Blockquote
Each lesson is a JSON object, containing the same properties.
The main properties are “teaching” where the AI teaches the user about the topic, “exercises” which is an object containing properties “practicalExercise” and “notesPrompt”, and “test” which is an array of objects containing “question” and “answer” properties.
I suppose I could split that up even further to produce the exercises and test separately and just include the lesson content in the context window?
Here is an example lesson:
{“content”:{“teaching”:“# The Perceptron: Understanding the Basics In this lesson, we’ll dive into the foundational concept of the Perceptron, a fundamental building block in the field of artificial neural networks. ## What is a Perceptron? ### History and Conceptual Overview The Perceptron is inspired by the way a single neuron in the human brain operates. It receives input signals, processes them, and produces an output. The output is determined by applying a set of weights to the inputs, summing them up, and then passing the result through an activation function. Let’s get into the nitty gritty of those fascinating processes eh? 1. Input Signals (x): The Perceptron takes multiple input signals, denoted as x_1, x_2, .., x_n. Each input is associated with a weight which determines its importance. Let’s say the weights are w_1, w_2, .., w_n. 2. Weighted Sum: The Perceptron calculates the weighted sum of the inputs and weights. This is done by computing: z = w_1 \\times x_1 + w_2 \\times x_2 + .. + w_n \\times x_n + b, where b is the bias term. 3. Activation Function: The result of the weighted sum is then passed through an activation function (often represented by a). The activation function introduces non-linearity (splits values into distinct categories) into the output and determines whether the Perceptron should ‘fire’ or not. - If the output of the activation function is above a certain threshold, the Perceptron will produce a ‘1’ or ‘firing’ output. Otherwise, it will produce a ‘0’ or non-firing output. This firing signal indicates that the Perceptron has classified the input data point as belonging to a particular category or class. In the context of binary classification (one or the other), if the Perceptron fires, it signifies that the input data point belongs to one class (often denoted as the positive class or class 1). Conversely, if the output is below the threshold, the Perceptron does not fire, indicating that the input data point belongs to the other class (often denoted as the negative class or class 0). 4. Learning and Training: The weights and the bias of the Perceptron which we talked about earlier, are adjusted during the training process. The goal is to learn the optimal set of weights that allow the Perceptron to make accurate predictions. E.g. if the perceptron applies a really low weight to certain inputs, and it’s predictions are pretty poor, it migh try applying higher weigths to those inputs. - One common algorithm used for training the Perceptron is the Perceptron Learning Rule. 6. Applications and Limitations: Perceptrons have been used in a variety of applications, including binary classification problems. However, they are limited to problems that can be linearly separable, where a single straight line can correctly separate the classes. To understand this, picture a graph with points scattered all over it. If this graph is linearly seperable graph, a line could be drawn through it to seperate the points accurately into categories. In mathematical terms, the Perceptron can be represented as a(w_1x_1 + w_2x_2 + ... + w_nx_n + b) where a is the activation function. Common activation functions include the step function, the sigmoid function, and the ReLU (Rectified Linear Unit) function. ### Multilayer Perceptrons (MLPs) While the single-layer Perceptron is limited to linear decision boundaries, Multilayer Perceptrons (MLPs) can overcome this limitation by introducing one or more hidden layers. These hidden layers allow MLPs to learn non-linear decision boundaries, making them more powerful for a wide range of tasks, including complex pattern recognition and classification problems. ### Backpropagation To train Multilayer Perceptrons, the backpropagation algorithm is commonly used. Backpropagation works by iteratively adjusting the weights of the network based on the error between the predicted output and the actual output. E.g. if the predicted output was 1, and the model output was 0.5, the gap would be 0.5, and the perceptron might increase the weights it was using to get it’s output closer to the predicted one. This process involves propagating the error backward through the network and updating the weights accordingly, allowing the network to learn from its mistakes and improve its performance over time. ### Activation Functions While the step function was historically used as the activation function for Perceptrons, modern neural networks make use of a variety of activation functions to introduce non-linearity into the network. Some commonly used activation functions include: - Sigmoid: S-shaped curve that squashes the output between 0 and 1, useful for binary classification tasks. - ReLU (Rectified Linear Unit): Returns 0 for negative inputs and the input value for positive inputs, providing faster training compared to sigmoid and addressing the vanishing gradient problem. - Tanh: Similar to the sigmoid function but squashes the output between -1 and 1, often used in hidden layers of neural networks. ### Conclusion The Perceptron laid the foundation for modern artificial neural networks, and its evolution into Multilayer Perceptrons paved the way for deep learning. Understanding these concepts is crucial for anyone interested in delving into the field of artificial intelligence and machine learning.”,“searchQuery”:“Introduction to single-layer perceptron in neural networks”},“exercises”:{“practical”:{“instructions”:“Implement a single Perceptron algorithm in your programming language of choice. You can start with a simple AND gate example and then extend it to other logical functions or linearly separable datasets.”,“solution”:null},“notesPrompt”:“Discuss the characteristics of a linear decision boundary in the context of the single-layer perceptron. Consider how it impacts the perceptron’s ability to classify data and its limitations.”},“test”:{“questions”:[{“question”:“Explain the role of the activation function in a single-layer perceptron.”,“answer”:“The activation function introduces non-linearity and determines the output of the perceptron based on the weighted sum of inputs.”,“qType”:“oneAnswer”,“options”:,“lNumbers”:[2]},{“question”:“A single-layer perceptron can model any function.”,“answer”:“False”,“qType”:“trueFalse”,“options”:,“lNumbers”:[2]},{“question”:“Backpropogation involves measuring the error between what?”,“answer”:“Predicted ouput and…”,“qType”:“multipleChoice”,“options”:[“actual output”,“perceptron weights”],“lNumbers”:[2]},{“question”:“Name two key elements of a single-layer perceptron?”,“answer”:“Any two from: inputs, weights, a weighted sum function, an activation function, and the output.”,“qType”:“oneAnswer”,“options”:,“lNumbers”:[2]},{“question”:“Name one activation function…”,“answer”:“ReLU/Sigmoid/Tanh”,“qType”:“oneAnswer”,“options”:,“lNumbers”:[2]},{“question”:“In the context of a single-layer perceptron, how are the weights related to the decision boundary?”,“answer”:“The weights determine the orientation of the decision boundary.”,“qType”:“oneAnswer”,“options”:,“lNumbers”:[2]},{“question”:“What is a common training algorithm used for single layer perceptrons?”,“answer”:“Perceptron Learning Rule”,“qType”:“oneAnswer”,“options”:,“lNumbers”:[2]}]}}
