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Neural Representation of AND, OR, NOT, XOR and XNOR Logic Gates Perceptron Algorithm by Obumneme Stanley Dukor

By April 18, 2024May 10th, 2024No Comments

They chose Exclusive-OR as one of the example and proved that Perceptron doesn’t have ability to learn X-OR. So, perceptron can’t propose a separating plane to correctly classify the input points. This incapability of perceptron to not been able to handle X-OR along with some other factors led to an AI winter in which less work was done in neural networks. Later many approaches appeared which are extension of basic perceptron and are capable of solving X-OR. The backpropagation algorithm is a learning algorithm that adjusts the weights of the neurons in the network based on the error between the predicted output and the actual output. It works by propagating the error backwards through the network and updating the weights using gradient descent.

The Inventor of LSTM Unveils New Architecture for LLMs to Replace Transformers

These powerful algorithms can solve complex problems by mimicking the human brain’s ability to learn and make decisions. However, certain problems pose a challenge to neural networks, and one such problem is the XOR problem. Artificial neural networks refer to any network of artificial neurons designed to mimic the functioning of the human brain.

  1. We are running 1000 iterations to fit the model to given data.
  2. Adversarial machine learning researchers are studying ways to strengthen neural networks against these attacks.
  3. Finally, we colour each point based on how our model classifies it.
  4. Traditional neural networks use linear activation functions that can only model linear relationships between input variables.


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. Tensorflow helps you to define the neural network in a symbolic way. This means you do not explicitly tell the computer what to compute to inference with the neural network, but you tell it how the data flow works. This symbolic representation of the computation can then be used to automatically caluclate the derivates.

OR logical function

We are running 1000 iterations to fit the model to given data. Batch size is 4 i.e. full data set as our data set is very small. In practice, we use very large data sets and then defining batch size becomes important to apply stochastic gradient descent[sgd]. If we imagine such a neural network in the form of matrix-vector operations, then we get this formula.

Is Reinforcement Learning Still Relevant?

LSTMs have memory cells that can store information over long periods of time which makes them suitable for processing sequential data. For a particular choice of the parameters w and b, the output ŷ only depends on the input vector x. I’m using ŷ (“y hat”) to indicate that this number has been produced/predicted by the model. By understanding the limitations of traditional logistic regression techniques and deriving intuitive as well as formal solutions, we have made the XOR problem quite easy to understand and solve. In this process, we have also learned how to create a Multi-Layer Perceptron and we will continue to learn more about those in our upcoming post.

Naturally, due to rising limitations, the use of linear classifiers started to decline in the 1970s and more research time was being devoted to solving non-linear problems. It is evident that the XOR problem CAN NOT be solved linearly. This is the reason why this XOR problem has been a topic of interest among researchers for a long time. Using the output values between this range of 0 and 1, we can determine whether the input \(x\) belongs to Class 1 or Class 0. In this post, we will study the expressiveness and limitations of Linear Classifiers, and understand how to solve the XOR problem in two different ways. Similarly, for the (1,0) case, the value of W0 will be -3 and that of W1 can be +2.

A neural network learns by updating its weights according to a learning algorithm that helps it converge to the expected output. The learning algorithm is a principled way of changing the weights and biases based on the loss function. This is true for neural networks, intense learning models. This makes the procedure pricey and inaccessible for consumers or small businesses. It may take days or weeks for complex models on big datasets. So, they cannot work well with limited processing power or time.

A neural network is a framework inspired by the neural networks in human brains. It lets machine learning algorithms model and solve complex patterns and issues through layers of connected nodes or neurons. Each node in one layer connects to nodes in the next layer. As the network learns, the weights of these connections change. Before we dive deeper into the XOR problem, let’s briefly understand how neural networks work. Neural networks are composed of interconnected nodes, called neurons, which are organized into layers.

Intuitively, it is not difficult to imagine a line that will separate the two classes. Now that we have a fair recall of the logistic regression models, let us use some linear classifiers to solve some simpler problems before moving onto the more complex XOR problem. AND gate operation is a simple multiplication operation between the inputs. In order to achieve 1 as the output, both the inputs should be 1. Our starting inputs are $0,0$, and we to multiply them by weights that will give us our output, $0$. However, any number multiplied by 0 will give us 0, so let’s move on to the second input $0,1 \mapsto 1$.

If the input is the same(0,0 or 1,1), then the output will be 0. The points when plotted in the x-y plane on the right gives us the information that they are not linearly separable like in the case xor neural network of OR and AND gates(at least in two dimensions). Let’s see what happens when we use such learning algorithms. The images below show the evolution of the parameters values over training epochs.

We can get weight value in keras using model.get_weights() function. 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 (similar to biological neurons in the brain of animals). Each connection (similar to a synapse) between artificial neurons can transmit a signal from one to the other. The artificial neuron receiving the signal can process it and then signal to the artificial neurons attached to it.

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