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Dropout and Its Mathematical Interpretation

Dropout is a regularization technique that switches neurons off at random during training, with retention probability p, and divides the surviving activations by p to preserve their scale. At inference the full network runs without dropping anything. Mathematically it amounts to averaging a huge ensemble of subnetworks that share weights.

Technology

L1 and L2 Regularization (Weight Decay)

L1 and L2 regularization adds a term to the loss function that penalises large weights. L2, or weight decay, shrinks the weights smoothly towards zero; L1 drives them exactly to zero and yields sparse models. Both curb overfitting and improve the generalisation ability of a neural network on unseen data.

Technology

Vector Norms (L1, L2) and Distance

A vector norm measures its length or magnitude. The L1 norm adds the absolute values of the components, while the L2 norm applies the Pythagorean theorem: the square root of the sum of squares. Both define different distances between points and underpin the regularisation that prevents overfitting in neural networks.