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Glossary

Every important term in the handbook, defined briefly. Chapters define each term properly the first time it appears. Use this page as a quick reminder.

A 路 B 路 C 路 D 路 E 路 F 路 G 路 H 路 I 路 K 路 L 路 M 路 N 路 O 路 P 路 Q 路 R 路 S 路 T 路 U 路 V 路 W 路 Z

A

A/B test
A randomized experiment that compares two versions (A, the control, and B, the treatment) by randomly assigning units such as users to each, then measuring the difference in a metric.
Accuracy
The fraction of predictions that are correct. Misleading on imbalanced data: predicting "not fraud" every time can be 99.9% accurate.
Activation function
A nonlinear function applied to a neuron's weighted input, such as ReLU, sigmoid, tanh, or GELU. Without nonlinearity, a stack of layers collapses into one linear map.
Actor-critic
An RL method that learns both a policy (the actor) and a value function (the critic), using the critic to reduce the variance of policy-gradient updates.
Adam
An optimizer that keeps running averages of the gradient (first moment) and the squared gradient (second moment) to give each parameter an adaptive step size. AdamW decouples weight decay from the gradient update.
Attention
A mechanism that computes a weighted average of value vectors, with weights given by how well a query matches each key: \(\mathrm{softmax}(QK^\top/\sqrt{d_k})\,V\).
AUC (area under the curve)
Usually the area under the ROC curve: the probability that a randomly chosen positive example is scored higher than a randomly chosen negative one.
Autoencoder
A network trained to reconstruct its input through a narrow bottleneck, which forces it to learn a compressed representation.
Autograd
Automatic differentiation: software that records the operations of a computation and applies the chain rule backward to compute exact gradients.

B

Backpropagation
The algorithm that computes the gradient of the loss with respect to every parameter by applying the chain rule backward through the computational graph, reusing intermediate results.
Bagging (bootstrap aggregating)
Training many models on bootstrap samples of the data and averaging their predictions, which reduces variance.
Batch normalization
Normalizing each feature of a layer's activations using the mean and variance of the current mini-batch, then applying a learned scale and shift.
Batch size
The number of examples used to compute one gradient estimate and parameter update.
Bayes' theorem
\(P(A \mid B) = P(B \mid A)\,P(A) / P(B)\). It updates a prior belief \(P(A)\) with evidence \(B\) to get a posterior.
Bias (statistical)
The difference between an estimator's expected value and the true value. In the bias-variance trade-off, the error from a model being too simple to capture the true pattern.
Bias (in a model)
The intercept term \(b\) in \(\mathbf{w}^\top\mathbf{x} + b\), which lets the output shift independently of the input.
Bias-variance trade-off
Expected prediction error splits into bias虏, variance, and irreducible noise. Simpler models tend to have high bias and low variance; flexible models have the reverse.
Bootstrap
Resampling the data with replacement many times to estimate the sampling distribution of a statistic, for example to build a confidence interval.
BPE (byte-pair encoding)
A subword tokenization method that starts from characters or bytes and repeatedly merges the most frequent adjacent pair into a new token.
Broadcasting
NumPy's and PyTorch's rules for combining arrays of different shapes by virtually stretching dimensions of size 1, without copying data.

C

Calibration
How well predicted probabilities match observed frequencies. Among examples scored 0.8, about 80% should be positive.
Categorical variable
A feature that takes values from a fixed set of categories, such as country or plan type.
Causal inference
Methods for estimating the effect of an intervention, rather than mere association, from experimental or observational data.
Central limit theorem
The sum or mean of many independent random variables with finite variance is approximately normally distributed, whatever their original distribution.
Chain rule
The derivative of a composition: \(\frac{d}{dx} f(g(x)) = f'(g(x))\,g'(x)\). The mathematical core of backpropagation.
Class imbalance
When one class is much rarer than the others, as in fraud or disease detection.
Classification
Supervised learning where the target is a category.
CLIP
A model trained contrastively to place matching images and text captions close together in a shared embedding space.
Clustering
Grouping unlabeled examples so that examples in the same group are similar, for example with k-means or DBSCAN.
Computational graph
A directed graph whose nodes are operations and whose edges carry values. Autograd records it on the forward pass and traverses it backward.
Concept drift
A change over time in the relationship between the inputs and the target, so a trained model's learned mapping goes stale.
Confidence interval
A range computed from data by a procedure that, over repeated samples, contains the true parameter a stated fraction of the time, such as 95%.
Confounder
A variable that influences both the treatment and the outcome, creating a spurious association between them.
Confusion matrix
A table of counts of true positives, false positives, true negatives, and false negatives.
Contrastive learning
Self-supervised learning that pulls representations of related pairs (two views of the same image, an image and its caption) together and pushes unrelated pairs apart.
Convex function
A function where any line segment between two points on its graph lies on or above the graph. Any local minimum is a global minimum.
Convolution
Sliding a small learned kernel over an input and computing a dot product at each position. It shares weights across positions and detects local patterns.
Correlation
A measure of association between two variables. Pearson correlation measures linear association; Spearman correlation measures monotonic association.
Cross-entropy
\(H(p, q) = -\sum_x p(x) \log q(x)\). As a loss, the negative log-probability the model assigns to the true class.
Cross-validation
Estimating generalization by splitting the data into \(k\) folds, training on \(k-1\) folds, evaluating on the remaining one, and averaging over all \(k\) rounds.
Curse of dimensionality
Phenomena in high-dimensional spaces, such as distances becoming similar and data becoming sparse, that make many methods (especially distance-based ones) work poorly.

D

Data augmentation
Creating modified copies of training examples (crops, flips, noise) to increase effective dataset size and improve robustness.
Data leakage
When information that won't be available at prediction time, such as the target or future data, leaks into training. It produces impressive validation scores that collapse in production.
DataFrame
pandas' two-dimensional labeled table: columns of possibly different types sharing a row index.
DBSCAN
A density-based clustering algorithm that grows clusters from dense regions and labels isolated points as noise.
Decision boundary
The surface in feature space where a classifier's prediction changes from one class to another.
Decision tree
A model that predicts by asking a sequence of feature-threshold questions, learned by recursively splitting the data to reduce impurity.
Deep learning
Machine learning with neural networks of many layers that learn hierarchical representations directly from raw data.
Diffusion model
A generative model trained to reverse a gradual noising process. It generates data by starting from noise and denoising step by step.
Dimensionality reduction
Mapping data to fewer dimensions while preserving important structure, for example with PCA, t-SNE, or UMAP.
Distillation
Training a small "student" model to match the outputs of a large "teacher" model.
DPO (direct preference optimization)
A method for aligning language models to human preferences directly from preference pairs, without training a separate reward model or running RL.
Dropout
A regularizer that randomly zeroes a fraction of activations during training, which discourages co-adaptation.

E

Early stopping
Halting training when validation performance stops improving. A simple and effective regularizer.
Eigenvector
A nonzero vector \(\mathbf{v}\) that a matrix only scales: \(A\mathbf{v} = \lambda \mathbf{v}\), where the scalar \(\lambda\) is its eigenvalue.
ELBO (evidence lower bound)
A tractable lower bound on the log-likelihood that variational autoencoders maximize. It combines a reconstruction term and a KL-divergence term.
Embedding
A learned dense vector representing a discrete item (a word, a user, a product) such that similar items have nearby vectors.
EM (expectation-maximization)
An algorithm for models with hidden variables that alternates between estimating the hidden variables (E-step) and re-fitting the parameters (M-step). It's used to fit Gaussian mixture models.
Ensemble
A model that combines the predictions of several models, as in bagging, boosting, or stacking.
Entropy
\(H(X) = -\sum_x p(x) \log p(x)\): the average uncertainty, or information content, of a random variable.
Epoch
One full pass over the training dataset.
Expected value
The probability-weighted average of a random variable's values.
Exploratory data analysis (EDA)
Systematically summarizing and visualizing data to understand it, find problems, and form hypotheses before modeling.

F

F1 score
The harmonic mean of precision and recall: \(2PR/(P+R)\).
False positive / false negative
A false positive is a negative predicted as positive (a Type I error). A false negative is a positive predicted as negative (a Type II error).
Feature
An input variable to a model, also called a predictor or attribute.
Feature engineering
Creating, transforming, and selecting input features to make patterns easier for a model to learn.
Fine-tuning
Continuing to train a pretrained model on a new, usually smaller, task-specific dataset.
FSDP (fully sharded data parallel)
A distributed training method that shards parameters, gradients, and optimizer state across GPUs to train models too large for one GPU.

G

GAN (generative adversarial network)
A generator and a discriminator trained against each other: the generator tries to produce realistic samples, and the discriminator tries to tell real from fake.
Gaussian mixture model (GMM)
A model of data as coming from a weighted mix of several Gaussian distributions, usually fit with EM.
Generalization
How well a model performs on new, unseen data from the same distribution as its training data.
Gini impurity
\(1 - \sum_k p_k^2\): the probability of misclassifying a randomly drawn example if it were labeled randomly according to the node's class distribution. Used to choose decision tree splits.
Gradient
The vector of partial derivatives of a function. It points in the direction of steepest increase.
Gradient boosting
Building an ensemble sequentially, where each new model (usually a small tree) fits the negative gradient of the loss of the current ensemble.
Gradient clipping
Scaling down gradients whose norm exceeds a threshold, to prevent exploding updates.
Gradient descent
Iteratively minimizing a function by stepping opposite the gradient: \(\theta \leftarrow \theta - \eta \nabla_\theta \mathcal{L}\).

H

Hallucination
When a language model generates fluent but false or unsupported content.
Hinge loss
\(\max(0, 1 - y\,f(\mathbf{x}))\) for labels \(y \in \{-1, +1\}\): the loss behind support vector machines.
Hyperparameter
A setting chosen before training rather than learned from data, such as learning rate, tree depth, or regularization strength.
Hypothesis test
A procedure for deciding whether data provide enough evidence against a null hypothesis, usually using a p-value.

I

Imputation
Filling in missing values, for example with the median, a model's prediction, or a constant plus a "was missing" indicator.
In-context learning
A language model performing a task from instructions or examples given in its prompt, without any weight updates.
Inference
In ML: using a trained model to make predictions. In statistics: drawing conclusions about a population from a sample.
Information gain
The reduction in entropy achieved by a split. Decision trees choose splits that maximize it.
Isolation forest
An anomaly detection method that isolates points with random splits. Anomalies are isolated in fewer splits.

K

k-fold cross-validation
See cross-validation.
k-means
Clustering that alternates between assigning each point to its nearest centroid and moving each centroid to the mean of its points.
k-nearest neighbors (kNN)
Predicting from the labels of the \(k\) closest training examples.
Kernel trick
Computing inner products in a high-dimensional feature space implicitly, through a kernel function, without ever constructing the features.
KL divergence
\(D_{\mathrm{KL}}(p \parallel q) = \sum_x p(x) \log \frac{p(x)}{q(x)}\): how much one distribution differs from another. It's not symmetric.
KV cache
During autoregressive generation, storing the keys and values of past tokens so they aren't recomputed at each step.

L

L1 / L2 regularization
Adding a penalty to the loss: the sum of absolute weights (L1, lasso), which drives some weights to exactly zero, or the sum of squared weights (L2, ridge), which shrinks all weights.
Label
The target value a supervised model learns to predict.
Language model
A model that assigns probabilities to sequences of tokens, usually by predicting the next token given the previous ones.
Layer normalization
Normalizing activations across the features of each individual example. The standard choice in transformers.
Learning curve
A plot of training and validation performance against training set size (or training time), used to diagnose bias and variance.
Learning rate
The step size \(\eta\) in gradient descent. The single most important hyperparameter in deep learning.
Likelihood
The probability (or density) of the observed data as a function of the model parameters.
Linear regression
Predicting a continuous target as a weighted sum of features plus a bias, usually fit by least squares.
Logistic regression
A linear classifier that passes a weighted sum through a sigmoid to output a probability, trained by minimizing log-loss.
Logit
The raw, unnormalized score before a sigmoid or softmax. For a probability \(p\), \(\mathrm{logit}(p) = \log\frac{p}{1-p}\).
LoRA (low-rank adaptation)
Parameter-efficient fine-tuning that freezes the pretrained weights and learns small low-rank update matrices \(BA\) added to them.
Loss function
A function measuring how wrong a model's predictions are. Training minimizes it.
LSTM (long short-term memory)
A recurrent unit with gates that control what to remember, forget, and output, which mitigates vanishing gradients over long sequences.

M

Machine learning
Building systems that improve at a task by learning patterns from data rather than following hand-written rules.
MAE / MSE / RMSE
Mean absolute error, mean squared error, and root mean squared error: regression metrics that measure average prediction error.
Matrix factorization
Approximating a matrix as a product of smaller matrices. Used in recommender systems to learn user and item embeddings.
Maximum likelihood estimation (MLE)
Choosing the parameters that make the observed data most probable.
Mini-batch
A small random subset of the training data used for one gradient update.
Mixed precision
Training with lower-precision numbers (fp16 or bf16) for most operations, while keeping critical values in fp32, to save memory and time.
MLOps
The practices and tools for deploying, monitoring, and maintaining ML models in production reliably.
Momentum
An optimizer technique that accumulates a velocity from past gradients to smooth updates and speed progress along consistent directions.
Multi-head attention
Running several attention operations in parallel on different learned projections and concatenating the results, so each head can attend to different relationships.

N

Naive Bayes
A probabilistic classifier that applies Bayes' theorem with the "naive" assumption that features are conditionally independent given the class.
Neural network
A model built from layers of units, each computing a weighted sum followed by a nonlinearity, trained with gradient descent.
Normal distribution
The bell-shaped Gaussian distribution, defined by its mean \(\mu\) and variance \(\sigma^2\).
Normalization (of features)
Rescaling features, for example to zero mean and unit variance (standardization) or to the range [0, 1] (min-max scaling).
Null hypothesis
The default assumption a hypothesis test tries to reject, usually "no effect" or "no difference".

O

One-hot encoding
Representing a category as a vector with a 1 in that category's position and 0 everywhere else.
Optimizer
The algorithm that updates parameters from gradients, such as SGD, momentum, RMSProp, or Adam.
Outlier
An observation far from the bulk of the data. It may be an error, or the most interesting point in the dataset.
Overfitting
When a model learns noise and quirks of the training data, so it performs well on training data but poorly on new data.

P

p-value
The probability, assuming the null hypothesis is true, of observing data at least as extreme as what was observed. It is not the probability that the null hypothesis is true.
Parameter
A value the model learns from data, such as a weight or a bias.
Perceptron
The original single-neuron linear classifier, trained with a simple mistake-driven update rule.
Perplexity
The exponential of the average per-token cross-entropy of a language model. Lower is better.
Pipeline
A chain of preprocessing steps and a model, fit together so that preprocessing is learned only from training data, which prevents leakage.
Policy gradient
RL methods that directly adjust a policy's parameters in the direction that increases expected reward, as in REINFORCE and PPO.
Positional encoding
Information about token positions added to transformer inputs, since attention by itself ignores order.
PPO (proximal policy optimization)
A policy-gradient algorithm that limits how far each update can move the policy, for stable training. Used in RLHF.
Precision
Of the examples predicted positive, the fraction that really are positive: \(TP/(TP+FP)\).
Principal component analysis (PCA)
Projecting data onto the orthogonal directions of maximum variance, computed from the covariance matrix's eigenvectors or the data's SVD.
Prior / posterior
In Bayesian inference, the belief before seeing data (the prior) and the updated belief after (the posterior).

Q

Q-learning
An RL algorithm that learns the value \(Q(s, a)\) of taking action \(a\) in state \(s\), using the Bellman equation as an update target.
Quantization
Storing and computing with lower-precision numbers, such as 8-bit or 4-bit integers instead of 32-bit floats, to shrink models and speed up inference.

R

RAG (retrieval-augmented generation)
Retrieving relevant documents, usually by embedding similarity, and adding them to a language model's prompt so its answer is grounded in them.
Random forest
An ensemble of decision trees, each trained on a bootstrap sample with a random subset of features considered at each split, whose predictions are averaged.
Recall
Of the actual positives, the fraction the model found: \(TP/(TP+FN)\). Also called sensitivity or the true positive rate.
Regression
Supervised learning where the target is a continuous number.
Regularization
Any technique that constrains a model to reduce overfitting, such as weight penalties, dropout, early stopping, or data augmentation.
Reinforcement learning (RL)
Learning to act by trial and error, where an agent takes actions in an environment to maximize cumulative reward.
ReLU
The rectified linear unit, \(\max(0, x)\): the default activation function in most deep networks.
Residual connection
Adding a layer's input to its output (\(x + f(x)\)), which eases gradient flow and makes very deep networks trainable.
RLHF (reinforcement learning from human feedback)
Fine-tuning a language model with RL against a reward model trained on human preference comparisons.
RNN (recurrent neural network)
A network that processes a sequence one step at a time, carrying a hidden state forward.
ROC curve
A plot of true positive rate against false positive rate as the decision threshold varies.

S

Sampling (from a language model)
Choosing the next token from the model's predicted distribution, controlled by temperature, top-k, or top-p (nucleus) settings.
Scaling laws
Empirical power-law relationships between model performance and model size, dataset size, and compute.
Self-attention
Attention in which the queries, keys, and values all come from the same sequence, so every position can attend to every other.
Self-supervised learning
Learning representations from unlabeled data by creating labels from the data itself, such as predicting masked words or the next token.
SHAP
A method that attributes a prediction to the features using Shapley values from cooperative game theory.
Sigmoid
\(\sigma(z) = 1/(1 + e^{-z})\): squashes any real number into (0, 1).
Simpson's paradox
A trend that appears in several groups but reverses or disappears when the groups are combined.
Softmax
\(\mathrm{softmax}(\mathbf{z})_i = e^{z_i} / \sum_j e^{z_j}\): turns a vector of scores into a probability distribution.
Stationarity
A time series property: the statistical properties (mean, variance, autocorrelation) don't change over time.
Stochastic gradient descent (SGD)
Gradient descent using the gradient from a single example or mini-batch rather than the whole dataset.
Stratified sampling
Splitting data so each split has the same class proportions as the whole dataset.
Supervised learning
Learning a mapping from inputs to known target labels.
Support vector machine (SVM)
A classifier that finds the boundary with the maximum margin between classes, optionally in a kernel-induced feature space.
SVD (singular value decomposition)
Factoring any matrix as \(U \Sigma V^\top\): a rotation, a scaling along orthogonal axes, and another rotation.

T

t-SNE
A nonlinear technique for visualizing high-dimensional data in 2D or 3D that preserves local neighborhoods. Distances between clusters in its plots aren't meaningful.
Teacher forcing
Training a sequence model by feeding it the true previous token, rather than its own prediction, at each step.
Tensor
A multidimensional array: the core data structure in PyTorch.
Test set
Data held out until the very end, used only once to estimate final performance.
TF-IDF
Term frequency 脳 inverse document frequency: a word's weight in a document, high when it's frequent in that document but rare across documents.
Token
The unit of text a language model processes: a word, a subword, a character, or a byte.
Transfer learning
Reusing a model trained on one task as the starting point for another.
Transformer
A neural network architecture built from self-attention and feed-forward layers with residual connections and normalization. The basis of modern LLMs.

U

UMAP
A nonlinear dimensionality reduction method, often faster than t-SNE, that tends to preserve more global structure.
Underfitting
When a model is too simple to capture the underlying pattern, so it performs poorly even on training data.
Universal approximation theorem
A neural network with one hidden layer and enough units can approximate any continuous function on a bounded domain to any accuracy. It says nothing about how to find the weights.
Unsupervised learning
Finding structure in data without labels, as in clustering, dimensionality reduction, and density estimation.

V

Validation set
Data held out from training and used to choose hyperparameters and models.
Vanishing / exploding gradients
Gradients that shrink toward zero or grow without bound as they're multiplied backward through many layers, which stalls or destabilizes training.
Variance (statistical)
The expected squared deviation from the mean. In the bias-variance trade-off, how much a model's predictions change across different training sets.
VAE (variational autoencoder)
A probabilistic autoencoder that learns a smooth latent space you can sample from, trained by maximizing the ELBO.
Vectorization
Replacing Python loops with whole-array operations that run in optimized compiled code.
Vision transformer (ViT)
A transformer applied to images by splitting them into patches and treating each patch as a token.

W

Weight decay
Shrinking weights toward zero at each step. It's equivalent to L2 regularization for plain SGD, but not for Adam, which is why AdamW exists.
Window function (SQL)
A SQL function that computes a value over a set of rows related to the current row, such as a running total or a rank, without collapsing the rows.
word2vec
A method that learns word embeddings by predicting words from their contexts (CBOW) or contexts from words (skip-gram).

Z

Zero-shot learning
Performing a task without any task-specific training examples, for example by following instructions in a prompt or by matching against text descriptions as in CLIP.