Introduction to Neural Networks and Backpropagation with micrograd

🧠 Neural network training involves using an autograd engine to implement backpropagation.

🔬 Micrograd is an autograd engine that allows you to build mathematical expressions and evaluate the gradient of a loss function with respect to the weights of a neural network.

📈 Micrograd's functionality is best illustrated through an example of building a mathematical expression and evaluating its derivative.

🔑 We have implemented value objects for addition and multiplication operations.

🔑 We have created a data structure to build mathematical expressions and visualize them.

🔑 We have started implementing backpropagation to calculate gradients for each value.

💡 The chain rule in calculus allows us to correctly differentiate through a function composition by multiplying the derivatives.

🔍 The chain rule helps us determine the instantaneous rate of change of one variable with respect to another in a complex equation.

✏️ Backpropagation is the process of recursively applying the chain rule backwards through a computation graph.

📝 Backpropagation is a technique used to calculate gradients in neural networks.

🧮 The local derivative of the tanh function is 1 - tanh^2(x).

🔀 In backpropagation, gradients are propagated from the output layer to the input layer.

📝 The video explains the issue of gradient overriding in neural networks when using the backward pass.

💡 To solve the issue, we need to accumulate gradients using the 'plus equals' operation instead of setting them directly.

🏋️‍♂️ The video also demonstrates how to implement complex mathematical expressions and neural networks using PyTorch's API.

🧠 Neural networks can be built using modules and classes to represent neurons, layers, and an entire multi-layer perceptron (mlp).

⚙️ The forward pass of a neuron involves multiplying the input values with randomly initialized weights, adding a bias, and applying a non-linearity.

🔁 The backpropagation algorithm allows us to update the weights of the neural network to minimize the loss, which is a measure of performance.

💡 Neural networks are mathematical expressions that take input data, weights, and parameters and use a loss function to measure the accuracy of predictions.

💭 Backpropagation is used to calculate the gradient, which allows us to tune the parameters to minimize the loss.

🔍 Gradient descent is an iterative process that follows the gradient to update the parameters and improve the predictions of the neural network.