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The principle is as follows. 1) is constructed using the known value of the derivative, namely the value of the right hand side. This is illustrated in Fig. 3. 3: Reconstruction of a function from a known derivative. For clarity, we will now change notation. 1) contains only one equation of the form ~ = f ( x , t ) . 2. NUMERICAL SOLUTION OF' T H E E Q U A T I O N S 73 Assume that Xo is the initial condition, at time t = to. The function x(t) will then be approximated by xt = x(to + h),x2 = x(to + 2h), etc.
Is the weight matrix of a layered network symmetric? 4. How would you use a neural network in a control problem? 5. In a backpropagation network, can you decrease the error it makes by introducing more hidden neurons? 6. Are the weights in a network derived from a biological concept? Chapter 3 N e u r o n s in the Brain One of the main attractions of neural networks is that they offer a model of computation based on the processes taking place in the brain. This neurobiological computation is parallel, and may suggest an efficient parallel architecture for computing.
Some require completely interconnected networks, not multi-layer ones, and so cannot be easily trained with backpropagation. But most will work well to some degree with multi-layer networks, trained with backpropagation. Some applications need hundreds of neurons. All the applications mentioned here have actually been demonstrated to work, the network being simulated in software. Between brackets is an estimate of the number of neurons one needs for a basic system. g. 100 means: between 10 and 1000 neurons.