Gradient

As explained in Data Without Labels

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

A gradient is a vector of partial derivatives showing how a scalar function changes across multiple variables. In deep learning, it points toward increasing loss; its negative gives the steepest descent direction for reducing error. section 8.2.6

Gradient-based optimization updates model parameters iteratively:

• Batch gradient descent evaluates the training dataset before each update and seeks a function's global minimum, but can be slow for large or high-dimensional data. section 8.2.6
• Stochastic gradient descent updates coefficients after each training instance, reducing the time required for an iteration. section 8.2.6
• Mini-batch gradient descent updates from small data subsets, balancing speed and accuracy while introducing batch size as a tunable hyperparameter. section 8.2.6

Backpropagation calculates the loss gradient with respect to every neural-network weight. It works backward from the final layer, combines layer derivatives through the calculus chain rule, and updates weights to reduce loss over repeated iterations. section 8.4.1

Gradient updates in Boltzmann learning

A Boltzmann learning rule derives weight updates from the gradient of an energy function. Training decreases system energy by aligning visible-hidden activity in the data distribution with activity generated by the model. section 8.8.1

Figure 8.8 The concept of gradient descent. It is the mechanism to minimize the loss function.

Use the figure to visualize gradient descent moving downward toward a global minimum while minimizing the loss function. section 8.2.6

How Data Without Labels covers it

How deep it goes

Explains steepest descent, batch variants, backward derivatives, and chain-rule calculation, but stops short of implementation code.

Examples

Uses batch, stochastic, and mini-batch updates, neural-network backpropagation, and Boltzmann energy minimization as examples.

What it assumes

Assumes loss functions, neural-network layers, weights, biases, and partial derivatives while introducing their roles in training.

What you can do after

Apply it via gradient-descent variants and backpropagation to understand iterative loss-reducing weight updates.

How it connects

Connects gradient descent with loss functions, optimizers, backpropagation, the chain rule, and energy functions.

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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 Data Without Labels. The section links point to the parts of the book it draws on.