Forcing compactness

[DorofeevKirillDev]

In my field of research, formulas like a * b^1.5 * c / d^2 + const are quite common. These are relatively compact, with minimal compositional depth for each variable.

However, while I’m currently achieving low error (around 1e-7) on toy formulas, the resulting expressions are overly complex. Here’s an example function:

X = 0.1 + np.random.random((500, 4)
f_help = (3.2+X[:, 2]) / (4.5 + X[:, 3])
y = X[:, 0] * X[:, 1]**2 / (f_help**2)

Is there a way to guide PySR toward searching for functions of this kind? I tried adjusting adaptive_parsimony_scaling but the results were inconsistent.

[MilesCranmer]

Have you tried out template expressions? There are a few examples on the docs: TemplateExpressionSpec is the object to check out

[DorofeevKirillDev]

Templates aren't very useful in my case (if I understand their capabilities correctly). I don't know the exact form of the solution, but I do know, for example, that the functions are mostly multiplicative. Because of this, I don't expect a huge expression in brackets —which I often got in the results. I was able to improve the outcomes by increasing the complexity for the '+' and '-' operators, but the results are still inconsistent.

[MilesCranmer]

Sorry I’m not sure I follow. So, PySR gives you a table of the best expression at each complexity. Why not just pick a simpler expression from the list?

[DorofeevKirillDev]

I can pick a smaller expression from the list, and I did find the correct one. However, when I apply these constraints, the losses become an order of magnitude smaller, making it easier to identify the right solution among the options.

[MilesCranmer]

Ah well the rest of the battle is hyperparam tuning and running for more niterations. There is a tuning page in the docs which might be useful