Is a Vector 1D or 5D? The Two Meanings of Dimension
A vector is called 1-dimensional, yet [1, 2, 3, 4, 5] is also a 5-dimensional vector. Dimension has two distinct meanings, and this post untangles both.
Deep Learning Fundamentals: The MNIST Dataset and the Cost Function
A neural network needs data to learn from and a way to score itself: the MNIST dataset, one-hot encoded labels, and the cost function that scores its weights and biases.
Machine Learning Basics: The Bias-Variance Tradeoff
A model's error splits into bias and variance, and reducing one raises the other. Learn underfitting, overfitting, and how to balance them via total error.
Why a Digit Classifier Needs 10 Output Neurons, Not 4
A digit classifier's output layer uses 10 neurons, not the sufficient 4. Seeing why means stepping into the network's own eyes to watch how it reads an image.
Deep Learning, Step One: Neural Network Terminology
Zooming out from a single sigmoid neuron to a full network: meet the input, hidden, and output layers, and see why feedforward and recurrent networks differ in one thing.
An Improved Perceptron: Understanding the Sigmoid Neuron
A perceptron's output flips between 0 and 1, so learning never accumulates. See how the sigmoid neuron's smooth activation turns that cliff into a gentle slope.
Beyond Text-to-SQL: Implementing OpenAI’s 6-Layer Context Data Agent and the Hidden Challenges
Explore the architecture of OpenAI’s in-house Data Agent. Learn how they leverage six layers of context, self-correction, and Evals to analyze 600 PB of data.