#sigmoid

Sigmoid bred/brexed by me!

In neural networks, activation functions are very important for figuring out what a cell will do when it is given an input or set of inputs. The Rectified Linear Unit (ReLU) and the Sigmoid function are two activation functions that are often used. We'll talk about the differences between these two tasks in easy-to-understand language. Definition of the ReLU Activation Function

This is how the Rectified Linear Unit (ReLU) activation function is written: $$ f(x) = \max(0, x) If $x$ is a positive number, then the result is also a positive number. If you put in something negative, the result is 0. Features and traits

Lack of linearity: ReLU adds non-linearity to the model, which helps it learn complicated patterns. Simplicity: It uses few calculations because it only needs to compare and find the highest. Sparse activation: In a network that is randomly set up, only about half of the hidden units are active (have a non-zero output), which can make the model work better. Gradient Propagation: The disappearing gradient problem is something that other activation functions, like Sigmoid and Tanh, also have. ReLU helps fix this problem.

Pros and cons

Dying ReLU Problem: Neurons can get stuck during training and always send out 0 no matter what. This happens when the weights are changed in a way that stops the cell from firing again. Non-zero Centered: The results are never negative, which can make it harder to find the best solution.

What Does Sigmoid Activation Function Mean? You can write the Sigmoid activation function as $$\sigma(x) = \frac{1}{1 + e^{-x}} $$ Any real number can be mapped to the range (0, 1) by this function, which makes an S-shaped curve. Features and traits Smooth Gradient: The Sigmoid function has a smooth gradient, which is helpful for optimization methods that use gradients. The result is always between 0 and 1, which makes it good for problems that need to classify things into two groups. It was one of the first activation functions used in neural networks, which makes it historically important.

Pros and cons

Vanishing Gradient Problem: When the input numbers are very high or very low, the Sigmoid function's gradient gets very small. This can make the training process go much more slowly. Non-zero Centered: The results are not zero-centered, which can cause updates to be less effective during training, just like with ReLU. Calculations Take a Lot of Time: The exponential function in the Sigmoid formula makes it take longer to calculate than ReLU. Compared to

How it Works Speed of Training: Because it doesn't have the disappearing gradient problem, ReLU usually makes training deep neural networks faster than Sigmoid. Complexity: ReLU is easier to process and set up, which makes it better for big neural networks.

Cases of Use In deep neural networks, especially convolutional neural networks (CNNs) and deep learning models, ReLU is often used in the hidden layers. Sigmoid: This type of function is often used in the output layer for problems that need a result between 0 and 1, like binary classification problems.

The Sigmoid function is the most frequently widely used activation function in the beginning of deep learning. It is a smoothing function that is easy to derive and implement.