https://sankethbk.github.io/blog/tags/computational-graphs/Recent content in Computational-Graphs on Sanketh's BlogHugo -- 0.166.0en-usSat, 12 Sep 2026 00:00:00 +0000https://sankethbk.github.io/blog/posts/ml/2026-09-12-1-branching-why-gradients-add/Sat, 12 Sep 2026 00:00:00 +0000https://sankethbk.github.io/blog/posts/ml/2026-09-12-1-branching-why-gradients-add/<h1 id="computational-graphs-part-2-branching--why-gradients-add">Computational Graphs, Part 2: Branching — Why Gradients Add</h1> <p>The <a href="https://sankethbk.github.io/blog/posts/ml/2026-09-09-computational-graphs-and-backpropagation">previous note</a> covered the forward pass, the chain rule, and the backward pass on a graph where every input had exactly one path to the output. This note adds the one remaining piece: what happens when an input feeds into <strong>more than one</strong> operation.</p> <p>When that happens, there are multiple paths from the input to the output. The chain rule tells us to <strong>add</strong> the contributions from those paths.</p>https://sankethbk.github.io/blog/posts/ml/2026-09-12-2-single-neuron-as-a-graph/Sat, 12 Sep 2026 00:00:00 +0000https://sankethbk.github.io/blog/posts/ml/2026-09-12-2-single-neuron-as-a-graph/<h1 id="computational-graphs-part-3-a-single-neuron-and-logistic-regression">Computational Graphs, Part 3: A Single Neuron and Logistic Regression</h1> <p>The <a href="https://sankethbk.github.io/blog/posts/ml/2026-09-12-1-branching-why-gradients-add">previous note</a> 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 <a href="https://sankethbk.github.io/blog/posts/ml/2026-09-07-ml-refresher-linear-logistic-regression">first note</a>.</p> <hr> <h2 id="1-what-you-will-learn">1. What you will learn</h2> <ul> <li>How a single neuron is a small computational graph.</li> <li>The forward pass through a weighted sum and an activation function.</li> <li>The backward pass through the same graph.</li> <li>Why logistic regression is exactly a one-neuron network with sigmoid activation.</li> <li>How the cross-entropy loss fits into the graph as an extra node.</li> <li>Why the gradient formula from logistic regression matches the chain-rule result.</li> </ul> <hr> <h2 id="2-a-single-neuron">2. A single neuron</h2> <p>A neuron with two inputs has three steps:</p>https://sankethbk.github.io/blog/posts/ml/2026-09-09-computational-graphs-and-backpropagation/Wed, 09 Sep 2026 00:00:00 +0000https://sankethbk.github.io/blog/posts/ml/2026-09-09-computational-graphs-and-backpropagation/<h1 id="computational-graphs-and-backpropagation">Computational Graphs and Backpropagation</h1> <p>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 <a href="https://sankethbk.github.io/blog/posts/ml/2026-09-07-ml-refresher-linear-logistic-regression">linear and logistic regression note</a> and the layered functions we will later call neural networks.</p> <p>The ideas are:</p> <ol> <li>Draw the function as a graph of operations.</li> <li>Evaluate the graph from inputs to output: the <strong>forward pass</strong>.</li> <li>Use the chain rule to carry sensitivities from the output back to the inputs: the <strong>backward pass</strong>.</li> </ol> <p>We build this on one tiny example and walk through every step.</p>