这个时代由学习型机器驱动，然而学习本身却隐藏在 API 之后。在这里它一览无余，每一步都呈现在屏幕上，并完全在你的浏览器中运行：一个神经网络实时勾勒出决策边界，一个智能体偶然撞上奖励，注意力决定该看哪个词，噪声在扩散模型下逐渐凝结成结构。没有云端，没有密钥——只有梯度、策略与概率，在发生的瞬间被绘制出来。
A real fully-connected neural network learning to read digits, drawn in 3D — every ball a neuron, every wire a weight. Press Train and watch backpropagation flow; open any neuron to read its exact weighted sum.
Draw any curve y=f(x) and watch a tiny MLP learn to fit it live by backpropagation — add neurons to chase wigglier targets and see the universal approximation theorem unfold as a sum of basis bumps.
Watch temperature, top-k and nucleus top-p reshape a language model’s next-token distribution as text streams out token by token.
Drive a real language model by hand: a word-level interpolated trigram trained on public-domain prose shows its top next-token candidates with live probabilities — click one to append it and watch the distribution shift.
A population of little cars, each driven by its own tiny neural network, evolves to race a procedural track — raycast sensors feed an MLP that learns to steer, and a genetic algorithm breeds the survivors generation after generation.
Draw a digit and a classifier trained in your browser on the real MNIST dataset recognises it live — per-class confidence bars and the top pick update on every stroke.
Watch real t-SNE run live: a random fog of high-dimensional points pulls itself apart frame by frame, gradient-descending the KL divergence until clean, separated clusters bloom — Gaussian blobs, interlocking rings, baked digits, concentric shells.
Train a real Byte-Pair Encoding live, then watch your text shatter into colored tokens — and finally see why "strawberry" trips up an LLM trying to count its r’s.
Watch an Echo State Network learn a chaotic signal the lazy, brilliant way: a big FIXED random recurrent reservoir is driven by the input, and only a single linear readout is trained — by ridge regression, no backprop — yet it learns to predict the series, then runs autonomously off its own output, continuing the signal until chaos finally pulls it apart.
Watch real Principal Component Analysis fold a high-dimensional cloud — a tilted 3D Gaussian, the classic Iris flowers, a Swiss-roll, clustered digits — onto its principal axes, points sliding into place while the explained-variance bars fill.
Train a real multinomial Naive Bayes spam filter in your browser, then type a message and watch each word tug the verdict toward spam or ham — with the log-odds math drawn live, word by word.
Solve a stochastic gridworld with value iteration — watch value flood out from the goal and the optimal policy re-point as discount, living reward, and action noise reshape the safest path.
High-dimensional data lives on a curved low-dimensional sheet — so "learning" is unrolling it. Watch a Swiss roll, S-curve, or severed sphere flatten in 3D, then see real Isomap and LLE recover the true 2D layout while linear PCA fails to unroll and folds the colours back on themselves.
Classify every pixel of a 2D plane by the majority vote of its k nearest training points — slide k from a jagged k=1 island map to a smooth large-k wash and watch overfitting melt into underfitting in real time.
Watch a population of genomes evolve over generations — selection, crossover and mutation — as a recognizable image rises from noise, rockets thread an obstacle, a phrase assembles itself, or a swarm climbs a rugged fitness landscape.
Watch a generative adversarial network duel in your browser: a tiny generator maps random noise into 2-D points trying to mimic a real target distribution while a discriminator fights to tell real from fake — the fakes migrate to cover the target, the discriminator surface flattens toward a coin-flip as the generator wins, the two loss curves duel, and on a grid of modes you can trigger the classic mode collapse on cue.
The tech behind image generators, made tractable in 2D — add Gaussian noise to a point cloud until a shape dissolves, then watch a tiny denoiser network you train in your browser flow pure noise back into the shape, guided by a learned score field.
Watch a real optimizer descend a 3D loss surface — switch between SGD, Momentum, RMSProp and Adam, then crank the learning rate until it visibly diverges.
Drop labelled points on a plane and watch four real classifiers — k-NN, logistic regression, a live-trained neural net, and an RBF kernel — carve the space into coloured decision regions before your eyes.
Drag a decision threshold across two overlapping score distributions and watch the confusion matrix, ROC and PR curves, and every metric recompute live — then crank the class imbalance to expose why accuracy lies.
Slide a 3×3 convolution kernel across a procedurally drawn image and watch the feature map light up — switch between blur, sharpen, Sobel edges, emboss and a Laplacian, or hand-craft your own kernel and chain a second layer.
Watch a reinforcement-learning agent teach itself to balance an inverted pendulum on a cart — from flailing in the first second to holding the pole upright for a full episode, with the reward curve climbing live as it learns.
Fit a model to many noisy training sets at once and watch the curve family swing from rigid-and-biased to wild-and-overfit — with the classic U-shaped test error and its sweet spot decomposed live into bias² + variance + noise.
Hunt the maximum of an expensive, hidden function in as few samples as possible — a Gaussian-process surrogate fits the points so far, draws its mean and a ±2σ uncertainty band, and an acquisition function picks the next, smartest place to look.
Train a real neural autoencoder live: tiny glyphs are squeezed through a 2-D bottleneck and rebuilt by a decoder, the reconstructions sharpening epoch by epoch while a latent map blooms into class clusters — then click anywhere in that latent plane to watch the decoder dream a new glyph into being.
一张 Kohonen 网格，它会褶皱、拉伸并披覆在任意数据分布之上——把拓扑结构的发现可视化呈现。
看一个表格型强化学习智能体从零开始构建导航策略——在陷阱中跌撞、发现奖励，并把最优箭头刻入网格的每一个格子。
看 1958 年的 Rosenblatt 神经元一次次修正，逐步在你的数据中划出一条决策线。
看一个手写的神经网络通过反向传播学习分离二维点云时，实时弯折它的决策边界。
GPT 的祖先——根据前面几个词元预测下一个，并看着连贯性随着阶数增长而逐渐浮现。
看 Lloyd 算法把散点图切割成鲜活的 Voronoi 区域，质心实时追踪并锁定各自的簇。
看一个带噪声或被半擦除的图案如何回弹到已存储的记忆，神经元网络一路下坡滚入吸引子。
五种基于梯度的优化器同时冲下同一片损失地形，揭示为何 Adam 在速度、稳定性和逃离鞍点方面胜过朴素的 SGD。
漫游一个手工构建的语义空间，其中 国王 − 男人 + 女人 恰好落到 王后，意义的簇团绽放出霓虹般的色彩。
看 CART 分类器把你的二维数据切分成轴对齐的区域——每次只做一次信息量最大的分裂。
看 ε-贪心、UCB1 与汤普森采样竞相找出最佳的老虎机臂——算法在探索与利用之间博弈时，累积遗憾被实时绘制出来。
看 Transformer 如何决定关注什么——通过实时热图和二部注意力流，让 softmax(QKᵀ/√d) 变得直观可感。