In the context of neural networks, saturation refers to a situation where the output of an activation function or neuron becomes very close to the function’s minimum or maximum value (asymptotic ends), and small changes in the input have little to no effect on the output. This limits the information propagated to the next layer. For example: In the sigmoid activation function, as the input becomes extremely positive or negative, the output approaches 1 or 0, respectively, and the gradient (derivative) of the function becomes very close to zero. In the hyperbolic tangent (tanh) activation function, a similar saturation occurs for very large positive or negative inputs, resulting in output values close to 1 or -1.

Saturation becomes a critical issue in neural network training as it leads to the vanishing gradient problem, limiting the model’s information capacity and its ability to learn complex patterns in the data. When a unit is saturated, small changes to its incoming weights will hardly impact the unit’s output. Consequently, a weight optimization training algorithm will face difficulty in determining whether this weight change positively or negatively affected the neural network’s performance. The training algorithm would ultimately reach a standstill, preventing any further learning from taking place.

To address saturation-related issues, many modern neural networks use activation functions like Rectified Linear Unit (ReLU) and its variants, which do not saturate for positive inputs and allow gradients to flow more freely during training. Additionally, techniques like batch normalization and skip connections have been introduced to mitigate saturation-related problems in deep networks.