How to build a neural network on Tensorflow for XOR

Designing a neural network in terms of writing code will be very hectic and unreadable to the users. Escaping all the complexities, data professionals use python libraries and frameworks to implement models. But we are designing an elementary neural network, so we will build it without using any framework like TensorFlow and PyTorch.

Actually, The word “Deep” in Deep Learning means the learning architecture with some numbers of layers. To bring everything together, we create a simple Perceptron class with the functions we just discussed. We have some instance variables like the training data, the target, the number of input nodes and the learning rate. That code creates a neural network with two input nodes, one hidden (or intermediate) layer with three neurons, and an output layer with one neuron.

XOR-jax

Here, we cycle through the data indefinitely, keeping track of how many consecutive datapoints we correctly classified. If we manage to classify everything in one stretch, we terminate our algorithm. These steps can be performed by writing a few lines of code in Keras or PyTorch using the inbuilt algorithms, but instead of using them as a black box, we should know in and out of those algorithms. And this was the only purpose of coding Perceptron from scratch.

Also, Matlab has a dedicated tool in its library to implement neural network called NN tool. Using this tool, we can directly add the data for input, desired output, or target. This conclusion lead to a significantly reduced interest in Frank Rosenblatt’s perceptrons as a mechanism for building artificial intelligence applications.

Part 1 of this notebook explains how to build a very basic neural network in numpy. This perceptron like neural network is trained to predict the output of a XOR gate. Hence, it signifies that the Artificial Neural Network for the XOR logic gate is correctly implemented. The loss function we used in our MLP model is the Mean Squared loss function. Though this is a very popular loss function, it makes some assumptions on the data (like it being gaussian) and isn’t always convex when it comes to a classification problem. It was used here to make it easier to understand how a perceptron works, but for classification tasks, there are better alternatives, like binary cross-entropy loss.

Technically, we call this a three layer network even though there are four actual layers because there are only three layers of processing units
(the input layer does not process anything). The XOR gate neural network implemention uses a two layer perceptron with sigmoid activation function. This portion of the notebook is a modified fork of the neural network implementation in numpy by Milo Harper. It turns out that TensorFlow is quite simple to install and matrix calculations can be easily described on it.

Neural Networks for XOR in tensorflow

The first step is to import all the modules and define training and testing data as we did for single-layer Perceptron. Now we can start making changes to our model and see how it affects the performance. Let’s try to increase the size of our hidden layer from 16 to 32. And that’s all we have to set up before we can start training our model.

If you don’t remember them or just don’t know what’s that we’ll show you.We have two binary entries ( 0 or 1) and the output will be 1 only when just one of the entries is 1 and the other is 0. It means that from the four possible combinations only two will have 1 as output. Its derivate its also implemented through the _delsigmoid function. The algorithm only terminates when correct_counter hits 4 — which is the size of the training set — so this will go on indefinitely.

A large number of methods are used to train neural networks, and gradient descent is one of the main and important training methods. It consists of finding the gradient, or the fastest descent along the surface of the function and choosing the next solution point. An iterative gradient descent finds the value of the coefficients for the parameters of the neural network to solve a specific problem. TensorFlow is an open-source machine learning library designed by Google to meet its need for systems capable of building and training neural networks and has an Apache 2.0 license. Some machine learning algorithms like neural networks are already a black box, we enter input in them and expect magic to happen. Still, it is important to understand what is happening behind the scenes in a neural network.

Basically, it makes the model more flexible, since you can “move” the activation function around. As we can see, the Perceptron predicted the correct output for logical https://forexhero.info/ OR. Similarly, we can train our Perceptron to predict for AND and XOR operators. But there is a catch while the Perceptron learns the correct mapping for AND and OR.

While creating these perceptrons, we will know why we need multi-layer neural networks. In the following section, we will introduce the XOR problem for neural networks. It is the simplest example of a non linearly separable neural network. It can be solved with an additional layer of neurons, which is called a hidden layer. In practical code development, there is seldom an use case for building a neural network from scratch. Neural networks in real-world are typically implemented using a deep-learning framework such as tensorflow.

• Such systems learn tasks (progressively improving their performance on them) by examining examples, generally without special task programming.
• The loss function we used in our MLP model is the Mean Squared loss function.
• This is a hands-on workshop notebook on deep-learning using python 3.
• The learning rate determines how much weight and bias will be changed after every iteration so that the loss will be minimized, and we have set it to 0.1.
• As a result, we will have the necessary values of weights and biases in the neural network and output values on the neurons will be the same as the training vector.
• Similiarily, almost same operation happens in neurons in Neural Network.

A perceptron with two input values and a bias corresponds to a general straight line. With the aid of the bias value b we can train the perceptron to determine a decision boundary with a non zero intercept c. He then went to Cornell Aeronautical Laboratory in Buffalo, New York, where he was successively a research psychologist, senior psychologist, and head of the cognitive systems section. This is also where he conducted the early work on perceptrons, which culminated in the development and hardware construction of the Mark I Perceptron in 1960. This was essentially the first computer that could learn new skills by trial and error, using a type of neural network that simulates human thought processes. This notebook is created to coincide the 90th birth anniversary of pioneering psychologist and artificial intelligence researcher, Frank Rosenblatt, born July 11, 1928 – died July 11, 1971.

We’ll be modelling this as a classification problem, so Class 1 would represent an XOR value of 1, while Class 0 would represent a value of 0. We know that a datapoint’s evaluation is expressed by the relation wX + b . A L-Layers XOR Neural Network using only Python and Numpy that learns to predict the XOR logic gates. Some algorithms of machine learning like Regression, Cluster, Deep Learning, and much more. We will update the parameters using a simple analogy presented below.

Artificial-Neural-Networks

Its differentiable, so it allows us to comfortably perform backpropagation to improve our model. Remember the linear activation function we used on the output node of our perceptron model? You may have heard of the sigmoid and the tanh functions, which are some of the most popular non-linear activation functions. The overall components of an MLP like input and output nodes, activation function and weights and biases are the same as those we just discussed in a perceptron. To train our perceptron, we must ensure that we correctly classify all of our train data. Note that this is different from how you would train a neural network, where you wouldn’t try and correctly classify your entire training data.

• They are initialized to some random value or set to 0 and updated as the training progresses.
• We will use the Unit step activation function to keep our model simple and similar to traditional Perceptron.
• TensorFlow is an open-source machine learning library designed by Google to meet its need for systems capable of building and training neural networks and has an Apache 2.0 license.
• So keeping this in mind, the weight matrix W will be (2,1).

In this notebook, we will learn how to implement a neural network from scratch using numpy. Once we have implemented this network, we will visualize the predictions generated by the neural network and compare it with a logistic regression model, in the form of classification boundaries. This workshop aims to provide an intuitive understanding of neural networks. The error function is calculated as the difference between the output vector from the neural network with certain weights and the training output vector for the given training inputs.

I recommend you to play with the parameters to see how many iterations it needs to achieve the 100% accuracy rate. There are many combinations of the parameters settings so is really up to your experience and the classic examples you can find in “must read” books. Here we define the loss type we’ll use, the weight optimizer for the neuron’s connections, and the metrics we need.

When the input or signal is entered into synapse, cell nucleus interprets the information contained in signals and generates the output through Axon. Similiarily, almost same operation happens in neurons in Neural Network. When the other axon sends the output, that is the input of next neurons ($x$), cell body interprets its information with embedded weight vector and bias($W, b$). Then, activation function filters information and send it to next neuron. We can see it was kind of luck the firsts iterations and accurate for half of the outputs, but after the second it only provides a correct result of one-quarter of the iterations.

Feel free to ask your valuable questions in the comments section below. You can also follow me on Medium to learn every topic of Machine Learning and Python. Before I get into building a neural network with Python, I will suggest that you first go through this article to understand what a neural network is and how it works.

I hope that the mathematical explanation of neural network along with its coding in Python will help other readers understand the working of a neural network. Following code gist shows the initialization of parameters for neural network. To design a hidden layer, we need to define the key constituents again first. Once we understood some basics and learn how to measure the performance of our network we can figure out a lot of exciting things through trial and error.

Then, in the 24th epoch recovers 50% of accurate results, and this time is not a coincidence, is because it correctly adjusted the network’s weights. A clear non-linear decision boundary is created here with our generalized neural network, or MLP. You’ll notice that the training loop never terminates, since a perceptron can only converge on linearly separable data. Linearly separable data basically means that you can separate data with a point in 1D, a line in 2D, a plane in 3D and so on.

The input for the logic gate consists of two values (T, F). T is for true and F for false, similar to binary values (1, 0). Input is fed to the neural network in the form of a matrix. So we have to define the input and output matrix’s dimension (a.k.a. shape). X’s shape will be (1, 2) because one input set has two values, and the shape of Y will be (1, 1). This is a hands-on workshop notebook on deep-learning using python 3.

We will take the help of NumPy, a python library famous for its mathematical operations and multidimensional arrays. Then we will switch to Keras for building multi-layer Perceptron. The Minsky-Papert collaboation is now believed to be a political maneuver and a hatchet job for contract funding by some knowledgeable scientists. These approaches xor neural network like backpropagation and CNN improves the AI technology, but still remains the problem in architecture. If we want to gather lots of information from the features, it requires some numbers of layers. But when the number of network layer is increased, the errors that need for backpropagation is vanished, so called Vanishing Gradient.

Try out some of the other inputs that we defined like False and False. Data Science Stack Exchange is a question and answer site for Data science professionals, Machine Learning specialists, and those interested in learning more about the field. We can see that none of these straight lines can be used as decision boundary nor any other lines going through the origin. The classic multiplication algorithm will have complexity as O(n3). Neural networks are now widespread and are used in practical tasks such as speech recognition, automatic text translation, image processing, analysis of complex processes and so on. Note that the input of second layer are the output of previous layer, so it requires to concatenate each output by 1.