Glossary

The derivative of a composition is the product of the derivatives of its parts, evaluated along the way.

A function is convex if it is bowl-shaped: any local minimum is the global minimum.

Scores how closely two vectors point the same way, from −1 (opposite) to 1 (identical direction), ignoring length.

A square matrix holding every feature's variance on its diagonal and every pair's covariance off it.

Multiplies two vectors entry by entry and sums the results, giving one number that grows when they point the same way.

A direction that a matrix only stretches or flips, never rotates; the stretch factor is its eigenvalue.

The vector of all partial derivatives of a function; it points in the direction of steepest increase.

The matrix of second derivatives of a function, describing how its slope bends: its curvature.

The matrix of all partial derivatives of a vector-valued function: how each output changes with each input.

A rectangular grid of numbers that can store a dataset or describe a linear transformation of vectors.

Combines an m×n and an n×p matrix into an m×p matrix whose entries are dot products of rows with columns.

A measure of a vector's size; the usual L2 norm is its straight-line length.

How fast a multi-input function changes when you nudge one input and hold all the others fixed.

Factors any matrix into a rotation, a scaling along perpendicular axes, and another rotation.

A multi-dimensional array of numbers: a scalar, vector and matrix are tensors with 0, 1 and 2 axes.

An ordered list of numbers, read either as a point in space or as an arrow with a direction and length.

A rule for updating a belief with evidence: the posterior is the likelihood times the prior, normalized.

The average surprise of the true outcomes under a model's predicted probabilities; the standard classification loss.

The average surprise of a distribution, in bits: how uncertain you are about its outcome.

The long-run average of a random quantity: each possible value weighted by its probability.

The extra bits wasted by using distribution q in place of the true distribution p; zero only when they match.

Picks the parameters that make the observed data most probable under the model.

Estimating a quantity, usually an expected value, by averaging the results of many random samples.

The bell-shaped distribution set by a mean μ (its center) and a standard deviation σ (its width).

A description of how likely each possible value of a random quantity is, with the probabilities summing to 1.

How spread out a random quantity is: the average squared distance from its mean.

The default deep-learning optimizer: momentum plus a per-parameter step size scaled by recent gradient magnitudes.

The algorithm that computes every weight's gradient by applying the chain rule backward from the loss through the network.

The number of training examples used to compute each gradient update.

One complete pass of the training algorithm over every example in the training set.

Caps the size of the gradient before each update so one huge gradient cannot wreck training.

Minimizes a loss by repeatedly stepping parameters a small amount against the gradient, the direction of steepest increase.

A setting chosen before training, such as the learning rate or batch size, rather than learned from the data.

The multiplier η that sets how far each optimizer step moves the parameters; usually the most important hyperparameter.

A rule that changes the learning rate during training, typically warming up, then decaying so the model settles.

A point lower than everything around it but not necessarily the lowest point overall.

A function that scores how wrong a model's predictions are; training adjusts the parameters to make it small.

An optimizer trick that keeps a running velocity of past gradients, speeding up consistent directions and damping zig-zags.

Gradient descent that estimates the gradient from one example or a small random batch instead of the whole dataset.

Gradients shrinking toward zero as they pass back through many layers or time steps, so early layers barely learn.

How a network's weights are set before training; the right random scale keeps signals from vanishing or exploding with depth.

Changing a trained network by operating on its weights directly (adding, averaging, editing or generating them) instead of only training it on more data.

The nonlinear function applied to each neuron’s weighted sum, which lets a network model more than straight-line relationships.

A mechanism that lets a model build each output as a weighted mix of inputs, with weights based on relevance.

A network trained to reproduce its input after squeezing it through a narrow bottleneck, learning a compact code.

A neural network that slides small learned filters across an image (or other grid) to detect local patterns.

A learned dense vector that represents a discrete item, such as a token or user, so similar items get nearby vectors.

An architecture in which one network encodes the input into a representation and a second network decodes it into the output.

A simpler gated recurrent cell than the LSTM, using an update gate and a reset gate and no separate cell state.

A recurrent network cell with forget, input and output gates that decide what to keep in a separate long-term memory.

Runs several attention operations in parallel on smaller projections, so different heads can track different relationships.

A neural network of stacked fully connected layers, each a linear map followed by a nonlinear activation.

A single artificial neuron: a weighted sum of inputs plus a bias, passed through a step function to output 0 or 1.

A downsampling step that summarizes each small patch of a feature map by its maximum or average.

A vector added to each token embedding that tells an attention model where in the sequence the token sits.

A neural network that reads a sequence one step at a time, carrying a hidden state that summarizes what it has seen.

An activation function that passes positive values through unchanged and replaces negative values with zero.

A shortcut that adds a block’s input to its output, so the block only has to learn a correction.

Attention in which every token of a sequence attends to every token of that same sequence, including itself.

An S-shaped function that squashes any real number into the range 0 to 1, often read as a probability.

Turns a vector of raw scores (logits) into probabilities that are all positive and sum to 1.

A sequence model that compresses the past into a fixed-size state updated by a linear recurrence, running in linear time.

A neural architecture built from stacked self-attention and feed-forward layers, the basis of modern language models.

A Transformer applied to images by cutting each image into fixed-size patches and treating the patches as tokens.

Normalizes each feature across the current mini-batch to zero mean and unit variance, then rescales it with learned parameters.

Simpler models make systematic errors (bias) while flexible models are sensitive to the particular training sample (variance).

Creates extra training examples by applying label-preserving changes, such as flips, crops or rotations, to existing data.

During training, randomly zeroes a fraction of neurons on every step so the network cannot rely on any single unit.

Stops training when validation performance stops improving and keeps the weights from the best epoch.

Combines L1 and L2 penalties, getting sparse weights like lasso while staying stable with correlated features like ridge.

How well a trained model performs on new data drawn from the same distribution, not just the examples it was trained on.

Adds the sum of absolute weight values to the loss, which pushes many weights to exactly zero.

Adds the sum of squared weights to the loss, shrinking all weights toward zero without making them exactly zero.

Normalizes the features of each individual example to zero mean and unit variance, independent of the batch.

When a model fits the training data, noise included, so closely that it performs worse on new data.

Any technique that discourages a model from fitting noise in the training data so it generalizes better to new data.

When a model is too simple to capture the real pattern, so it does poorly even on its training data.

The fraction of all predictions that are correct; it can be misleading when one class is much more common than the others.

A table counting predictions against true labels, showing true and false positives and negatives for each class.

Estimates performance by splitting the data into k folds, training on k − 1 of them and validating on the remaining one, k times.

When information that would not be available at prediction time, often from the test set, sneaks into training and inflates scores.

The harmonic mean of precision and recall, high only when both are high.

The average of the squared differences between predictions and true values, the standard loss for regression.

Of everything the model labeled positive, the fraction that really is positive.

Of all the truly positive cases, the fraction the model managed to find.

The ROC curve plots true positive rate against false positive rate across all thresholds; AUC is the area under it.

Dividing data into a training set to fit the model, a validation set to tune it, and a test set used once for the final score.

Trains many copies of a model on random resamples of the data drawn with replacement and averages their predictions.

Builds an ensemble sequentially, with each new weak model focusing on the mistakes of the models before it.

Grouping unlabeled data points so that points in the same group are more similar to each other than to points in other groups.

A clustering algorithm that grows clusters from dense regions of points and labels isolated points as noise.

A model that predicts by asking a sequence of yes/no questions about the features, following branches down to a leaf.

Combining the predictions of several models so their individual errors partly cancel out.

Builds a tree of nested clusters by repeatedly merging (or splitting) groups, so you can choose the number of clusters afterward.

Partitions data into k clusters by repeatedly assigning points to the nearest centroid and moving each centroid to its points’ mean.

Predicts the label of a new point from the k most similar training points, by majority vote or by averaging.

Lets a linear algorithm learn non-linear boundaries by computing dot products in a higher-dimensional feature space without building that space.

Predicts a number as a weighted sum of the input features plus a bias, choosing the weights that minimize squared error.

A classifier that passes a weighted sum of the features through a sigmoid to output the probability of the positive class.

A fast probabilistic classifier that applies Bayes’ theorem while assuming features are independent given the class.

Reduces dimensionality by projecting data onto the few orthogonal directions along which it varies most.

An ensemble of decision trees, each trained on a bootstrap sample with random feature subsets, whose predictions are averaged or voted.

Learning a mapping from inputs to outputs using examples that come with the correct answer (labels).

A classifier that picks the boundary separating the classes with the widest possible margin to the nearest points.

Finding structure such as groups or low-dimensional patterns in data that has no labels.

Represents a document as a vector of word counts over a vocabulary, ignoring word order entirely.

A decoding method that keeps the b most probable partial sequences at each step instead of only the single best token.

An encoder-only transformer pretrained to fill in masked words using context from both sides.

Prompting a language model to write out intermediate reasoning steps before giving its final answer.

The maximum number of tokens a language model can take into account at once, prompt and output combined.

A word vector computed from the whole sentence, so the same word gets different vectors in different contexts.

Continuing to train a pretrained model on a smaller task-specific dataset so it adapts to that task.

When a generative model states fluent, confident content that is false or unsupported by its sources.

Stored attention keys and values for past tokens, so generating each new token does not recompute them.

A model that assigns probabilities to sequences of tokens, usually by predicting the next token from the ones before it.

A transformer language model with billions of parameters, pretrained on huge text corpora to predict the next token.

Finding spans of text that name real-world things and labeling each as a type such as person, organization or location.

The exponential of a language model's average per-token cross-entropy on held-out text; lower is better.

Storing a model's weights (and sometimes activations) in fewer bits, such as 8 or 4, to cut memory and speed up inference.

A setting that divides logits before softmax: below 1 sharpens the next-token distribution, above 1 flattens it.

Weights a word by how often it appears in a document, discounted by how many documents in the corpus contain it.

Splitting raw text into tokens (words, subword pieces or characters) that a model maps to integer IDs.

Reusing what a model learned on one large task or dataset as the starting point for a different, usually smaller, task.

A dense vector for each word, learned so that words used in similar contexts end up close together.

A model that generates a sequence one element at a time, each predicted from all the elements before it.

Learns representations by pulling embeddings of matching pairs together and pushing non-matching pairs apart.

A generative model that learns to reverse a gradual noising process, creating data by denoising pure noise step by step.

Two networks trained against each other: a generator makes fake samples and a discriminator tries to tell them from real data.

A model that learns the distribution of its training data so it can produce new, similar examples.

The compressed space of hidden codes a model learns, in which similar inputs map to nearby points.

A generative model that turns a simple distribution into a complex one through a chain of invertible transformations.

An autoencoder whose encoder outputs a probability distribution over latent codes, so new data can be generated by sampling.

Combines a policy (the actor) that picks actions with a value estimate (the critic) that judges them, giving lower-variance updates.

A recursive identity: the value of a state equals the immediate reward plus the discounted value of the states that follow.

Q-learning with a neural network approximating the Q-values, stabilized by experience replay and a periodically updated target network.

The dilemma between trying new actions to learn more and choosing the action that currently looks best.

The standard mathematical model of a reinforcement learning problem: states, actions, transition probabilities, rewards and a discount factor.

In reinforcement learning, the agent’s rule for choosing an action in each state, either fixed or as a probability distribution.

RL methods that directly adjust policy parameters by gradient ascent to make high-return actions more likely.

A model-free algorithm that learns the value of each action in each state from experience, nudging estimates toward reward plus the best next value.

Learning to make a sequence of decisions by trial and error, guided by rewards from an environment rather than labeled answers.

The expected total future reward from a state, or from taking a given action in a state, when following a particular policy.

An LLM-driven system that pursues a goal by repeatedly reasoning, calling tools and observing results until done.

A keyword ranking function that scores documents by query-term frequency, term rarity and document length.

Splitting documents into smaller passages before embedding them, so retrieval can return just the relevant piece.

Combining keyword (sparse) and embedding (dense) retrieval so results catch both exact terms and paraphrases.

A network of entities connected by labeled relationships, stored as (subject, predicate, object) triples.

A second retrieval stage that reorders a shortlist of candidates with a slower but more accurate relevance model.

Answering with a language model after first retrieving relevant passages from an external corpus and adding them to the prompt.

Search that ranks documents by closeness in meaning, comparing embeddings rather than matching exact words.

Letting a language model request a function call by emitting structured arguments that application code then executes.

A database built to store embedding vectors and quickly find the ones nearest to a query vector.