Neural network A neuron is a cell in

Neural network A neuron is a cell in the brain whose principal function is the collection, processing, and dissemination of electrical signals.

Neural network a simple mathematical model of the neuron devised by Mc. Culloch and Pitts

Single layer feed-forward neural networks (perceptrons) A network with all the inputs connected directly to the outputs is called a single-layer neural network , or a perceptron network. Since each output unit is independent of the others-each weight affects only one of the outputs.

Single layer feed-forward neural networks (perceptrons) Unfortunately, there are many Boolean functions that the threshold perceptron cannot represent. We see that the threshold perceptron returns 1 if and only if the weighted sum of its inputs(including the bias) is positive Now, the equation W. x = 0 defines a hyperplane in the input space, so the perceptron returns 1 if and only if the input is on one side of that hyperplane.

Single layer feed-forward neural networks (perceptrons) Black dots indicate a point in the input space where the value of the function is 1, and white dots indicate a point where the value is 0.

Single layer feed-forward neural networks (perceptrons) Despite their limited expressive power, threshold 1 perceptrons have some advantages. In particular, there is a simple learning algorithm that will jit a threshold perceptron to any linearly separable training set.

Multilayer feed-forward neural networks The advantage of adding hidden layers is that it enlarges the space of hypotheses that the network can represent Think of each hidden unit as a perceptron that represents a soft threshold function in the input space

Multilayer feed-forward neural networks by adding two opposite-facing soft threshold functions and thresholding the result, we can obtain a "ridge" function as shown in (a). Combining two such ridges at right angles to each other (combining the outputs from four hidden units), we obtain a "bump" as shown in (b).