tensor + the -arium of aquarium, planetarium: a place where you observe tensors flowing. Playful and distinctive.
Four ways to find groups in unlabeled data. Every page runs live in the browser — click to place points, step the algorithm one move at a time, and see exactly where each one succeeds and where it breaks.
Place the centroids yourself, then alternate two steps: reassign every point to its nearest centroid, move every centroid to the mean of its points. Watch J fall — and watch it settle on the wrong answer when the clusters are not round.
Start with every point its own cluster and merge the closest pair, over and over, until one remains. Compare single, complete and average linkage, then cut the tree by cluster count or by height.
Cluster by density instead of distance to a center. Set ε and minPts, and the algorithm grows clusters of any shape from their core points — and labels whatever is left over as noise.
Soft clustering. Each cluster is an ellipse with its own size and tilt, and each point gets a probability of belonging rather than a label. Step through the E-step and M-step by hand.
Three ways to decide a reading does not belong. Two of them are arithmetic you could do on paper; the third is a model. Each page generates its own data, so press the button a few times and watch how much the answer moves.
How many standard deviations from the mean? Generate a fresh bell curve, pick a cut-off, and see the z-scores. Then add a few odd readings and watch them inflate the very σ you are measuring them against.
The middle half of the data, drawn as a box plot. Quartiles barely move when you add outliers, which is exactly why this rule survives contamination that defeats a z-score.
Cut the plane at random until one point sits alone, and count the cuts. Anomalies are the points that are easy to isolate. Watch a single tree do it, then grow a hundred.
Four pages on how a neural network learns, from one neuron's arithmetic to picking the next word. Every number is worked out live in the browser — step through it and check it with a calculator.
One input, two hidden neurons, one output: seven weights and biases. Step through the forward pass and the backward pass one line at a time, check each number with a calculator, then update and watch the loss fall.
Without an activation, a network of any size is one straight line. Fit a curve with ReLU, sigmoid, tanh or leaky ReLU and watch each neuron add one bend — then find a dead neuron.
Gradient descent, SGD, momentum and Adam on the same loss map. Watch each path find the bottom, then race all four on three landscapes. No optimizer wins everywhere.
A language model finishes “The cat sat on the ___”. Softmax turns word scores into probabilities, temperature sharpens or flattens them, and greedy or sampling picks the word.
Eleven pages on how a computer sees, from the numbers in one pixel to a small CNN naming a drawing, then on to finding each object and drawing a box around it, and finally to making new pictures. Every filter, pool and score is worked out live in the browser — click a pixel and check the math.
A picture is just numbers. Zoom in to the RGB values of single pixels, turn color into gray, split the three channels, shrink the image, and change brightness and contrast.
Slide a 3×3 filter over a grayscale picture: nine weights, one sum per position. Sobel filters find vertical and horizontal edges; see the raw signed sums, only the positives, or the strength.
Keep one number per tile: the largest, or the average. Pool an edge map again and again, 118×88 down to 7×5, and see what survives.
Draw a stroke and follow it through a tiny network with every weight set by hand: filters, ReLU, pooling, five class scores and softmax. Then find the drawing it gets wrong.
Turn four class scores into probabilities that add up to 100%. Slide the temperature to make the network more or less sure, then pick at random with the bars as the odds.
Not just what is in the picture, but where. Slide a cat template over every position, score each window, keep the ones above the cut-off, and clean up the duplicates with NMS.
One number for how well a box fits: the shared area divided by the area both boxes cover. Drag the boxes and see why the same 5-pixel mistake hurts a small box far more.
Propose regions, then check each one. Count the CNN runs as R-CNN becomes Fast R-CNN and then Faster R-CNN: 111 runs, then one.
One pass, every grid cell at once. Click a cell to see the seven numbers it predicts, then watch the score cut-off and NMS turn a pile of boxes into one per animal.
Two networks play a game: a forger turns random numbers into dots, a detective tries to tell them from real ones. Watch the fakes move onto the real shape, and see what breaks when only one side learns.
Mix noise into a smiley until only static is left. Then train a network to guess the noise, and watch it turn a random cloud of dots back into a smiley, one small step at a time.