Neural networks for XOR function with training data set MATLAB Answers MATLAB Central

23. августа 2022. • Uncategorized • by


Created by the Google Brain team, TensorFlow presents calculations in the form of stateful dataflow graphs. The library allows you to implement calculations on a wide range of hardware, from consumer devices running Android to large heterogeneous systems with multiple GPUs. ANN is based on a set of connected nodes called artificial neurons . Each connection between artificial neurons can transmit a signal from one to the other.

spiking neural networks

It takes a transpose of the input vector, multiplies it with the weight vector and adds the bias vector. Alone, this basic perceptron, no matter what the weights and bias are, can never accurately predict the XOR output since it is a linear function and XOR is not. 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 bring everything together, we create a simple Perceptron class with the functions we just discussed.

1.3. But “Hidden Layers” Aren’t Hidden¶

In the xor neural network problem, we are trying to train a model to mimic a 2D XOR function. The central object of TensorFlow is a dataflow graph representing calculations. The vertices of the graph represent operations, and the edges represent tensors . 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.

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With the network designed in the previous section, a code was written to show that the ANN can indeed solve an XOR logic problem. When the inputs are replaced with X1 and X2, Table 1 can be used to represent the XOR gate. Here, the loss function is calculated using the mean squared error . As the basic precursor to the ANN, the Perceptron is designed by Frank Rosenblatt to take in several binary inputs and produce one binary output. Neural nets used in production or research are never this simple, but they almost always build on the basics outlined here. Hopefully, this post gave you some idea on how to build and train perceptrons and vanilla networks.

A Two Layer Neural Network Can Represent The Xor Function

The inputs of the NOT AND gate should be negative for the 0/1 inputs. This picture should make it more clear, the values on the connections are the weights, the values in the neurons are the biases, the decision functions act as 0/1 decisions . Using a two layer neural network to represent the XOR function has several advantages. First, it is a relatively simple and efficient method for representing the XOR function.

Since Simulink is integrated with Matlab we can also code the Neural Network in Matlab and obtain its mathematically equivalent model in Simulink. 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. After inserting the required data, we can train the network with the given dataset and receive appropriate graph‘s which will be helpful in analyzing the data. It is difficult to prove the existence of local minima, which exerts a bad influence upon learning of neural networks. For example, it was proved that there are no local minima in the finite weight region for the XOR problem (Hamney, 1998; Sprinkhuizen-Kuyper & Boers, 1998).

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Its derivate its also implemented through the _delsigmoid function. If not, we reset our counter, update our weights and continue the algorithm. We know that a datapoint’s evaluation is expressed by the relation wX + b .

We have two binary entries 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. You can just read the code and understand it but if you want to run it you should have a Python development environment like Anaconda to use the Jupyter Notebook, it also works with the python command line. Once the Neural Network is trained, we can test the network through this tool and verify the obtained results. When expanded it provides a list of search options that will switch the search inputs to match the current selection.

The first layer is the input layer, which receives input from the environment. The second layer is the output layer, which produces the output of the network. Each neuron in the network is connected to all of the neurons in the other layer.

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The closer the resulting value is to 0 and 1, the more accurately the neural network solves the problem. In common implementations of ANNs, the signal for coupling between artificial neurons is a real number, and the output of each artificial neuron is calculated by a nonlinear function of the sum of its inputs. Twitter is a social media platform, and its analysis can provide plenty of useful information. In this article, we will show you, using the sentiment140 dataset as an example, how to conduct Twitter Sentiment Analysis using Python and the most advanced neural networks of today – transformers. Here, the model predicted output for each of the test inputs are exactly matched with the XOR logic gate conventional output () according to the truth table and the cost function is also continuously converging. In this paper, the error surface of the XOR network with two hidden nodes (Fig. 1) is analysed.

  • 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.
  • Very often when training neural networks, we can get to the local minimum of the function without finding an adjacent minimum with the best values.
  • As mentioned, a value of 1 was included with every input dataset to represent the bias.
  • Following the creation of the activation function, various parameters of the ANN are defined in this block of code.
  • Its differentiable, so it allows us to comfortably perform backpropagation to improve our model.

This software is used for highly calculative and computational tasks such as Control System, Deep Learning, Machine Learning, Digital Signal Processing and many more. Matlab is highly efficient and easy to code and use when compared to any other software. This is because Matlab stores data in the form of matrices and computes them in this fashion. Matlab in collaboration with Simulink can be used to manually model the Neural Network without the need of any code or knowledge of any coding language.

Neurons in the brain are complex machines with distinct functional compartments that interact nonlinearly. In contrast, neurons in artificial neural networks abstract away this complexity, typically down to a scalar activation function of a weighted sum of inputs. Here we emulate more biologically realistic neurons by learning canonical activation functions with two input arguments, analogous to basal and apical dendrites. We use a network-in-network architecture where each neuron is modeled as a multilayer perceptron with two inputs and a single output.

Training a Two Layer Neural Network to Represent the XOR Function

We consider the problem of numerically solving the Schrödinger equation with a potential that is quasi periodic in space and time. We introduce a numerical scheme based on a newly developed multi-time scale and averaging technique. We demonstrate that with this novel method we can solve efficiently and with rigorous control of the error such an equation for long times. A comparison with the standard split-step method shows substantial improvement in computation times, besides the controlled errors. We apply this method for a free particle driven by quasi-periodic potential with many frequencies.


Section 2 discusses the main components of the networks, i.e. the LIF neurons, RFs and Boolean logic. The XOR function is a non-linear function that is not easily represented by other methods. However, a two layer neural network can represent the XOR function by adjusting the weights of the connections between the neurons. The weights of the connections are adjusted during the training process, allowing the network to learn the desired function.

Keras and Tensorflow

Lastly, the list ‘errorlist’ is updated by finding the average absolute error for each forward propagation. This allows for the plotting of the errors over the training process. For this ANN, the current learning rate (‘eta’) and the number of iterations (‘epoch’) are set at 0.1 and respectively.

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Training becomes similar to DNN thanks to the closed-form solution to the spiking waveform dynamics. In addition, we develop a phase-domain signal processing circuit schema… The empty list ‘errorlist’ is created to store the error calculated by the forward pass function as the ANN iterates through the epoch. A simple for loop runs the input data through both the forward pass and backward pass functions as previously defined, allowing the weights to update through the network.

This is a prominent property of the complex-valued neural network. Next, the activation function (and the differentiated version of the activation function is defined so that the nodes can make use of the sigmoid function in the hidden layer. With the added hidden layers, more complex problems that require more computation can be solved.

However, these can be changed to refine and optimize the performance of the ANN. Lastly, the logic table for the XOR logic gate is included as ‘inputdata’ and ‘outputdata’. As mentioned, a value of 1 was included with every input dataset to represent the bias. While there are many different activation functions, some functions are used more frequently in neural networks.


Now let’s build the simplest neural network with three neurons to solve the XOR problem and train it using gradient descent. Using the fit method we indicate the inputs, outputs, and the number of iterations for the training process. This is just a simple example but remember that for bigger and more complex models you’ll need more iterations and the training process will be slower.

Following code gist shows the initialization of parameters for neural network. Most usual mistake is to set it too high, so the network will oscillate or diverge instead of learn. One potential decision boundary for our XOR data could look like this. Remember that a perceptron must correctly classify the entire training data in one go. If we keep track of how many points it correctly classified consecutively, we get something like this.

  • It means that from the four possible combinations only two will have 1 as output.
  • The vertices of the graph represent operations, and the edges represent tensors .
  • Otherwise you risk that input signal to a neuron might be large from the start in which case learning for that neuron is slow.
  • Sprinkhuizen et al. have also stated that the listed local minima are in fact saddle points .
  • A network with one hidden layer containing two neurons should be enough to seperate the XOR problem.

Such understanding is valuable in the development of new training algorithms. It is also important to note that ANNs must undergo a ‘learning process’ with training data before they are ready to be implemented. Above is the equation for a single perceptron with no activation function.

We have some instance variables like the training data, the target, the number of input nodes and the learning rate. Using a two layer neural network to represent the XOR function has some limitations. First, it is limited in its ability to represent complex functions. Finally, it is limited in its ability to learn from a small amount of data. It turns out that TensorFlow is quite simple to install and matrix calculations can be easily described on it.

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