BIC/AIC issues

[schmidtfa]

BIC and AIC seem to often favor knee over fixed models, even if the spectrum looks pretty "linear" in loglog

[schmidtfa]

So the problem is as follows:
I have implemented akaike (AIC) and bayesian (BIC) information criteria, but they always tend to favor the more complex model (even if i know that its the wrong model via simulation) so I have the feeling sth is going wrong. The formula for information criteria is in general quite simple.

IC = -2ll + An * p

IC = Generalized information criteria
An = Penalty Weight (e.g "log(n)" in BIC and "2" in AIC)
p = Number of parameters (i.e. predictors)
-2ll = 2times the negative log-likelihood, which becomes in linear regression equivalent to nsamples * log(mean squared error)

see also https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7299313/#ref6a

I also looked at some other resources and I am pretty sure this formula is correct (e.g. https://robjhyndman.com/hyndsight/lm_aic.html).

So the weird thing is that when I slightly adjust the way I compute "-2ll" everything works as expected.
Most information criteria I specify always suggest the correct model. I really simulated a lot of different settings (different exponents, different frequency resolutions, different knees etc.) and it basically always works out and tells me correctly whether I am having a knee in my data or not, which is cool but I am also drifting apart from how its usually done. So what I am changing is essentially that instead
of doing:
nsamples * log(mean squared error) [where samples refers to the frequency bins]

I am doing:
log(nsamples) * log(mean squared error) [where samples refers to the frequency bins]

[schmidtfa]

I am removing the label of bug as everything works as expected right now (at least based on the simulations i ran and also from visually inspecting real data). However, I want to keep the issue open for now in case a user ends up having a problem with their data and/or someone has an idea why the classical formula fails.