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The simplest artificial neural network

The following image represents a simple two-layer neural network:

Simple two-layer neural net

The first layer is the input layer and the last layer is the output layer. The middle layer is the hidden layer. If there is more than one hidden layer, then such a network is a deep neural network.

The input and output of each neuron in the hidden layer is connected to each neuron in the next layer. There can be any number of neurons in each layer depending on the problem. Let us consider an example. The simple example which you may already know is the popular hand written digit recognition that detects a number, say 5. This network will accept an image of 5 and will output 1 or 0. A 1 is to indicate the image in fact is a 5 and 0 otherwise. Once the network is created, it has to be trained. We can initialize with random weights and then feed input samples known as the training dataset. For each input sample, we check the output, compute the error rate and then adjust the weights so that whenever it sees 5 it outputs 1 and for everything else it outputs a zero. This type of training is called supervised learning and the method of adjusting the weights is called backpropagation. When constructing artificial neural network models, one of the primary considerations is how to choose activation functions for hidden and output layers. The three most commonly used activation functions are the sigmoid function, hyperbolic tangent function, and Rectified Linear Unit (ReLU). The beauty of the sigmoid function is that its derivative is evaluated at z and is simply z multiplied by 1-minus z. That means:

dy/dx =σ(x)(1−σ(x))

This helps us to efficiently calculate gradients used in neural networks in a convenient manner. If the feed-forward activations of the logistic function for a given layer is kept in memory, the gradients for that particular layer can be evaluated with the help of simple multiplication and subtraction rather than implementing and re-evaluating the sigmoid function, since it requires extra exponentiation. The following image shows us the ReLU activation function, which is zero when x < 0 and then linear with slope 1 when x > 0:

The ReLU is a nonlinear function that computes the function f(x)=max(0, x). That means a ReLU function is 0 for negative inputs and x for all inputs x >0. This means that the activation is thresholded at zero (see the preceding image on the left). TensorFlow implements the ReLU function in tf.nn.relu():

Backpropagation, an abbreviation for "backward propagation of errors", is a common method of training artificial neural networks used in conjunction with an optimization method such as gradient descent. The method calculates the gradient of a loss function with respect to all the weights in the network. The optimization method is fed with the gradient and uses it to get the weights updated to reduce the loss function.