Are there many higher order compositions?

[nicholasturner1]

Elhage et al. and the mechanisms they've talked about since have only involved "first-order" compositions (key in layer i is generated using output of layer j). Are higher order compositions apparent in the larger structure?

We'll need to at least partially address the baseline question (#1) in order to evaluate this correctly.

[nicholasturner1]

Analyzing the input path complexity of sets of nodes in the network suggests that many higher-order compositions exist for quite high thresholds of the composition term values.
https://github.com/nicholasturner1/gpt-omics/blob/main/notebooks/220514_graphs.ipynb
We should compare this to comparable randomized networks in case this isn't truly surprising.

[nicholasturner1]

#14 did a version of this. Stronger baselines still seem useful.