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Songjianbo (talk | contribs) Equivariance |
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== Equivariance ==
Invariance represents representation that does not vary with transformation; Equivariance means that a transformation is equivalent to an expression of a transformation.
Equivariance is the detection of objects that can transform to each other.<ref>{{Cite web|url=https://jhui.github.io/2017/11/14/Matrix-Capsules-with-EM-routing-Capsule-Network/|title=“Understanding Matrix capsules with EM Routing (Based on Hinton's Capsule Networks)”|website=jhui.github.io|access-date=2017-12-31}}</ref> A spatial relationship can be characterized represented by its ''pose'', data that describes the object's [[Translation (geometry)|translation]] and [[Rotation (mathematics)|rotation]]. Translation is a change in ___location in one or more dimensions, while rotation is a change in orientation.<ref name=":1"/>▼
From the perspective of computer vision, invariance means that objects are not recognized by some transformations, which include translation, rotation, viewpoint, scale and so onWhatever the object of translation, rotation of 2 d, 3 d rotation and scale, we can according to the invariance to identify its nature, hence invariance in object recognition has its importance, but when our task becomes more complex and difficult, for example, when we want to explore how much object moving unit, how many degrees rotated, put the shrinkage ratio of the relative specific questions such as how much, just rely on invariance can't reach it, then we need to degeneration.
▲Equivariance is the detection of objects that can transform to each other.<ref>{{Cite web|url=https://jhui.github.io/2017/11/14/Matrix-Capsules-with-EM-routing-Capsule-Network/|title=“Understanding Matrix capsules with EM Routing (Based on Hinton's Capsule Networks)”|website=jhui.github.io|access-date=2017-12-31}}</ref> A spatial relationship can be characterized represented by its ''pose'', data that describes the object's [[Translation (geometry)|translation]] and [[Rotation (mathematics)|rotation]]. Translation is a change in ___location in one or more dimensions, while rotation is a change in orientation.<ref name=":1" />
[[Unsupervised learning|Unsupervised]] capsnets learn a global [[Affine space|linear manifold]] between a whole object and its pose (as a matrix of weights). As such, the ''translation invariance'' is encapsulated in the weights, rather than in neural activity (recognition), making the network ''translation equivariant''. Multiplying the object by the manifold thereby poses the object (for an object, in space).<ref>{{Cite web|url=https://kndrck.co/posts/capsule_networks_explained/|title=Capsule Networks Explained|last=Tan|first=Kendrick|date=November 10, 2017|website=kndrck.co|language=en|archive-url=|archive-date=|dead-url=|access-date=2017-12-26}}</ref>
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