Logarithms for AI: Keep Tiny Probability Products from Vanishing
Learn logarithms as inverse powers, derive the product-to-sum laws, and use NumPy log scores to distinguish probability products that float64 rounds to zero.
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Mathematical Foundations
8articlesin this category.
Powers for AI: Why Doubling Context Can Quadruple Attention Work
Learn exponent laws and roots, then use a log-scale explorer and NumPy to see why doubled model dimensions or context can create four times as many quantities.
Sigma Notation for AI: How Losses Become One Training Objective
Learn sigma and product notation, expand bounds into loops, and use NumPy sums and means to turn per-example errors into a mean squared error objective.
Tensor Indices for AI: Reading Samples, Tokens, and Features
Learn to read tensor subscripts, translate batch-token-feature addresses into NumPy, and catch valid-looking axis mistakes in AI code.
Set Notation for AI Datasets: Membership, Splits, and Leakage
Learn sets, membership, union, intersection, and partitions by finding and fixing overlap in an AI training, validation, and test split.
Domain and Codomain: The Input Contract Every AI Function Needs
Learn how domains and codomains specify valid model inputs and promised output types, then diagnose shape, range, and undefined-operation failures.
Functions Are Reusable Machines for AI Calculations
Move from variables to functions: evaluate input-rule-output mappings, compose simple calculations, and see why one model can process many examples.
Variables, Values, and the Three Roles Inside an AI Model
Learn to read model equations by separating variable names from their current values, then trace inputs, parameters, and outputs through a tiny scoring model.