Concept Glossary: V¶

This page lists English glossary entries for this letter. Entry bodies are generated from per-term source files with includes.

variance¶

• Meaning: Variance measures how widely values spread around their mean.
• Why it matters: Values can have the same average but very different spread. In PCA, variance is also the criterion for deciding which directions carry large overall variation.
• Related concepts: mean, standard deviation, distribution
• Core Section: P2-5.2
• Appears in: P2-5.3, P2-5.5, P2-13.2, P4-18.1

validation data¶

• Meaning: Validation data is data used during model development to check and adjust model settings. It is separate from data used directly for training and from test data kept for final checking.
• Why it matters: A low training loss alone does not guarantee real-world performance. Validation data gives a separate sample for checking whether the model still fits new data while tuning hyperparameters or deciding when to stop training.
• Related concepts: training data, test data, generalization, hyperparameter
• Core Section: P2-6.2
• Appears in: P4-4.1, P4-4.2, P4-5.1, P4-5.2

value-based reinforcement learning¶

• Meaning: Value-based reinforcement learning is an approach that learns expected long-term reward values for states or state-action pairs, then uses those values to choose better actions. It learns how good a choice is over time before or alongside deriving the policy.
• Why it matters: This concept connects algorithms through their shared focus on long-term reward value estimates for states or state-action pairs. It also separates the value-based view from policy-based reinforcement learning, where the policy itself is adjusted more directly.
• Related concepts: reinforcement learning, reinforcement learning policy, reward, policy-based reinforcement learning
• Core Section: P4-19.1
• Appears in: P4-19.4, P4-19.5

variable¶

• Meaning: A variable is a name used to refer to a value. The variable is not the value itself; it is a label that lets a calculation or program refer to the value again.
• Why it matters: Readers need variables to follow formulas and code. The concept separates a name from the data it currently refers to, which helps with assignment, updates, function inputs, and intermediate calculations.
• Related concepts: function, model input, feature
• Core Section: P2-2.1
• Appears in: P2-8.5, P2-10.3

variable transformation¶

• Meaning: Variable transformation converts the same structure or value into another expression, such as a mean, difference, ratio, slope, or token. It does not discard the original meaning; it rewrites it into a form that is easier to compare for the current question.
• Why it matters: In feature design, deciding what expression to compute and deciding which computed expressions to keep are different judgments. Variable transformation helps separate using summary-table values as-is from rewriting them into structure expressions such as level, change, or stability. With this distinction, feature selection becomes the act of choosing useful candidate expressions, not merely deleting columns.
• Related concepts: feature, feature selection, summary table, intermediate representation
• Core Section: P3-6.1
• Appears in: P3-6.1

vector¶

• Meaning: A vector represents multiple ordered values as one unit. In mathematics it can be read as an object with magnitude and direction, and in AI it often means a one-dimensional bundle of numbers that represents one object.
• Why it matters: A vector is closer to a computable representation than to a simple storage list. Feature vectors, embedding vectors, and gradient vectors all require readers to ask what object is being represented across several numerical dimensions. Vectors with the same dimensionality can also be compared through distance, direction, and related vector operations.
• Related concepts: matrix, dimension, representation
• Core Section: P2-3.1
• Appears in: P1-3.3, P1-4.3, P1-13.1, P2-3.2, P2-3.3, P2-4.3, P2-11.3, P6-3.1

vector database¶

• Meaning: A vector database is a retrieval system that stores embedding vectors and manages search indexes, metadata, filtering, and updates together. It is an infrastructure layer for actual search service behavior, not just a place to keep a few vectors.
• Why it matters: RAG implementation depends not only on a vector comparison algorithm, but also on storage, metadata filtering, permissions, updates, and operations. This concept helps readers connect the mathematical problem of finding nearby vectors with the service problem of retrieving safe, fast, current documents.
• Related concepts: search index, ANN, approximate nearest neighbor, metadata
• Core Section: P6-13.1
• Appears in: P1-13.4, P6-3.2, P6-13.2

vector space¶

• Meaning: A vector space is a representation space where vectors can be compared by position, distance, and direction.
• Why it matters: Embeddings are easier to understand when they are read as points in a comparison space rather than as bare lists of numbers. Vector space gives similarity search and recommendation a geometric basis.
• Related concepts: vector, embedding, similarity search
• Core Section: P1-13.1
• Appears in: P6-3.1, P6-3.2

vectorization¶

• Meaning: Vectorization is a way to express repeated computation as one array operation instead of writing a Python for loop. The repetition has not disappeared; it has been moved into an array-level operation.
• Why it matters: Readers need this idea to understand NumPy and later machine learning code as whole-array computation. Vectorization changes the reading unit from one element at a time to an entire array or axis at a time.
• Related concepts: broadcasting, tensor, matrix
• Core Section: P2-11.3
• Appears in: P2-12.1, P2-15.1, P3-6.2

data visualization¶

• Meaning: Data visualization turns numerical or tabular data into visual forms such as points, lines, bars, or ranges so patterns can be inspected.
• Why it matters: Visualization helps reveal changes, relationships, and distributions that may not be obvious in a table. It is an analysis tool for deciding what pattern to observe first, not just decoration.
• Related concepts: distribution, loss curve
• Core Section: P2-13.1
• Appears in: P2-13.2, P2-13.3, P2-15.1, P4-18.2

vocabulary¶

• Meaning: A tokenizer vocabulary is the internal list of token pieces that a tokenizer can produce and the IDs assigned to those pieces. In this context, vocabulary is not a human dictionary; it is a computational lookup table for model input pieces.
• Why it matters: The same source string can become different token pieces, token counts, and token IDs depending on the vocabulary and splitting rules. This concept helps readers treat token IDs as vocabulary item numbers, not definitions, and explains why tokenizer choice affects cost and context length.
• Related concepts: token, tokenization, token ID, embedding
• Core Section: P6-2.2
• Appears in: P6-2.2, P6-2.5, P7-4.1

vector search¶

• Meaning: A search method that represents items as vectors and retrieves nearby vectors by distance or similarity.
• Why it matters: It connects embeddings to retrieval systems and explains how semantic search differs from exact keyword matching.
• Related concepts: Read together with the surrounding glossary entries and the linked Sections for this term.
• Core Section: P1-13.4
• Appears in: P1-13.2, P1-13.3

vector calculus¶

• Meaning: The extension of calculus to vector-valued and multivariable functions.
• Why it matters: It supports gradients, optimization, and the mathematics behind neural network learning.
• Related concepts: Read together with the surrounding glossary entries and the linked Sections for this term.
• Core Section: P2-4.5