Ml

Computational Graphs, Part 3: A Single Neuron and Logistic Regression The previous note showed how gradients add when one input feeds multiple operations. With that in place, we can now look at a real model: a single neuron. We will draw it as a graph, run the forward pass and backward pass by hand, and then connect it back to the logistic regression from the first note. 1. What you will learn How a single neuron is a small computational graph. The forward pass through a weighted sum and an activation function. The backward pass through the same graph. Why logistic regression is exactly a one-neuron network with sigmoid activation. How the cross-entropy loss fits into the graph as an extra node. Why the gradient formula from logistic regression matches the chain-rule result. 2. A single neuron A neuron with two inputs has three steps: ...

Computational Graphs and Backpropagation This note explains how to compute gradients for any function by breaking it into a graph of simple operations. It is the bridge between the gradient-descent picture from the linear and logistic regression note and the layered functions we will later call neural networks. The ideas are: Draw the function as a graph of operations. Evaluate the graph from inputs to output: the forward pass. Use the chain rule to carry sensitivities from the output back to the inputs: the backward pass. We build this on one tiny example and walk through every step. ...

ML Refresher: Linear and Logistic Regression This is the first note in the ML → Deep Learning → Transformers → LLMs series. The goal is to rebuild working memory of the basics before we get to neural networks: what a model is, how a loss function measures error, and how gradient descent tunes parameters. We will implement linear regression and logistic regression from scratch in NumPy, then compare with scikit-learn. If the code and gradients feel obvious, you are ready for the next note (computational graphs and backprop). If not, this is exactly the foundation to lock down first. ...