THE PLAYGROUND / 19 LIVE EXPERIMENTS
Experiments.
Small things, built for the joy of it.
The best way to understand? Play with it.
A little theory.
A lot of “what if?”
ON THE WORKBENCH
TRY THIS FIRSTOPTIMIZATION / LIVE DEMO
Gradient descent playground
Roll downhill on a loss surface: dial the learning rate up until the steps overshoot and diverge, and watch the trajectory pick its way across a bowl, a ravine, or a saddle.
THE COLLECTION
A few things to tinker with.
19 experiments
Showing all 19 experiments
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UUID v7 inspector
Generate a UUID v7 and watch the timestamp hiding in its first 48 bits. The reason your database indexes love them.
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Diffie–Hellman playground
Watch two parties agree on a secret while you see every byte they exchange — then switch sides and try to break it as Eve.
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Least squares playground
Drag the points around and watch the best-fit line argue back — then see the same fit as the bottom of a bowl-shaped loss surface.
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Linear regression playground
Resample noisy data from a known line and watch the OLS fit jitter around the truth — with a confidence band and a cloud of fits that makes variance something you can see.
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Gradient descent playground
Roll downhill on a loss surface: dial the learning rate up until the steps overshoot and diverge, and watch the trajectory pick its way across a bowl, a ravine, or a saddle.
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Logistic regression playground
Slide two classes apart and watch a fitted sigmoid steepen into confidence — or overlap them and see it flatten as cross-entropy climbs. The decision boundary is a single point where the S-curve crosses one-half.
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Cross entropy playground
Drag the predicted probability and watch the −log(p) loss spike — then push a predicted distribution against a one-hot truth and see cross entropy and KL react.
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Softmax playground
Drag the logit bars, turn the temperature knob, and watch raw scores become a probability distribution that always sums to one — plus the log-sum-exp stability trick.
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ReLU playground
Tilt the leaky slope to watch ReLU's variants morph near zero — then stack a handful of ReLU bumps into a piecewise-linear curve and tune it toward a target.
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Adam playground
Race SGD, momentum, RMSProp and Adam across the same loss surface from the same start — and watch memory and per-parameter scaling earn their keep.
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A matrix is a verb playground
Drag the four entries of a 2×2 matrix and watch it warp a grid live — the determinant is right there as the area it stretches or flips.
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The four fundamental subspaces playground
Drag a target b around the output space and watch it fall inside or outside the column space — the reachable set — as the solvable/not-solvable badge flips.
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The shadow of a vector playground
Drag the vector b and watch its shadow b̂ slide along a fixed subspace while the gold residual b − b̂ holds its right angle — projection you can feel with your hand.
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Eigenvectors playground
Set a 2×2 matrix and watch which directions on the unit circle refuse to turn — the eigenvectors — then step power iteration onto the dominant one.
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Positive definite playground
Set the three entries of a symmetric 2×2 matrix and watch the contour map of its quadratic form bend from a bowl to a saddle — with the eigenvalues and definiteness verdict updating live.
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SVD playground
Set a 2×2 matrix and watch it map the unit circle to an ellipse in three acts — rotate, stretch, rotate — with the singular values as the ellipse's semi-axes.
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PCA playground
Scatter a 2-D point cloud and watch its principal axes swing to follow — PC1 along the direction of greatest variance, PC2 perpendicular — then project onto PC1 and see how little of the story you lose.
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RAIDZ1 reconstruction
Kill one disk in a single-parity stripe and watch it come back as the XOR of the survivors — then try to kill a second and watch the one equation refuse.
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RAIDZ2 reconstruction
Take out two disks at once and watch RAIDZ2 solve a 2×2 system over GF(2⁸) — two independent syndromes P and Q, a nonzero determinant, one field inverse.
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