Gradient descent is a basic method used to train deep learning models. It works closely with loss functions, which are important for fine-tuning the model's settings.

Let’s break this down.

First, we have the loss function. This function measures how well the model's guesses match the real answers. We can think of it as a score that tells us how far off the model is. A lower score means the model is doing better.

As the model trains, gradient descent's goal is to make this score (or loss) as low as possible. To do this, we need to find the gradient. The gradient is like a guide that shows us how to change the model's settings to reduce the loss.

Mathematically, the gradient looks like this:

$$\nabla L(\theta) = \left( \frac{\partial L}{\partial \theta_1}, \frac{\partial L}{\partial \theta_2}, \ldots, \frac{\partial L}{\partial \theta_n} \right)$$

This notation represents how much the loss changes when we change each of the model's settings, which are called parameters.

But here’s the catch. We want to lower the score, so we actually move in the opposite direction of the gradient. We update the model settings like this:

$$\theta_{\text{new}} = \theta_{\text{old}} - \alpha \nabla L(\theta_{\text{old}})$$

In this formula, $\alpha$ is the learning rate. This is a number that controls how big of a step we take when adjusting the settings.

Finding the right learning rate is very important. If it’s too high, we might miss the low point we’re aiming for. If it’s too low, it could take a really long time to get there.

By making these small adjustments over and over, the model gets closer to the right settings that minimize the loss function. This helps the model make better predictions.

In simple terms, the way gradient descent and loss functions work together is a key part of how deep learning models learn.