Continuous normalizing flows (CNF) use differential equations to transform probability distributions. This article presents a simpler derivation of the key equation and its interpretation.

2025-03-23

Normalizing flows require efficient calculation of Jacobians of transformations of input and intermediate data. This article covers three well known transformations for which the Jacobians can be efficiently calculated.

2025-03-03

Kronecker product is a way to multiply two matrices of any shape. This apparently simple product has a lot of desirable properties and finds applications in different areas.

2024-04-05

This article revisits the building blocks of linear algebra - matrix-vector and matrix-matrix products. It provides animations to quickly grasp the different ways to interpret these products. It also talks about scenarios where each interpretation is useful.

2024-02-25

Essentially born from shuffling the rows or columns of an identity matrix, these matrices carry a distinctive set of properties that make them valuable in various mathematical applications. This article explores some of their fundamental properties and applications in various fields.

2024-02-03

This is a further generalization of the problem of calculating the inverse of a matrix after removing a row and a column. But what about removing k-rows and k-columns? Exploring this problem also leads us to a well known matrix - the Schur Complement.

2024-01-28

We explore two methods to derive the isometric projection matrix. The first one involves two rotations of a unit cube. The second one is a first principles approach to arrive at the solution without any rotation.

2024-01-18

How is the inverse of a matrix related to the inverse of the matrix with a specific row and column removed? I encountered this problem while reading a paper on post-training quantization. This article digs deeper into the original problem and some of its variants.

2023-12-24

Type (almost) whatever you want to visualize in plain English - you can add vectors, polygons, points on a circle. You can rotate the input vectors or the transformation matrix.

2023-10-13

A neat little trick to assess image quality using CLIP. Roughly speaking, an image assessment model gives a score to an image based on its quality, aesthetics etc. While there are specifically trained models for this, we can also achieve this functionality using a multi-modal model like CLIP.

2023-08-14