Demystifying Neural Networks: Solving the XOR Problem with Backpropagation by Rajeshwar Vempaty

We look forward to learning more and consulting you about your product idea or helping you find the right solution for an existing project. Jupyer notebook will help to enter code and run it in a comfortable environment. To overcome this challenge, we need to use LSTM architecture which has memory cells that can store information over long periods of time.

Weight Analysis

There are no fixed rules on the number of hidden layers or the number of nodes in each layer of a network. The best performing models are obtained through trial and error. 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. These parameters are what we update when we talk about “training” a model.

1. Neural Networks¶

However, neural networks are a type of algorithm that’s capable of learning. 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.

MGMT 4190/6560 Introduction to Machine Learning Applications @Rensselaer

This is particularly visible if you plot the XOR input values to a graph. As shown in figure 3, there is no way to separate the 1 and 0 predictions with a single classification xor neural network line. It is the setting of the weight variables that gives the network’s author control over the process of converting input values to an output value.

Approaching the XOR Problem with Feedforward Neural Networks

The data flow graph as a whole is a complete description of the calculations that are implemented within the session and performed on CPU or GPU devices. DEV Community — A constructive and inclusive social network for software developers. The XOR problem can be solved using just two neurons, according to a statement made on January 18th, 2017. It will be the same logistic regression as before, with addition of a third feature. The rest of the code will be identical  to the previous one.

  1. Deep networks have multiple layers and in recent works have shown capability to efficiently solve problems like object identification, speech recognition, language translation and many more.
  2. We will create a for loop that will iterate for each epoch in the range of iteration.
  3. For this step, we will take a part of the data_set function that we created earlier.
  4. Supervised learning approach has given amazing result in deep learning when applied to diverse tasks like face recognition, object identification, NLP tasks.
  5. Artificial neural networks (ANNs), or connectivist systems are computing systems inspired by biological neural networks that make up the brains of animals.

There are various schemes for random initialization of weights. In Keras, dense layers by default uses “glorot_uniform” random initializer, it is also called Xavier normal initializer. Weight initialization is an important aspect of a neural network architecture. But, Similar to the case of input parameters, for many practical problems the output data available with us may have missing values to some given inputs. And it could be dealt with the same approaches described above.

The end result of training are simply weights (and biases) connecting layer nodes. A simple guide on how to train a 2x2x1 feed forward neural network to solve the XOR problem using only 12 lines of code in python tflearn — a deep learning library built on top of Tensorflow. Some machine learning algorithms like neural networks are already a black box, we enter input in them and expect magic to happen.

They can handle many kinds of data and adjust to many tasks. The model’s versatility is shown when, for example, a neural network is trained on one language for machine translation. It is then fine-tuned to translate a second language with some extra training. Understanding the human brain and simulating its functions is the goal. In the 1940s, mathematician Walter Pitts and neurophysiologist Warren McCulloch made a computational model for neural networks.

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. We get our new weights by simply incrementing our original weights with the computed gradients multiplied by the learning rate. In any iteration — whether testing or training — these nodes are passed the input from our data. Using a game-theoretic methodology, Generative Adversarial Networks (GANs) present a novel framework in which two models (the discriminator and the generator) are simultaneously trained competitively.

Both forward and back propagation are re-run thousands of times on each input combination until the network can accurately predict the expected output of the possible inputs using forward propagation. A limitation of this architecture is that it is only capable of separating data points with a single line. This is unfortunate because the XOR inputs are not linearly separable.

I believe they do so because the gradient descent is going around a hill (a n-dimensional hill, actually), over the loss function. It doesn’t matter how many linear layers we stack, they’ll always be matrix in the end. In this representation, the first subscript of the weight means “what hidden layer neuron output I’m related to? The second subscript of the weight means “what input will multiply this weight?

Let’s look at a simple example of using gradient descent to solve an equation with a quadratic function. Gradient descent is an iterative optimization algorithm for finding the minimum of a function. To find the minimum of a function using gradient descent, we can take steps proportional to the negative of the gradient of the function from the current point. XOR is an exclusive or (exclusive disjunction) logical operation that outputs true only when inputs differ. 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. Transfer learning is a technique where we use pre-trained models to solve new problems.

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