Imagine you're trying to find an equation that works universally (like F=ma in physics), but you don't know what makes up the equation (the "ma" part of F=ma). But you have "F" (aka the resulting data). The traditional way is to derive the equation from first principles, but what if you don't know how to do that? What if it's impossible? That's where the Cross-Universe Symbolic Regression Tournament comes in (CU-SRT - pronounced "cursed" because it's cooler that way).

​

In machine learning, there is a concept known as "symbolic regression". The idea is simple: you take a dataset (like how much force a granny smith apple experiences when dropped from a tree) and let a computer play with blocks of math (mass of apple, height of tree, +, -, x, sin, cos, ...) like legos until it builds a formula that matches your data. Once this is done, it's possible that you'd get a formula that works really well for the particular dataset you trained it on. But more often than not, this same formula doesn't work very well on other datasets (e.g., how much force a McIntosh apple experiences when dropped from a different tree). This is called "overfitting", and it's usually considered a bad thing, because it means you don't actually have the master formula that works universally - you just have a really good imposter that only works for the specific context you trained it on.

​

I was thinking about this, and also about Darwin and evolution, and thought to myself: what if we flipped the narrative on overfitted equations? I viewed them as analogous to genetic mutation. Perhaps through widespread competition, the true universal equation would prevail, similar to how genes compete and propagate through natural selection.​ CU-SRT proposes exactly this. The core structure is as follows:

​

1. We generate a bunch of overfitted equations (I call them "candidates") within a single dataset (called "universe" in the paper). These are great in their local universe, but we don't know if they will hold true across the board yet.

2. We repeat this process across many different data universes (e.g., many different apple + tree combinations)

3. We cross-test candidates from one universe with all other universes and repeat this for all candidates. This creates a cross-universe tournament, where candidate equations are now competing for survival based on how well they can generalize themselves across universes (aka mimic what a master equation would do). The ones that aren't able to perform well outside of their original universe are culled from the surviving candidates, just like how an unfavorable gene is purged from the gene pool.

4. At the end, we are left with a winner equation, which should, in theory, provide a reasonable substitute for what the true master equation should be, if not actually just be the master equation itself.

​​