Gradient

As explained in Transformers in Action

A gradient is a vector of partial derivatives indicating how a function changes with respect to its parameters.

A gradient is a vector of partial derivatives of the loss function with respect to model parameters. It indicates how each weight or bias should change, so gradient descent updates parameters in the opposite direction. section 8.1.1

Gradient-based training connects the update direction to several training controls:

• The learning rate scales each update; excessive values can overshoot a minimum, while small values slow convergence or stall progress. section 8.1.1
• Batch size determines how many data points contribute to each gradient calculation, affecting convergence stability and speed. section 8.1.1
• Epoch count controls how often the dataset is revisited; excessive training can overfit, making early stopping a regularization measure. section 8.1.1

Figure 8.1 Gradient descent with lr = 0.1, demonstrating faster convergence

Compare a larger learning rate with faster convergence in gradient descent. section 8.1.1

Figure 8.2 Gradient descent with lr = 0.01, illustrating stability in convergence

Contrast a smaller learning rate with more stable convergence in gradient descent. section 8.1.1

How Transformers in Action covers it

How deep it goes

Explains loss-relative parameter updates and training controls, without deriving partial derivatives or detailing their implementation.

Examples

Contrasts gradient-descent convergence with learning rates of 0.1 and 0.01.

What you can do after

Apply it via gradient descent to understand parameter updates and choose learning-rate, batch-size, and epoch settings.

How it connects

Connects model parameters, loss functions, gradient descent, learning rate, batch size, epochs, overfitting, and early stopping.

liveBookmanning.com

Read Transformers in Action on liveBook Get the book at manning.com

Also explained in

• 

  liveBookmanning.com
  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.
• 

  liveBookmanning.com
  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.
• 

  liveBookmanning.com
  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.
• 

  liveBookmanning.com
  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.
• 

  liveBookmanning.com
  Geometry for ProgrammersA gradient is a vector of partial derivatives describing the direction and rate of greatest increase of a multivariable function.
• 

  liveBookmanning.com
  Grokking Machine LearningA vector of partial derivatives that indicates how a multivariable function changes with respect to its parameters.
• 

  liveBookmanning.com
  Deep Learning with JAXThe derivative of a function with respect to its inputs, used here in the optimization sense for training neural networks.
• 

  liveBookmanning.com
  Ensemble Methods for Machine LearningA gradient is the vector of partial derivatives of a scalar function with respect to its input variables.
• 

  liveBookmanning.com
  Inside Deep Learning: Math, Algorithms, ModelsThe vector of partial derivatives of a function with respect to its variables or model parameters.
• 

  liveBookmanning.com
  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.
• 

  liveBookmanning.com
  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.
• 

  liveBookmanning.com
  Sutskever's ListA gradient is the vector of partial derivatives describing how a function changes with respect to its parameters.
• 

  liveBookmanning.com
  Deep Learning with PyTorch, Second EditionA vector of derivatives describing a function’s change with respect to its inputs or parameters.
• 

  liveBookmanning.com
  Advanced Algorithms and Data StructuresA gradient is the vector of partial derivatives of a multivariable scalar function, indicating the direction of greatest local increase.
• 

  liveBookmanning.com
  Data Without LabelsA gradient is a vector of partial derivatives that indicates how a scalar function changes with respect to multiple variables.
• 

  liveBookmanning.com
  How Large Language Models WorkA gradient is a vector of derivatives indicating how an objective function changes as its parameters change.
• 

  liveBookmanning.com
  Reinforcement Learning from Human FeedbackA gradient is a vector of derivatives indicating how a scalar function changes with respect to its parameters.
• 

  liveBookmanning.com
  Machine Learning Algorithms in DepthA gradient is a vector of partial derivatives that indicates how a scalar function changes with respect to its variables.
• 

  liveBookmanning.com
  Distributed Machine Learning PatternsA gradient is a vector of partial derivatives that indicates how a function changes with respect to its parameters.

Compare how 20 books explain gradient →

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.

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