momentum accumulates an exponentially decaying average of past gradients, making step size depend on gradient magnitude and alignment. section 10.4
Nesterov momentum evaluates the gradient after applying the current velocity, adding a correction to the update. section 10.4
Learning-rate schedules control update size; rates that are too high can miss optima, while rates that are too low prolong training. section 10.4

Training a convolutional network

A CNN trained on CIFAR-100 can compare cross-entropy loss and validation accuracy under different gradient-based optimizers. section 10.4

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Also explained in

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Deep Learning with R, Third EditionA gradient is the tensor-valued derivative of a function whose inputs are tensors, with each coefficient indicating how the output changes with respect to one input coefficient.
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Math and Architectures of Deep LearningThe vector of partial derivatives indicating the local direction of steepest increase of a function, used here to choose the steepest ascent or descent direction.
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Natural Language Processing in Action, Second EditionA gradient is the vector of partial derivatives that indicates how a function changes with respect to its parameters or inputs.
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Machine Learning for Tabular Data: XGBoost, Deep Learning, and AIA gradient is a quantity indicating the direction and rate of greatest local increase of an objective with respect to parameters.
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Geometry for ProgrammersA gradient is a vector of partial derivatives describing the direction and rate of greatest increase of a multivariable function.
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Grokking Machine LearningA vector of partial derivatives that indicates how a multivariable function changes with respect to its parameters.
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Deep Learning with JAXThe derivative of a function with respect to its inputs, used here in the optimization sense for training neural networks.
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Ensemble Methods for Machine LearningA gradient is the vector of partial derivatives of a scalar function with respect to its input variables.
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Inside Deep Learning: Math, Algorithms, ModelsThe vector of partial derivatives of a function with respect to its variables or model parameters.
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Grokking AI Algorithms, Second EditionA gradient is a vector or matrix of partial derivatives that describes how a function changes with respect to multiple parameters.
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Deep Learning with Python, Third EditionThe generalization of a derivative to a tensor-valued function, representing the local rate and direction of change with respect to each input component.
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Sutskever's ListA gradient is the vector of partial derivatives describing how a function changes with respect to its parameters.
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Deep Learning with PyTorch, Second EditionA vector of derivatives describing a function’s change with respect to its inputs or parameters.
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Advanced Algorithms and Data StructuresA gradient is the vector of partial derivatives of a multivariable scalar function, indicating the direction of greatest local increase.
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Data Without LabelsA gradient is a vector of partial derivatives that indicates how a scalar function changes with respect to multiple variables.
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How Large Language Models WorkA gradient is a vector of derivatives indicating how an objective function changes as its parameters change.
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Reinforcement Learning from Human FeedbackA gradient is a vector of derivatives indicating how a scalar function changes with respect to its parameters.
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Distributed Machine Learning PatternsA gradient is a vector of partial derivatives that indicates how a function changes with respect to its parameters.
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Transformers in ActionA gradient is a vector of partial derivatives indicating how a function changes with respect to its parameters.

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Related concepts

backpropagationproduced by · Backpropagation is a procedure for computing derivatives of an output or loss with respect to inputs and parameters by applying the chain rule backward through a computational graph.
gradient descentused by · Gradient descent is an iterative optimization method that updates parameters opposite the gradient of an objective function to reduce its value.
jax.gradproduced by · jax.grad is a JAX transformation that creates a function computing derivatives, typically gradients of a scalar-output function with respect to specified inputs.
optimizationused by · Optimization is the systematic selection or adjustment of values, actions, or system designs to improve a specified objective, often subject to constraints.
PyTorchused by · PyTorch is an open-source machine-learning framework for Python that provides tensor computation, automatic differentiation, and tools for building and training neural networks.
tf.GradientTapeproduced by · tf.GradientTape is a TensorFlow context manager that records tensor operations so gradients can subsequently be computed automatically.

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