// The Math Behind The Models

Graphs & Maths in ML

Calculus, linear algebra, probability, and optimization — made visual. Pick a lab below.

$Slope & Functions$ Math Lab

Slope & Functions

Play with a function's slope live and build intuition for rate of change.

$The Derivative$ Math Lab

The Derivative

See what a derivative actually measures, one tangent line at a time.

$Chain Rule (Signal Chain)$ Math Lab

Chain Rule (Signal Chain)

Watch a signal pass through a chain of functions and see how the chain rule links them.

$Partial Derivatives & the Gradient$ Math Lab

Partial Derivatives & the Gradient

Explore partial derivatives and see how they combine into the gradient vector.

$Gradient Descent$ Math Lab

Gradient Descent

Follow gradient descent step by step as it finds its way downhill.

$Vectors & Dot Product$ Math Lab

Vectors & Dot Product

Build geometric intuition for vectors and what the dot product really measures.

$Matrices & Transformations$ Math Lab

Matrices & Transformations

See how a matrix stretches, rotates, and reshapes space.

$Eigenvalues & PCA$ Math Lab

Eigenvalues & PCA

Discover eigenvalues and eigenvectors, and how PCA uses them to reduce dimensions.

$Probability Distributions$ Math Lab

Probability Distributions

Shape different probability distributions live and see how they behave.

$Bayes' Theorem$ Math Lab

Bayes' Theorem

Update a belief with new evidence and watch Bayes' theorem in action.

$Mean, Variance & Std Dev$ Math Lab

Mean, Variance & Std Dev

Build intuition for mean, variance, and standard deviation with live data.

$Loss Functions$ Math Lab

Loss Functions

Compare loss functions side by side and see how each penalizes error differently.

$Softmax & Cross-Entropy$ Math Lab

Softmax & Cross-Entropy

Watch raw scores turn into probabilities, and see cross-entropy measure the gap.

$Activation Functions, Compared$ Math Lab

Activation Functions, Compared

Compare activation functions and see how each shapes a neuron's output.

$Normal Distribution & the Bell Curve$ Math Lab

Normal Distribution & the Bell Curve

Stretch and shift the bell curve and see what mean and variance really control.

$Mean & Variance: Spread vs. Certainty$ Math Lab

Mean & Variance: Spread vs. Certainty

Morph a distribution's spread and center and watch certainty change live.

$L1 vs L2: Lasso & Ridge$ Math Lab

L1 vs L2: Lasso & Ridge

See how L1/Lasso and L2/Ridge pull model weights in different directions.

$MLE vs. MAP$ Math Lab

MLE vs. MAP

Compare maximum likelihood and MAP estimation as evidence and priors change.

$Tangent Slope Dashboard$ Math Lab

Tangent Slope Dashboard

A live dashboard for tangent lines and instantaneous slope.

$Convex vs. Non-Convex Optimization$ Math Lab

Convex vs. Non-Convex Optimization

See why convex loss surfaces are easy to optimize — and non-convex ones aren't.

$Support Vector Machines$ Math Lab

Support Vector Machines

Watch an SVM find its separating hyperplane, margin, and kernel trick live.

$The Jacobian Matrix$ Math Lab

The Jacobian Matrix

Explore the Jacobian and how it maps small input changes to output changes.

$ROC & AUC$ Math Lab

ROC & AUC

Slide a classification threshold and watch the ROC curve and AUC respond live.

$The Chain Rule Gearbox$ Math Lab

The Chain Rule Gearbox

A gearbox metaphor for the chain rule — turn one gear, watch the rest follow.

$Jaccard Similarity$ Math Lab

Jaccard Similarity

Compare sets visually and see how Jaccard similarity measures overlap.