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A arXiv:1609.02907v4 [cs.LG] 22 Feb 2017

2.2 LAYER-WISE LINEAR MODEL A neural network model based on graph convolutions can therefore be built by stacking multiple convolutional layers of the form of Eq. 5, each layer followed by a point-wise non-linearity. Now, imagine we limited the layer-wise convolution operation to K= 1 (see Eq. 5), i.e. a function that is

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CHAPTER A - Stanford University

A.2•THE HIDDEN MARKOV MODEL 3 First, as with a first-order Markov chain, the probability of a particular state depends only on the previous state: Markov Assumption: P( q i j 1::: i 1)= i i 1) (A.4) Second, the probability of an output observation o i depends only on the state that produced the observation q i and not on any other states or ...

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satisfying the completeness theorem (due to K. G¨odel) which essentially says that any formula either has a proof or it has an interpretation in which it is false (but not both!). In all these proof systems we have the usual logical equivalences which are common to everyday mathematics. For example: For any formulas Φ and Ψ: (∃v i i

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The Community Builder’s Approach to Theory of Change

Contents Section One: Theory Development Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1