How (not) to compare 2D scatter plots
How to calculate the statistical distance between two 2D distributions of points. But first a lesson in bad statistics, the pitfalls of visual solutions and over-complicating a solved problem.
Pegasus by Satoshi Kamiya, folded by me
How to calculate the statistical distance between two 2D distributions of points. But first a lesson in bad statistics, the pitfalls of visual solutions and over-complicating a solved problem.
Calculating probabilities for matching games like Dobble.
Classifier-free guidance for denoising diffusion probabilistic model in Julia.
A denoising diffusion probabilistic model for generating numbers based on the MNIST dataset. The underlying machine learning model is a U-Net model, which is a convolutional autoencoder with skip connections. A large part of this post is dedicated to implementing...
Denoising diffusion probabilistic models for AI art generation from first principles in Julia. This is part 1 of a 3 part series on these models.
Derivation of the backpropagation equations for layer normalization.
Transformers for natural language processing from first principles. This a long post which details a full implementation of transformers and the mathematics behind them. The use case is predicting Amazon review stars based on the review text. The language of...
Interpolation using quaternions.
A detailed foundation of quaternion mathematics.
Rotations in 2D.