By Ben Krose, Patrick van der Smagt
This manuscript makes an attempt to supply the reader with an perception in man made neural networks.
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Extra info for An Introduction to Neural Networks (8th Edition)
1. 2: Example of clustering in 3D with normalised vectors, which all lie on the unity sphere. The three weight vectors are rotated towards the centres of gravity of the three di erent input clusters. selected and is subsequently rotated towards the input. Consequently, weight vectors are rotated towards those areas where many inputs appear: the clusters in the input. 2. w1 w1x w2 a. x w2 b. 3: Determining the winner in a competitive learning network. a. Three normalised vectors. b. , but with di erent lengths.
To control the object, forces F must be applied, since the object su ers from friction and perhaps other external forces. To tackle this problem, we use an Elman net with inputs x and x d , one output F , and three hidden units. The hidden units are connected to three context units. In total, ve units feed into the hidden layer. 3. 3: Training an Elman network to control an object. The solid line depicts the desired trajectory x d the dashed line the realised trajectory. The third line is the error.
As a result, the crystal lattice will be highly ordered, without any impurities, such that the system is in a state of very low energy. 11) where T is a parameter comparable with the (synthetic) temperature of the system. This stochastic activation function is not to be confused with neurons having a sigmoid deterministic activation function. 12) where P is the probability of being in the th global state, and E is the energy of that state. Note that at thermal equilibrium the units still change state, but the probability of nding the network in any global state remains constant.
An Introduction to Neural Networks (8th Edition) by Ben Krose, Patrick van der Smagt
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