In mathematics, a tangent is a straight line that touches a curve at only one point. It is used to understand the slope, or steepness, of a curve at a specific point.

Imagine you're standing at the bottom of a hill and looking up. The slope of the hill at your feet is the steepness of the hill at that point. If you take a step forward, the slope may change, it could be steeper or less steep. The tangent line is a mathematical representation of the slope of the hill at that specific point.

Tangents are often used in geometry, calculus and other branches of mathematics, and it is also used to understand the behavior of a curve.

## Tangent in machine learning

In machine learning, tangents are used in a technique called gradient descent to optimize the parameters of a model. A model's parameters are the values that determine its behavior, such as the weights and biases in a neural network. To make a model perform well, we need to find the best values for these parameters.

In order to find the best parameters, the algorithm starts with a set of initial values and then repeatedly updates the parameters by taking small steps in the direction of the tangent line of the model's performance curve.

The tangent line represents the direction of the steepest descent of the curve, and the algorithm aims to reach the lowest point of the curve, which represents the best model parameters.

For each step, the algorithm calculates the gradient of the performance curve at the current parameter values. The gradient is a vector that points in the direction of the steepest ascent. The algorithm then takes a step in the opposite direction of the gradient, which is the direction of the steepest descent. This is where the term gradient descent comes from.

In summary, tangent is used in machine learning to optimize the parameters of a model by using a technique called gradient descent. The algorithm starts with initial values and repeatedly updates the parameters by taking small steps in the direction of the tangent line of the model's performance curve until it finds the best parameters.