Clarification about the high-dimensional example in pysr demo notebook

[yippiez]

In the demo notebook, under High-dimensional input: Neural Nets + Symbolic Regression the time series is defined as:

$$z = y^2,\quad y = \frac{1}{10} \sum(y_i),\quad y_i = x_{i0}^2 + 6 \cos(2*x_{i2})$$

is the 1/10 here a constant or is the time step $Nt$ since in the below code in the notebook the shape is used to divide

PySR/examples/pysr_demo.ipynb

Line 1153 in 6508cf5

" y = torch.sum(y_i, dim=1, keepdim=True) / y_i.shape[1]\n",

Also in the inductive bias definition:

$$z=f(\sum g(x_i))$$

There is no averaging in the formula but in code below it there is averaging. Is this a typo or am i misunderstanding it?

[MilesCranmer]

You are right, this is a typo. Good catch.

I suppose since Nt is fixed it could also be considered part of g - it would divide its outputs by a constant.