# Tilt Equivalence in Symbolic Volume Integration

I’ve been continuing my involvement in “Algorithmic Fairness” research. In particular, I’ve been working on an improvement to the Symbolic Volume Integration (SVI) method mentioned in a previous post. The idea is to modify SVI in a way that makes it converge faster. While the previous SVI method depends on the construction of rectangles that are aligned with the axes, we’re aiming to allow rectangles that are “rotated” or “tilted” with respect to the axes.

To that end, I showed that rotating a rectangle for SVI is equivalent to applying the inverse rotation to the region of integration.

Here’s a link to the writeup. \( \blacksquare\)