Word
manifold
Phoneticsman·i·fold, stress on the first syllable
US/ˈmænəˌfoʊɫd/
UK/mˈænɪfˌəʊld/
Countable noun TechnicalMathematics
Definition
n. a mathematical shape or space that looks flat and simple up close, even if it is curved and complex overall.
n. a topological space that locally resembles Euclidean space; in machine learning, the lower-dimensional curved surface embedded within a high-dimensional data space.
Examples
“The surface of the Earth is a two-dimensional manifold embedded in three-dimensional space.”
“The manifold hypothesis suggests that real-world images live on a smooth, low-dimensional surface within pixel space.”
“Non-linear dimensionality reduction algorithms like UMAP preserve the local geodesic geometry of the underlying data manifold.”
Examples
simple
“The surface of the Earth is a two-dimensional manifold embedded in three-dimensional space.”
contextual
“The manifold hypothesis suggests that real-world images live on a smooth, low-dimensional surface within pixel space.”
complex
“Non-linear dimensionality reduction algorithms like UMAP preserve the local geodesic geometry of the underlying data manifold.”
Usage
Typically used as an attributive adjective before a noun, or predicatively after a linking verb like 'be'.
Real-World Examples
“The questions running through the play are manifold, complex and echo those asked by sci-fi writers for decades: can robots hurt humans?” Etymology
From Old English manigfeald ('various, numerous, many-layered'), from manig ('many') + feald ('-fold'). Mathematically defined by Bernhard Riemann in 1851 (German Mannigfaltigkeit).
Etymology adapted from Wiktionary, available under CC BY-SA 4.0.
Related words
Domain
- Exam level
- CambridgeCambridgeCambridge English QualificationsThe exam suite from Cambridge University Press & Assessment, from A1 Movers up to C2 Proficiency. The benchmark names double as CEFR labels.C1 AdvancedIELTSIELTSInternational English Language Testing SystemThe 0–9 band test co-owned by the British Council, IDP, and Cambridge. Used for university entry, work, and migration.7.0–8.0TOEFL iBTTOEFL iBTTest of English as a Foreign Language, Internet-Based TestETS's academic English test, the standard route for US university admissions. Scored 0–120, with a 1–6 scale since 2026.1–6 scale: 5.0–5.595–113TOEICTOEICTest of English for International CommunicationETS's workplace English test, big in Japan and Korea. Listening & Reading scores 10–990 and tops out at C1.945–990
- Frequency
- Frequent
- Level
- C1 · Advanced
- Updated
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