In machine learning, neural networks learn to classify data points or predict continuous values. This separation or prediction is achieved through a decision boundary, which is a kind of invisible dividing line (or surface in higher dimensions)Â in the feature space.
Here's a breakdown of decision boundaries in neural networks:
How they are determined:
Neural networks don't explicitly learn the decision boundary itself.
During training, they adjust internal parameters (weights and biases) based on the training data.
These adjustments aim to minimize the error between the network's predictions and the actual labels.
As the network learns, the decision boundary emerges implicitly as a consequence of these weight adjustments.
How they develop during training:
The complexity of the decision boundary depends on the network architecture (number of layers and neurons) and the activation functions used.
Simpler networks with one layer can only learn linear decision boundaries, which are straight lines in two dimensions or hyperplanes in higher dimensions.
More complex networks with hidden layers and non-linear activation functions (like ReLU) can learn non-linear decision boundaries, allowing them to handle more intricate patterns in the data.
As training progresses, the decision boundary iteratively adjusts to better separate the data points according to their labels.
Common observations:
Overfitting: If the network memorizes the training data too closely, the decision boundary might become too complex and not generalize well to unseen data.
Underfitting: Conversely, a simple network might underfit the data, resulting in a straight line (or hyperplane) that doesn't capture the underlying relationships.
Special observations about ReLU networks:
Rectified Linear Unit (ReLU) is a popular activation function known for its efficiency.
ReLU outputs the input directly if it's positive, and zero otherwise. This introduces a kind of "piecewise linearity" in the network.
ReLU networks can still learn complex decision boundaries due to the way multiple ReLU neurons are combined in layers. However, the boundaries might have a more piecewise linear character compared to networks using smoother activation functions.