This is because the only parameters that are adjusted in the learning process are the linear mapping from hidden layer to output layer.
12.
Thus we can regard covector fields not just as sections of the cotangent bundle, but also linear mappings of vector fields into functions.
13.
On the Lie algebra level, there is a corresponding linear mapping from the Lie algebra of G to Lie bracket [, ].
14.
This linear mapping is an isomorphism in finite dimensions, and it is often then expedient to identify " V " with its double dual.
15.
Here G is a non-linear operator and cannot be separated to represent a linear mapping of the model parameters that form m into the data.
16.
As is the case in general for partial derivatives, some formulae may extend under weaker analytic conditions than the existence of the derivative as approximating linear mapping.
17.
Linear subspace learning algorithms are traditional dimensionality reduction techniques that represent input data as vectors and solve for an optimal linear mapping to a lower-dimensional space.
18.
For example, as the courses progressed, the concept of mappings were used to describe, and visually illustrate, the traditionally disparate topics of linear mappings.
19.
Writing about planar affine mapping, Rafael Artzy made a similar trichotomy of planar, linear mapping in his book " Linear Geometry " ( 1965 ).
20.
Relative to the church interior, the stained-glass window is displayed at a much lower brightness than a linear mapping between scene radiance and pixel intensity would produce.
