Implementing Simple Neural Network Backpropagation from Scratch by Siq Sun Mar, 2024

It is easier to repeat this process a certain number of times (iterations/epochs) rather than setting a threshold for how much convergence should be expected. You might notice that the weights of the NOT a1 AND NOT a2 neuron aren’t the same as those in the a1 AND a2 neuron. This is due to the NOT gate which I didn’t want to get bogged down in because it wouldn’t be fun to see this gate again. It may be fun however to try to figure this out yourself. We don’t want to have to hard code this logical network, but it would be good if someone or something else, could do it for us in a systematic way.

XOR-Gate with Multilayer Perceptron

As parameters we will pass number 2 and 1 because our  x now has two features, and we want one output for the y. Then, we will create a criterion where we will calculate the loss using the function torch.nn.BCELoss() ( Binary Cross Entropy Loss). Also we need to define an optimizer by using the Stochastic Gradient descent.

Representation Space Evolution

  1. Notice this representation space (or, at least, this step towards it) makes some points’ positions look different.
  2. The purpose of hidden units is the learn some hidden feature or representation of input data which eventually helps in solving the problem at hand.
  3. These logical gates are summarized in the table below so that we can refer back to them later.
  4. And, in my case, in iteration number 107 the accuracy rate increases to 75%, 3 out of 4, and in iteration number 169 it produces almost 100% correct results and it keeps like that ‘till the end.

I believe they do so because the gradient descent is going around a hill (a n-dimensional hill, actually), over the loss function. Let’s see what happens when we use such learning algorithms. The images below show the evolution of the parameters values over training epochs. It doesn’t matter how many linear layers we stack, they’ll always be matrix in the end. However, is it fair to assign different error values for the same amount of error? For example, the absolute difference between -1 and 0 & 1 and 0 is the same, however the above formula would sway things negatively for the outcome that predicted -1.

Training algorithm

As usual with categorical variables, we would use one-hot-encoding and so the record for each patient is a vector of ones and zeros. Obviously, you can code the XOR with a if-else structure, but the idea was to show you how the network evolves with iterations in an-easy-to-see way. Now that you’re ready you should find some real-life problems that can be solved with automatic learning and apply what you just learned. A L-Layers XOR Neural Network using only Python and Numpy that learns to predict the XOR logic gates.

This is also an open research field, with new kinds of architectures often leading to breakthroughs. 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.

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. The input layer receives the input data passed through the hidden layers.

We’ll be looking at exactly what each neuron in the network is doing and how this fits into the whole. Using this example I hope that you will get a better insight into what goes on inside neural networks. In a real-world situation, we have to use a method called backpropagation to train this multilayer perceptron. After training, we will get the weights we have used here. But for this post, I have just shown the possibilities that we have if we want to solve such problems using perceptron.

As I said, there are many different kinds of activation functions – tanh, relu, binary step – all of which have their own respective uses and qualities. For this example, we’ll be using what’s called the logistic sigmoid function. Backpropagation is an algorithm for update the weights and biases of a model based on their gradients with respect to the error function, starting from the output layer all the way to the first layer. M maps the internal representation to the output scalar.

Transfer learning reduces the amount of training data required and speeds up the training process. It also improves the accuracy of models by leveraging knowledge learned from related tasks. To solve the XOR problem with RNNs, we need to use a special type of RNN called Long Short-Term Memory (LSTM).

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. Activation used in our present model are “relu” for hidden layer and “sigmoid” for output layer. The choice appears good for solving this problem and can also reach to a solution easily. Convolutional neural networks (CNNs) are a type of artificial neural network that is commonly used for image recognition tasks.

Backpropagation is a supervised learning algorithm used to train neural networks. It is based on the chain rule of calculus and allows us to calculate the error at each layer of the network and adjust weights and biases accordingly. xor neural network A neural network with hidden layers is referred to as a deep neural network, from which many industry buzzwords like deep learning originate. They are especially useful in learning non-linear relationships between two variables.

Leave a Reply