Interactive Demos
Build intuition by playing with the math. Every demo runs in your browser with zero setup. Sliders, toggles, and live animations.
Featured
Diagnostic Loop Demo
Watch a seeded learner start easy, miss a Hoeffding assumption, see it return later, and earn a finite-class generalization readiness signal.
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Adaptive Test Flight Recorder
Inspect local diagnostic runs while testing: missed topics, skipped questions, recovered retries, and the route checklist for the adaptive loop.
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Gold Diagnostic Report
Inspect three gold diagnostic lanes: coverage, Q-matrix links, claim links, quality risks, and synthetic learner simulations.
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Optimizer Pinball
An entry lab for optimization intuition: tune GD, Momentum, Nesterov, and Adam on real loss surfaces and watch the optimizer balls search for the minimum.
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Matrix Mechanics Lab
An entry lab for linear algebra intuition: turn matrices into moving geometry before spectra, PDEs, and random matrices.
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ReLU Family Lab
Compare ReLU, Leaky ReLU, ELU, GELU, and Softplus on one board: dead neurons, rescue slopes, smooth gates, and rounded hinges.
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Normalization Lab
See BatchNorm, LayerNorm, and RMSNorm normalize different axes: batch coupling, mean centering, and scale-only control.
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Diffusion Lab
Watch clean structure turn into noise, then tune guidance, sampler choice, and step budget as the reverse path tries to recover it.
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Factor Graph / World Model Lab
Use one visual language for GraphSLAM, energy models, latent planning, and video simulators: observed nodes filled, latent nodes hollow, factors local, functions explicit.
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NUTS / Funnel Lab
Compare centered and non-centered hierarchies, then watch divergence risk and effective sample size change as weak data turns a smooth posterior into a funnel.
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High-Dimensional Probability Lab
Watch random vectors concentrate, Marchenko-Pastur spectra widen with aspect ratio, and PCA spikes separate from noise only past the threshold.
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Probability Mechanics Lab
Build sample spaces, random-variable maps, expectation, variance, conditioning, transformations, and L2 geometry by hand.
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Random Matrix / Spectral Geometry Lab
See the noise spectrum before trusting PCA: Marchenko-Pastur bulk, conditioning, ridge stabilization, and spiked covariance.
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Overfitting Arena
Tune flexibility, sample count, and label noise. Watch train error, test error, and the generalization gap split apart.
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Interactive (sliders and controls)
Bias-Variance Tradeoff
Drag the complexity slider. Watch the polynomial fit change. See train and test error diverge.
Softmax Temperature
Slide temperature from 0.1 to 10. Watch the probability distribution sharpen or flatten.
Dropout Visualization
Toggle dropout on and off. Watch neurons mask and rescale by 1/(1-p).
Gradient Descent Contours
The full optimizer pinball embedded in the convex optimization theory page.
Distribution Explorer
Slide parameters of Gaussian, Bernoulli, Poisson. Watch PDF and CDF change.
MLE Likelihood Surface
Add data points. Watch the likelihood surface shift. See the MLE move.
Learning Rate Schedules
Compare cosine decay, step decay, warmup, and constant LR side by side.
Activation Functions
ReLU, GELU, SiLU (Swish), tanh. See the function and its derivative simultaneously.
Hessian Curvature
Visualize curvature at different points on a loss surface. See where saddle points live.
Fat Tail Comparison
Gaussian vs Cauchy vs Student-t. See how tail heaviness changes concentration behavior.
Induction Head Circuit
Visualize the two-layer attention circuit that enables in-context learning.
Teaching Diagrams
RLHF Pipeline
SFT, reward model, PPO flow
Kalman Filter
Predict-update cycle
Gibbs Sampling
Variable cycling + staircase trajectory
Fisher Information
Log-likelihood curvature
Hypothesis Classes
Linear vs polynomial vs neural net boundaries
Implicit Bias
GD on interpolation manifold
Joint Distribution
2D scatter with marginals
Rademacher Complexity
Random labels + class correlation
PAC Learning
Sample complexity curves
Measure Theory
Sigma-algebra Venn diagram
SGD Convergence
O(1/T) vs O(1/sqrt(T)) comparison
Optimizer Comparison
SGD/Momentum/Adam/Muon update rules