Demystifying Neural Networks: Part 2

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the network’s performance on the validation dataset. If performance starts to degrade or doesn’t improve significantly, it could be a sign that the network is beginning to overfit, much like when kids need guidance to get back on track. In such cases, the training process should be stopped, helping programmers find the optimal number of epochs.Now, taking a cue from ‘early stopping,’ let’s pause and ask ourselves: Are we ready to dive deeper into the inner workings of neural networks? If you’re nodding, buckle up and let’s go! During forward propagation, input data travels through the neural network from the input layer through the hidden layers and finally reaches the output layer. In each layer, the neurons process the inputs they receive, multiply them by their respective weights, sum the products, and then apply an activation function to generate their output (see Figure 1 for a visual depiction of forward propagation in a very simple neural network). There’s also a bias parameter, initially set to a small positive constant value (e.g., 0.01 or 0.1) or any non-zero random number, added to the weighted sum of inputs before passing it through the activation function. The bias parameter helps the activation function better fit the data and adds flexibility to capture the underlying relationship between input and output data. The bias parameter is then updated along with the weights during backpropagation.<figure id="2554"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*MP3IGtqM7jYdQjR-3LsDZg.png"><figcaption>Figure 1. Author’s illustration of forward propagation in a simple neural network with one hidden layer. Each neuron in the input layer receives a single input and its associated weight. The weighted sums are calculated and passed to all neurons in the hidden layer. Typically, input layer neurons do not have activation functions. Neurons in the hidden layer calculate the weighted sum of their inputs, apply their activation functions, and send the results to the output layer. In this illustration, the output layer has just one neuron, which calculates the weighted sum of its inputs, applies its activation function, and produces the final output. For simplicity, bias parameters are not shown in the figure.</figcaption></figure>Backpropagation is all about fine-tuning the neural network's weights and bias parameters by minimizing the error between its predictions and the actual target values. First, we calculate the output layer's error (or loss), representing the difference between the network’s prediction and the tr

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ue target value. Next, using the chain rule of calculus and the power of math, we calculate the gradients (partial derivatives) of the error concerning each weight in the network, moving backward from the output layer through the hidden layers toward the input layer. There, you have it, backpropagation in a nutshell! For a visual representation of backpropagation, please see below.<figure id="e081"><img src="https://cdn-images-1.readmedium.com/v2/resize:fit:800/1*-JXCEgC7VWKF7Hw8UiCFIw.png"><figcaption>Figure 2. Author’s illustration of one iteration of backpropagation in a simple three-layer neural network. The yellow arrows represent the flow of information through the layers. Panel (A) shows that backpropagation begins by calculating the error between the actual target value and the predicted value for each neuron in the output later. For simplicity, only one output neuron is included in the figure. Next, the error gradient for the output layer neuron is calculated, which is equal to the error times the derivative of the activation function. The error gradient calculated for each neuron and in each layer is used to update the weights and biases of every neuron across all layers. Panels (B) and (C) show the calculation of error and error gradient for each neuron in every layer. Panels (D) and (E) depict the repetition of this process for every neuron in the input layer to complete one iteration of backpropagation.</figcaption></figure>In conclusion, neural networks can be likened to a game of catch, where players are organized in layers and pass the ball to one another, much like neurons transmitting information through layers in a forward propagation process. But neural networks also have a mechanism to learn from their mistakes and improve their performance. This learning process, called backpropagation, involves calculating the error and its gradient, starting from the last neuron in the output layer, and adjusting the weights and biases accordingly. Just as players in a game of catch become better at throwing and catching the ball with practice, neural networks refine their predictions through iterative training. This fascinating combination of forward propagation and backpropagation makes neural networks powerful for various data applications, including imputations, open-ended survey write-in data recoding, and constructing survey weights. If you need to refamiliarize yourself with the basics of neural networks, check out <a href="https://readmedium.com/demystifying-neural-networks-part-1-a99b36d91134">part 1</a> of this series.</article></body>

Demystifying Neural Networks: Part 2

Ah, so you’ve decided to plunge deeper into the world of neural networks, huh? Trust me. It’ll be worth it (famous last words)! Neural networks are a subfield of Artificial Intelligence (AI) that takes their cues straight from the human brain. A neural network consists of an input layer, one or more hidden layers, and an output layer. As information flows from one layer to the next, it’s processed and refined, efficiently handling high-dimensional and large datasets. It’s like a super-smart, ultra-efficient brain-inspired assembly line!

Just like humans go through stages in life, from young and learning to old and wise, neural networks experience stages too: forward propagation and backpropagation (and no, this is not a typo. There’s no space between back and propagation like there is in forward propagation). During forward propagation, the network makes predictions based on its current weights (that’s all we can ask of anyone, right? Make the best decision given their information!) Then comes the “learning from our mistakes” stage, also known as backpropagation. Here, the network calculates the error between its predictions and the actual target values, and adjusts the weights step-by-step, layer-by-layer, working backward from the output layer to the input layer. This process helps the network learn and improve its predictions.

These two stages — forward propagation and backpropagation — are repeated over many iterations (called epochs) during the training process. Programmers can set the number of epochs, but striking the right balance is crucial, just like mastering the art of parenting. Parents who are overprotective and don’t let their kids make their own decisions might hinder their growth and development. Similarly, by allowing too few epochs, programmers might leave the network ill-equipped to make accurate predictions. However, just like kids given too much freedom might struggle, too many epochs could lead to overfitting the training data, making the network less effective on unseen data.

Continuing to use parents as our inspiration because there are so many amazing ones out there, including mine, who have mastered the art of finding balance by recognizing signs of trouble early and addressing them, programmers can employ a common approach called ‘early stopping’ to strike that balance. Programmers use a validation dataset, a portion of the training dataset set aside to evaluate the model’s performance. After each epoch, they assess the network’s performance on the validation dataset. If performance starts to degrade or doesn’t improve significantly, it could be a sign that the network is beginning to overfit, much like when kids need guidance to get back on track. In such cases, the training process should be stopped, helping programmers find the optimal number of epochs.

Now, taking a cue from ‘early stopping,’ let’s pause and ask ourselves: Are we ready to dive deeper into the inner workings of neural networks? If you’re nodding, buckle up and let’s go! During forward propagation, input data travels through the neural network from the input layer through the hidden layers and finally reaches the output layer. In each layer, the neurons process the inputs they receive, multiply them by their respective weights, sum the products, and then apply an activation function to generate their output (see Figure 1 for a visual depiction of forward propagation in a very simple neural network). There’s also a bias parameter, initially set to a small positive constant value (e.g., 0.01 or 0.1) or any non-zero random number, added to the weighted sum of inputs before passing it through the activation function. The bias parameter helps the activation function better fit the data and adds flexibility to capture the underlying relationship between input and output data. The bias parameter is then updated along with the weights during backpropagation.

Figure 1. Author’s illustration of forward propagation in a simple neural network with one hidden layer. Each neuron in the input layer receives a single input and its associated weight. The weighted sums are calculated and passed to all neurons in the hidden layer. Typically, input layer neurons do not have activation functions. Neurons in the hidden layer calculate the weighted sum of their inputs, apply their activation functions, and send the results to the output layer. In this illustration, the output layer has just one neuron, which calculates the weighted sum of its inputs, applies its activation function, and produces the final output. For simplicity, bias parameters are not shown in the figure.

Backpropagation is all about fine-tuning the neural network's weights and bias parameters by minimizing the error between its predictions and the actual target values. First, we calculate the output layer's error (or loss), representing the difference between the network’s prediction and the true target value. Next, using the chain rule of calculus and the power of math, we calculate the gradients (partial derivatives) of the error concerning each weight in the network, moving backward from the output layer through the hidden layers toward the input layer. There, you have it, backpropagation in a nutshell! For a visual representation of backpropagation, please see below.

Figure 2. Author’s illustration of one iteration of backpropagation in a simple three-layer neural network. The yellow arrows represent the flow of information through the layers. Panel (A) shows that backpropagation begins by calculating the error between the actual target value and the predicted value for each neuron in the output later. For simplicity, only one output neuron is included in the figure. Next, the error gradient for the output layer neuron is calculated, which is equal to the error times the derivative of the activation function. The error gradient calculated for each neuron and in each layer is used to update the weights and biases of every neuron across all layers. Panels (B) and (C) show the calculation of error and error gradient for each neuron in every layer. Panels (D) and (E) depict the repetition of this process for every neuron in the input layer to complete one iteration of backpropagation.

In conclusion, neural networks can be likened to a game of catch, where players are organized in layers and pass the ball to one another, much like neurons transmitting information through layers in a forward propagation process. But neural networks also have a mechanism to learn from their mistakes and improve their performance. This learning process, called backpropagation, involves calculating the error and its gradient, starting from the last neuron in the output layer, and adjusting the weights and biases accordingly. Just as players in a game of catch become better at throwing and catching the ball with practice, neural networks refine their predictions through iterative training. This fascinating combination of forward propagation and backpropagation makes neural networks powerful for various data applications, including imputations, open-ended survey write-in data recoding, and constructing survey weights. If you need to refamiliarize yourself with the basics of neural networks, check out part 1 of this series.