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This leads to a sufficient and necessary condition of a certain estimability Gramian matrix having full rank.
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We can see that being trained to generalize like the teacher network using soft targets produces hidden layer weight matrices having fuller rank than training with hard targets.
Let ϕ be an analytic self-map of the n-ball, having 0 as the attracting fixed point and having full-rank near 0. We consider the generalized Schröder's equation, F∘ϕ="ϕ′(0 kF with k a positive integer and prove there is always a solution F with linearly independent component functions, but that such an F cannot have full rank except possibly when k="1.
Suppose that F ′ ( x ∗ ) has full rank.
We assume that and have full rank.
provided that the has full rank.
Since has full rank, for all.
If r=K, the channel has full rank.
Exponential correlation matrices defined above have full rank.
which has full rank but is not necessarily orthogonal.
We assume that B has full rank, i.e., rank(B)= m.
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