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Instead of
trying to explicitly extract the coordinates of a
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datapoint on the
manifold, map the datapoint to an
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energy valley in
a high-dimensional space.
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The learned
energy function in the high-dimensional
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space restricts
the available configurations to a low-
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dimensional
manifold.
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– |
We
do not need to know the manifold dimensionality
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in
advance and it can vary along the manifold.
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We
do not need to know the number of manifolds.
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Different
manifolds can share common structure.
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But we cannot
create the right energy valleys by direct
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interactions
between pixels.
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So
learn a multilayer non-linear mapping between the
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data
and a high-dimensional latent space in which we
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can
construct the right valleys.
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