The Core Principle of Neural Network Learning: Gradient Descent

Gradient Descent is an algorithm used in machine learning and deep learning for AI models to find optimal weights.

Gradient descent is often compared to descending a mountain to find the lowest point.

To minimize the difference between predicted values and actual values, it finds the steepest direction (gradient) and moves step-by-step.

AI models repeat this process to optimize weights for increasingly accurate predictions.

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Loss Function = Height of the Mountain
Weight Adjustment = Adjusting the Descent Direction
Gradient = Indicates how steep it is
Learning Rate = Determines how much to move in one step

Gradient descent optimizes weights by repeating the following steps:

Compute the difference between predicted values and actual values with the current weights.

Use a loss function to quantify the error.

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Actual Value: 1.0, Predicted Value: 0.6
Loss (MSE) = (1.0 - 0.6)^2 = 0.16

Differentiate the loss function to find the gradient, which points in the direction that reduces the loss function's value the fastest from the current position.

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Current Weight: 0.5
Gradient: -0.3 (Direction of Decrease)

Adjust the weight based on the gradient.

The step size is determined by multiplying the gradient by the learning rate (α).

The formula is as follows:

$$\text{New Weight} = \text{Current Weight} - (\text{Learning Rate} \times \text{Gradient})$$

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Current Weight: 0.8
Gradient: -0.2
Learning Rate: 0.1
New Weight: 0.8 - (0.1 * -0.2) = 0.82

Repeating this process gradually moves the weights closer to their optimal values, resulting in more accurate predictions by the neural network.

Gradient descent is a key method for neural networks to find optimal weights, with appropriate learning rate settings being crucial.

A learning rate that's too large may overshoot the optimal value, while one that's too small could slow down learning.

To address this, various gradient descent algorithms such as Stochastic Gradient Descent (SGD), Batch Gradient Descent (BGD), Momentum, and Adam are used.

In the next lesson, we will explore stochastic gradient descent in detail.