Construct · 2 fields · 3 citations

Where does tensor collide?

One name. Different field. Different construct. One map.

● jingle · one word, two constructs Nearest construct by meaningmetriccompare the meanings
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Every construct on the map is compared with every other by the meaning of its definitions, and the closest one is surfaced here. The nearest construct to tensor is metric.

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tensor2 CONSTRUCTSMath tensorRICCI · TRANSFORMS BY RULEML tensorPYTORCH · NUMERIC ARRAY

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1900Math tensor2019ML tensor
2026

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Mathematics and physics

a geometric object, linear in each of several vectors, whose components change in a fixed way when coordinates change.

A geometric object that takes several vectors and produces a number by a rule that is linear in each of them, generalising scalars, vectors, and matrices: its numerical components depend on the coordinate system chosen, but they must change under a change of coordinates in a fixed, definite way so that the object itself is unchanged. Ricci and Levi-Civita's 1900 Méthodes de calcul différentiel absolu founded the calculus of such objects, which Einstein's 1916 Die Grundlage der allgemeinen Relativitätstheorie used to write the metric and stress-energy tensors of general relativity. The referent is defined by its transformation law, and that law is exactly what tells it apart from a mere grid of numbers stored in a computer or a muscle in the body.[1][2]

Unit
A multilinear map of a fixed rank on a vector space and its dual, with components carrying that many indices
Recovery means
Not applicable
Measured by
Pinned down by its transformation law: its components change from one coordinate system to another so that the object it names stays the same

Machine learning and computing

a multidimensional array of numbers with a shape and rank, used as the basic data structure of deep-learning frameworks.

A multidimensional array of numbers used as the basic data structure of deep-learning frameworks: it has a shape (a size along each axis), a rank (how many axes it has), and stored values, and the framework moves it efficiently across hardware to compute with it. Paszke and colleagues' 2019 PyTorch: An imperative style, high-performance deep learning library built such an object at the centre of its system, as did the earlier TensorFlow. Mathematicians regard this as a loose use of the word, because it keeps the array but drops the transformation law that defines the mathematical tensor, so despite the shared name it is closer to a plain table of numbers than to a coordinate-invariant geometric object or a muscle.[3]

Unit
An n-dimensional array of numbers, described by its shape and its data type
Recovery means
Not applicable
Measured by
Specified by its shape, rank, and stored values, with no requirement that it transform in any particular way under a change of coordinates

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Nearby collisions

vector3 fields · 3 citationsjingle · one word, three constructsscalar2 fields · 2 citationsjingle · one word, two constructsmatrix3 fields · 4 citationsjingle · one word, three constructs

References

  1. Ricci, G., & Levi-Civita, T. (1900). Méthodes de calcul différentiel absolu et leurs applications. Mathematische Annalen, 54(1–2), 125–201. https://doi.org/10.1007/BF01454201
  2. Einstein, A. (1916). Die Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik, 354(7), 769–822. https://doi.org/10.1002/andp.19163540702
  3. Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., ... Chintala, S. (2019). PyTorch: An imperative style, high-performance deep learning library. arXiv preprint arXiv:1912.01703. https://doi.org/10.48550/arXiv.1912.01703

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