Gradient

Gradients are a core concept in machine learning algorithms that operate by optimizing a model to minimize a loss function. The gradient points in the direction of steepest ascent of the loss function, so taking steps against the gradient leads to lower loss values and better model fits.

Mathematically, the gradient is a partial derivative that gives the slope or rate of change of the loss function with respect to each parameter in the model. For neural networks, parameters refer to the weights and biases that connect the neurons. By adjusting weights slightly in the negative gradient direction, the loss decreases most rapidly during training.

Computationally, the gradient is obtained via backpropagation. The model makes predictions on the training data, compares it to known labels to compute the loss, and then propagates this error signal backwards to attribute portions of the loss to specific parameters. The rate of error change for each parameter forms its gradient.

The learning rate hyperparameter determines the step size taken against the gradient. A properly tuned learning rate will lead to smooth and rapid convergence to an optimal set of parameters that minimizes the loss. Learning rates that are too small lead to slow training, while large rates may cause divergent oscillations.

Thus, gradients are essential for "steering" machine learning models towards optimal parameters by providing localized error signals specific to each parameter. They enable efficient navigation of high dimensional spaces to the lowest regions of the loss function across many training iterations. Tuning the gradient descent process is key to achieving good model performance.