Concept and notation
A plain-language explanation, process breakdown, readable formula, and definition of every important symbol.
Complete learning library
Learn 40 machine learning, LLM, and sorting algorithms through clear theory, readable formulas, from-scratch Python, practical library workflows, evaluation guidance, and interactive visualizations.
A complete learning path
Each page is written as a standalone tutorial, so you can start with one concept and progress from intuition to a reproducible implementation.
A plain-language explanation, process breakdown, readable formula, and definition of every important symbol.
A compact from-scratch implementation followed by a practical example using a widely adopted library.
Task-appropriate checks, common mistakes, reproducibility advice, and a project-readiness checklist.
A linked visualization for replaying the algorithm, adjusting parameters, and connecting code to behavior.
Common tools
The examples favor approachable, established tools. You can run them locally in JupyterLab or VS Code, or in a hosted notebook such as Google Colab.
sorted() and list.sort().20 guides
Prediction, clustering, representation learning, neural-network training, and sequential decision-making.
Fits a straight line that minimizes squared prediction errors.
Read guide →Maps a weighted feature score to a class probability.
Read guide →Splits the feature space into rule-based regions.
Read guide →Combines diverse decision trees trained on sampled data.
Read guide →Predicts from the labels or values of nearby observations.
Read guide →Finds a separating boundary with the widest possible margin.
Read guide →Partitions observations around movable cluster centroids.
Read guide →Rotates data onto directions that preserve the most variance.
Read guide →Adds weak models sequentially to correct earlier residual errors.
Read guide →Learns layered nonlinear transformations through connected units.
Read guide →Predicts class probabilities using feature independence assumption.
Read guide →Groups points that are closely packed together into dense regions.
Read guide →Builds a hierarchy of clusters using distance metrics.
Read guide →Fits a regression model while shrinking large coefficients to reduce overfitting.
Read guide →Represents data as overlapping probability clouds with soft cluster membership.
Read guide →Finds anomalies by measuring how quickly random splits isolate each observation.
Read guide →Compresses an input through a bottleneck and learns to reconstruct it.
Read guide →Learns the long-term value of actions by exploring rewards in an environment.
Read guide →Computes how much every network weight contributed to an error, then updates it.
Read guide →Places similar high-dimensional observations near one another on a 2D map.
Read guide →10 guides
Tokenization, representation, attention, transformer architecture, caching, and decoding.
Builds a compact vocabulary by repeatedly merging frequent neighboring symbols.
Read guide →Maps discrete token IDs to dense vectors whose geometry can encode meaning.
Read guide →Adds a position-dependent signal so identical tokens at different places remain distinguishable.
Read guide →Lets each token gather information from other tokens according to learned relevance.
Read guide →Prevents each token from looking at future tokens during autoregressive generation.
Read guide →Runs several attention projections in parallel so different relationships can be learned.
Read guide →Alternates contextual attention with token-wise nonlinear processing and residual paths.
Read guide →Reuses earlier key and value vectors instead of recomputing the whole prompt every step.
Read guide →Turns model logits into a probability distribution and chooses the next token.
Read guide →Keeps several high-scoring partial sequences instead of committing to one token at a time.
Read guide →10 guides
Comparison, divide-and-conquer, heap, insertion, and distribution-based sorting strategies.
Repeatedly swaps adjacent values that are in the wrong order.
Read guide →Selects the smallest remaining value and places it into its final position.
Read guide →Builds a sorted prefix by inserting each new value into its correct place.
Read guide →Recursively sorts halves, then merges them in order.
Read guide →Partitions values around a pivot, then recursively sorts both sides.
Read guide →Builds a max heap and repeatedly moves its root to the sorted suffix.
Read guide →Runs insertion sort across shrinking gaps before the final adjacent pass.
Read guide →Counts each integer value, then emits values in numeric order.
Read guide →Stably groups integers by one digit at a time, from least to most significant.
Read guide →Distributes values into ranges, sorts each bucket, and concatenates them.
Read guide →