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deep-learning.mm
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deep-learning.mm
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<!--To view this file, download free mind mapping software Freeplane from http://freeplane.sourceforge.net -->
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Representation learning: achieving great power and flexibility by representing the world as a nested <b>hierarchy</b> of concepts
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A type of ML technique that enables computers to improve with <b>experience</b>  and data
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<node TEXT="Historical trends in Deep Learning" ID="ID_1666263722" CREATED="1537225345130" MODIFIED="1537225755340">
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<b>The central idea</b>: a large number of simple computational units can achieve intelligent behaviour when networked together
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<b>Distributed representation</b>
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<node TEXT="Long and rich history" ID="ID_1914048452" CREATED="1537226383176" MODIFIED="1537226417002">
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Larger datasets, a trend driven by the increasing <b>digitisation</b> of society
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<node TEXT="Part I: Applied Maths and Machine Learning Basics" POSITION="right" ID="ID_619172001" CREATED="1537225208185" MODIFIED="1537226771147">
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<p>
Vectors: matrices that contain only one <b>column</b>
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Tensors: an array of numbers arranged on a regular grid with a <b>variable number of axes</b>, i.e. a <b>generalised matrix</b>
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<b>Element-wise</b> product or <b>Hadamard</b> product
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<b>Dot product</b> between two vectors
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Inverse matrices are primarily a <b>theoretical tool</b>
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<b>Affine combinations</b> of solutions to Ax = b are also solutions
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Linear dependence as a form of <b>redundancy</b>
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<b>Singular</b>: square matrix with linearly dependent columns
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Motivation: <b>measure the size of a vector</b>
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Special kind of <b>functions</b> (f) mapping vectors to <b>non-negative values</b>
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f(<b>x</b>) = 0 => <b>x</b> = <b>0</b> (being <b>positive definite</b>)
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f(<b>x</b> + <b>y</b>) <= f(<b>x</b>) + f(<b>y</b>) (the <b>triangle inequality</b> or being <b>sub-additive</b>)
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f(a<b>x</b>) = |a|f(<b>x</b>), \forall a \in R (being absolutely <b>homogeneous</b>)
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