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###########################################################################
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# A machine learning model is a *function*, with inputs and outputs. For
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- # this discussion, we’ll treat the inputs a as an *i*-dimensional vector
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+ # this discussion, we’ll treat the inputs as an *i*-dimensional vector
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# :math:`\vec{x}`, with elements :math:`x_{i}`. We can then express the
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# model, *M*, as a vector-valued function of the input: :math:`\vec{y} =
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# \vec{M}(\vec{x})`. (We treat the value of M’s output as
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# of which should be :math:`2 * cos(a)`. Looking at the graph above,
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# that’s just what we see.
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#
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- # Be aware than only *leaf nodes* of the computation have their gradients
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+ # Be aware that only *leaf nodes* of the computation have their gradients
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# computed. If you tried, for example, ``print(c.grad)`` you’d get back
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# ``None``. In this simple example, only the input is a leaf node, so only
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# it has gradients computed.
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