Real numbers in a neural network →
A real number is any point on the number line. In the quantization equation, r is one numerical model value before it is represented by a compact integer code.
Mathematical compendium
Learn the mathematical ideas
These illustrated guides explain the operations and notation used in the equations. Each equation and symbol page links to the concepts it uses.
Quantization: from a value to an integer code →
Quantization maps many possible numerical values onto a smaller set of codes. It helps a small device store and process a neural network using compact integer arithmetic.
Scale factor S →
The scale S is the size of one step on the decoded number line. It must be positive.
Zero-point Z →
The zero-point is the integer code chosen to mean the real value zero.
Equality: what the equals sign claims →
An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.
Fractions: division written vertically →
A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.
Addition and subtraction in an equation →
Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.
Exponents: repeated multiplication and powers →
An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.
Logarithms: the exponent you need →
A logarithm answers an inverse question about powers. log_b(x) is the exponent y for which bʸ = x.
Derivatives: instantaneous rate of change →
A derivative describes how quickly one quantity changes as another changes. It is the slope of a curve at a particular point.
Integrals: accumulated change and area →
An integral adds many small contributions. A definite integral accumulates a quantity over an interval; geometrically it can represent signed area under a curve.
Inequalities: bounds and allowed ranges →
An inequality compares values without claiming they are equal. It describes a range, threshold, or bound that a quantity may satisfy.
Probability: a quantified chance →
Probability assigns a number from 0 to 1 to an event under a stated model. Zero means impossible within that model; one means certain.
Variables: a letter stands for a value →
A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.
Subscripts: which member of a family? →
A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.
Multiplication: combining factors →
Multiplication scales one quantity by another. A dot, a cross, or adjacent symbols can indicate a product.
Sums and products: repeat an operation over an index →
Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.
Functions: inputs become outputs →
A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.
Quantum phase and two-path entanglement →
A quantum phase is an angle attached to a complex amplitude. One path’s phase can be changed by convention; phase differences between alternative paths can change interference and entanglement.
Units and dimensions: a formula’s consistency check →
Units describe how a quantity is measured. A valid physical equation must combine compatible dimensions.