Explanation

Explanation is the discussion that deepens understanding. A reader arrives wanting to know why — why a method works, why it was designed this way, why one approach is preferred over another.

Explanation is read rather than consulted, and it is the one section where the prose may take a position and argue for it.

What belongs here

• Derivations. The chain rule applied through a network, worked out in full.
• The reasoning behind a design: why bias correction matters early in training, why initialisation variance depends on fan-in.
• Comparisons that argue, as opposed to tabulate: what momentum buys over plain gradient descent, and what it costs.
• Context and history: what problem a method was introduced to solve, and what it replaced.
• Connections between topics that no single implementation owns.

An explanation is free to be discursive. It is the right place for a caveat, an alternative view, or an admission that a practice is convention rather than consequence.

What does not belong here

• Instructions. The moment a page tells a reader what to type to achieve their own goal, it is a how-to guide.
• A lesson for a newcomer. That is a tutorial. An explanation may assume a reader who already knows the vocabulary.
• The definitive table of defaults. That is reference. An explanation may discuss why 0.9 is a reasonable momentum coefficient without becoming the page a reader consults to find that number.
• Restated API documentation. Link to the generated reference instead.

Planned contents

Drawn from the conceptual material currently embedded in the source documents:

• Forward and backward propagation — the full derivation from the L-layer document, including the recursive formula for hidden layers.
• Matrix calculus for neural networks — the chain rule in matrix form, and why vectorisation changes the complexity.
• The optimization landscape — why optimization is difficult, and what gradient descent variants trade against each other.
• Exponential weighted averages — the shared mechanism underneath momentum, RMSprop, and Adam, and why bias correction is needed.
• Adaptive methods — what per-parameter learning rates buy, and their costs.
• Why initialisation matters — vanishing and exploding gradients, symmetry breaking, and the variance argument behind each scheme.
• Regularisation theory — the bias-variance tradeoff, and how L1, L2, dropout, and batch normalisation each act on it.
• How gradient checking works — the finite-difference approximation and why it is a debugging tool rather than a training one.
• The hyperparameter tuning landscape — why some hyperparameters matter far more than others, and why random search beats grid search.