Gradient

As explained in How Large Language Models Work

A gradient is a vector of derivatives indicating how an objective function changes as its parameters change.

A gradient is a set of measurements showing the direction and amount to change a neural network’s parameters to reduce error. It connects a loss function, which scores how poorly the model performs, with gradient descent, the repeated process that adjusts the model. section 4.1 section 4.1.2

A training step follows this pattern:

• Compare the model’s actual outputs with the expected outputs. section 4.1.2
• Use the loss function to turn the error into a single numeric score. section 4.1
• Use the gradient to make many parameters slightly better, then repeat the process. section 4.1.2

Rolling a ball downhill

Imagine a ball on a hilly landscape. The ball’s position represents a parameter value, while the hill’s height represents loss. The gradient indicates which direction and how far to move; repeated small moves aim for a valley with lower loss. The method can still settle in a local valley rather than the best one, and it offers no guarantee of a good solution. section 4.1.2

Figure 4.3 Inputs and labels (the known correct answers for each input) are used to tweak the neural network during gradient descent. A network is made of parameters that are altered a small amount each time gradient descent is applied. We eventually transform the network into something useful by applying gradient descent millions or billions of times.

Follow the figure to see how inputs and known labels produce small parameter updates that gradually transform a neural network. section 4.1.2

How How Large Language Models Work covers it

How deep it goes

Defines direction and amount of parameter change, then traces repeated updates while stopping short of mathematical derivation.

Examples

Uses a ball rolling downhill, loss landscapes, training inputs, expected outputs, and parameter-update diagrams.

What it assumes

Introduces loss functions and parameter adjustment together, assuming no advanced machine-learning background.

What you can do after

Evaluate how gradients guide neural-network training and why repeated updates may still miss the best solution.

How it connects

Connects gradients with loss functions, gradient descent, neural networks, parameters, training data, and local minima.

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Also explained in

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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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  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.

This explainer was generated by Manning's knowledge graph from the text of How Large Language Models Work. The section links point to the parts of the book it draws on.