We can see that now only one point with coordinates (0,0) belongs to class 0, while the other points belong to class 1. As you can see, the classifier classified one set of points to belong to class 0 and another set of points to belong to class 1. Now, we can also plot the loss that we already saved in the variable all_loss. Now, remember, because we are using PyTorch we need to convert our data to tensors.

## Perceptrons, Logical Functions, and the XOR problem

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 https://traderoom.info/ the scenes in a neural network. Coding a simple neural network from scratch acts as a Proof of Concept in this regard and further strengthens our understanding of neural networks.

## The Limitations and Drawbacks of Using Neural Networks for Solving Problems Like the XOR Problem

What we now have is a model that mimics the XOR function.

## Last Linear Transformation in Representational Space

- It abruptely falls towards a small value and over epochs it slowly decreases.
- This data is the same for each kind of logic gate, since they all take in two boolean variables as input.
- Now that we have seen how we can solve the XOR problem using an observational, representational, and intuitive approach, let’s look at the formal solution for the XOR problem.
- Such systems learn tasks (progressively improving their performance on them) by examining examples, generally without special task programming.

The XOR problem with neural networks can be solved by using Multi-Layer Perceptrons or a neural network architecture with an input layer, hidden layer, and output layer. So during the forward propagation through the neural networks, the weights get updated to the corresponding layers and the xor neural network XOR logic gets executed. The Neural network architecture to solve the XOR problem will be as shown below. To solve the XOR problem using neural networks, one can use either Multi-Layer Perceptrons or a neural network that consists of an input layer, a hidden layer, and an output layer.

The XOR problem can be solved using just two neurons, according to a statement made on January 18th, 2017. However, unsupervised learning techniques may not always provide accurate results compared to supervised learning techniques that rely on labeled examples. To overcome this challenge, we need to use LSTM architecture which has memory cells that can store information over long periods of time.

Backpropagation is a way to update the weights and biases of a model starting from the output layer all the way to the beginning. The main principle behind it is that each parameter changes in proportion to how much it affects the network’s output. A weight that has barely any effect on the output of the model will show a very small change, while one that has a large negative impact will change drastically to improve the model’s prediction power. 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. Though there are many kinds of activation functions, we’ll be using a simple linear activation function for our perceptron.

Thus we tend to use a smooth functions, the sigmoid, which is infinitely differentiable, allowing us to easily do calculus with our model. 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. But keep it in mind that it is only symbolic as this makes a few things more complicated and different from what you might be used to. Although RNNs are suitable for processing sequential data, they pose a challenge when it comes to solving the XOR problem.

Let’s meet the ReLU (Rectified Linear Unit) activation function. The solution to this problem is to expand beyond the single-layer architecture by adding an additional layer of units without any direct access to the outside world, known as a hidden layer. This kind of architecture — shown in Figure 4 — is another feed-forward network known as a multilayer perceptron (MLP).

However, with the 1969 book named ‘Perceptrons’, written by Minsky and Paper, the limitations of using linear classification became more apparent. For the XOR gate, the truth table on the left side of the image below depicts that if there are two complement inputs, only then the output will be 1. If the input is the same(0,0 or 1,1), then the output will be 0.