Interactive Lab
Scroll-driven articles that make the mechanism visible: concrete examples first, live figures second, and formal math only when it earns its place.
Deep learning 68
- ReLU Classification Playground Train a small ReLU classifier, then inspect the signed functions that assemble its decision surface.
- ReLU Function Lab Construct a continuous function from fixed ReLU hinges, then test what deterministic gradient descent finds.
- From Likelihood to Loss Every loss function is a noise model in disguise — pick the density, read off the loss
- Softmax & Cross-Entropy Turn logits into probabilities, read off the loss, and watch the gradient become p minus y
- A Bayes Classifier, by Hand Two Gaussians and a prior — build the optimal classifier and watch the decision boundary move
- MAP = Likelihood × Prior Watch regularization appear as a prior multiplying the likelihood in parameter space
- The Derivative is a Local Line Zoom into any smooth curve and it becomes a straight line — its slope is the derivative
- Partial Derivatives are Slices Freeze one variable, take an ordinary derivative — the gradient just collects the slopes
- The Jacobian is a Local Warp Near a point, a nonlinear map acts like its Jacobian — a circle becomes an ellipse
- Pooling, Cell by Cell Slide a pooling window over a feature map and watch max vs average downsample it live
- Padding, Stride & Output Size Move four sliders and watch one floor formula predict a convolution's output size exactly
- Why 1×1 Convolutions Save Compute Compare a direct 3x3 conv with a 1x1 bottleneck and watch the FLOP bars diverge several-fold
- Freeze or Fine-tune? Set the dataset size and cut point, and watch freezing vs fine-tuning trade places on the accuracy curves
- Box Regression Losses Drag a predicted box around a ground-truth box and watch L1, L2, and smooth-L1 disagree about how much to care
- Assigning Anchors by IoU Detection is classification in disguise: every pre-placed anchor box asks 'is the object here?', and I
- Weight Decay Shrinks the Fit Add one penalty term, lambda times the squared weight norm, and watch a wild overfit calm into a smooth genera
- Augmentation & Mixup Two cheap ways to invent training data: scatter neighbors around each point, or place soft-labeled points alon
- Embeddings are a Lookup Table An embedding layer is just indexing a learned table of vectors — one row per token
- A Char-MLP Language Model, Step by Step Walk one forward-and-backward pass of a tiny character-level MLP, one Step at a time
- Watch an RNN's State Evolve Step a scalar RNN by hand and watch a whole sequence fold into one running number
- Backprop Through Time Unroll an RNN, walk the backward pass, and watch truncation cut the chain of credit
- GRU Gates: Keep or Update The update gate is a learned dial between remembering the past and taking the new candidate
- Causal Convolution Slide a kernel over a sequence without ever peeking into the future — with left-padding and dilation as the tw
- A Gated Residual Block Step through the WaveNet/TCN unit where a tanh proposes content, a sigmoid gates it, and skip plus residual pa
- Inside a Transformer Block Step the residual stream through one block and watch attention mix positions while the FFN works on each alone
- Generate, Token by Token An autoregressive decoding sandbox where temperature, top-k and top-p reshape what the model samples next
- Shifted Windows (Swin) Window attention is linear, not quadratic — and shifting alternate layers stitches the seams
- Vector Quantization (VQ-VAE) Replace a continuous latent with the nearest entry of a learned discrete codebook
- Guidance Bends the Trajectory Guidance steers diffusion sampling toward a class — and trades diversity for fidelity
- A Visual Proof That One Layer Can Compute Anything Flatten sigmoids into steps, glue bumps, stack towers — Nielsen's visual proof of universality, made inter
- Vanishing & Exploding Gradients Where the magic 0.25 comes from — and what stops it from ruining deep networks
- Positional Encodings — Sinusoid, RoPE, ALiBi Attention is permutation-invariant. Three ways to break that symmetry — visualized.
- MLE vs MAP, on a Coin Flip Slide the prior, flip some coins, watch the estimate move from MLE toward MAP.
- BatchNorm vs LayerNorm vs RMSNorm Three normalizations, one tensor — see exactly what each averages over.
- ELBO, Decomposed Reconstruction vs KL — see exactly what each term costs you.
- The KV-Cache, Made Concrete Why LLM inference is memory-bound — sized in megabytes per token.
- Quantization & Pruning, Side by Side Shrink a model to int8 / int4 / sparse — and see exactly when accuracy falls off the cliff
- In-Context Learning, From the Inside Why a frozen Transformer learns a new task from a few examples in its prompt
- Domain Shift, Adapted When the training distribution and the deployment distribution disagree — and what to do about it
- Graph Neural Networks, Step by Step Message passing on a sensor-network graph — every round, watch the signal spread
- Mamba & State-Space Models, Visualised An RNN that scales linearly with sequence length — and beats attention on long contexts
- Beyond Gradient Descent Newton, BFGS, natural gradient, evolutionary, gradient-free — five non-SGD ideas, live on a 2D loss
- Double Descent, Made Concrete More parameters than data points should overfit. They sometimes generalize better instead.
- Attention, Calculated From the Q/K/V projections to a tiny attention head trained live in your browser
- Knowledge Distillation, Live A small student copies a big teacher's softened predictions — and beats hard-label training
- Residual Connections, Why They Work Watch a 50-layer net die without skips, then heal in one click
- U-Net, Section by Section Why the same architecture wins at biomedical segmentation, satellite parsing, and modern diffusion
- Mixture of Experts, Live Why Mixtral and DeepSeek-MoE scale parameters without scaling compute
- Vision Transformers, on Real Photos Patches, positions, self-attention, and multi-layer rollout — all computed over real pretrained features
- CLIP, Zero-Shot, from the Embeddings Up Type any labels, see real cosine similarities from a real CLIP model
- Convolution, Step by Step Watch a kernel slide across an image, one dot product at a time
- Numerical Tricks of the Trade Log-sum-exp, log-softmax, BCE-with-logits, and the fixes that keep floating point honest
- Softmax & Temperature How temperature reshapes a probability distribution — and samples from it
- Dropout Playground Feel why silencing neurons regularizes — live masks, p-slider, ensemble view
- Receptive Field Grower Stack convolutions, watch the reach of a deep feature spread
- LR Schedule Visualizer Feel why Transformers need warmup — sliders for every schedule
- LSTM Gates Playground Drag the forget/input/output gates, watch the cell state flow
- The Seq2Seq Bottleneck Watch translation quality collapse as source sentences grow
- BPE Tokenizer Step by Step Watch a tokenizer grow its vocabulary, merge by merge
- LoRA · Low-Rank Adapter Playground Slide the rank, watch trainable parameters shrink 500×
- VAE Latent-Space Explorer See the KL penalty straighten out a noisy 2D latent space
- Diffusion · Forward Noise & Reverse Denoise Watch a 2D shape dissolve into Gaussian noise and reassemble itself
- Classifier-Free Guidance Scale Slide the guidance weight w, watch the generated shape stretch toward the prompt
- Feeling GAN training through the forger-and-detective game Walk through seven steps of the adversarial game — manual discriminator, optimal D*, generator gradi
- The Optimizer Race Why we use Adam instead of pure Gradient Descent
- RAG, From Scratch Retrieve neighbours, condition the LM — how retrieval-augmented generation actually works
- Text Diffusion, Tiny Mask, predict, reveal — how diffusion generates text without going left to right
- Autograd, Seen What autodiff is, what it is not, and how gradients move through a graph
Computer Vision 6
- Perceptual Quality, Pixel by Pixel PSNR, SSIM, MS-SSIM, LPIPS — same images, four numbers, often contradictory
- Equivariant Networks, Live Rotate the input — the right architecture rotates the output too. Vanilla CNNs don't.
- Saliency, Side by Side Which pixels does your classifier actually use? Four attribution methods, one image
- Concept Bottleneck Models Make the model predict human-named concepts first, then read off the label — and intervene if it's wrong
- Earth-Observation Foundation Models, in Depth Why satellite-pretrained backbones are different — modalities, recipes, downstream evaluation, and the 2026 mo
- Vision Pretraining, Without Labels Mask 75% of an image, predict the rest — and four cousin recipes that all work
Multimodal 1
Probability & inference 9
- Probabilistic Programming, in Practice PyMC / NumPyro / Stan are the same idea — declare a model, hand it to an inference engine
- Calibration & Reliability Diagrams Why a softmax of 0.97 doesn't mean 97% — and the one-parameter fix that often heals it
- Kernel Methods, and Why DL Cares From SVM kernels to the Neural Tangent Kernel — the through-line that connects classical ML to deep nets
- The Posterior, Built Up Prior × likelihood = posterior — eight live experiments that turn Bayesian inference from a formula into a fee
- Information Theory for ML, by Hand Entropy, cross-entropy, KL divergence and mutual information made visible — every quantity recomputed live as
- Active Learning, Picked Live Spend your labelling budget on the points the model already finds confusing
- Bayesian Optimization, Step by Step Optimise an expensive black-box function in 10 evaluations — and watch the surrogate update
- Neural Processes, Live A neural net that learns 'priors over functions' the way a Gaussian process does — but amortised
- Conformal Prediction, by Hand Prediction intervals with a coverage guarantee — assumption-free, and one quantile away
Time series 1
Astronomy 1
Classical ML 3
- Random Forests, Tree by Tree Bagging + random feature sampling — why a forest of weak trees beats a strong one
- Decision Trees, Live Watch a CART tree split a 2-D plane axis-aligned, slice by slice — and see exactly when it overfits
- XGBoost, Tree by Tree Each new tree fits the residual of the last — watch the regression curve land, click by click
Computer vision 3
- Optical Flow, Frame by Frame Watch real Lucas-Kanade and dense flow compute live on a sports clip
- Image Segmentation, with a Real Segmenter Upload a photo, run a real DeepLab model, and grade your own mask against it
- Object Detection, with a Real Detector Upload any photo, run a real COCO-SSD model live, and inspect every decision
Data structures 4
- Trees, Branch by Branch BSTs, heaps, traversals — build them, query them, watch them sift up and down
- Sorting, Race by Race Five algorithms, one array — watch insertion, bubble, merge, quick, and heap sort run side by side
- Graph Search, Frontier by Frontier BFS, DFS, Dijkstra, A* — four search strategies racing on the same grid maze
- Hash Tables, Collision by Collision Chaining, open addressing, robin hood — see where keys actually land