Information-theoretic generalization bounds go brrrrr....
https://arxiv.org/abs/2005.08044 

Nice ideas in here combining Catoni's single draw setting and the @shortstein @zakynthinou framework. I appreciate multiple cites to my group's recent work.

Our most recent paper extending Steinke--Zakynithinou is most relevant: https://arxiv.org/abs/2004.12983 

Yes, we assume bounded loss, but subG bounds are trivial.

They also refer to our NeurIPS paper on data-dependent estimates:

https://arxiv.org/abs/1911.02151 

Until our new CMI-style bounds, these bounds were the tightest for Langevin by a large factor.

Finally they cite the work that started @KDziugaite and I down this road, i.e., our UAI 2017 paper on nonvacuous bounds. We've learned a lot since then, but the key messages are still valid: we don't know why our bounds are so loose.

https://arxiv.org/abs/1703.11008 

One thing I've learned though: if you make your title sound as if it summarizes the entire content of the paper, people will happily forego reading your paper and think they know what it's about. If you're in that category, go read the paper.

I thought I recognized these authors. Indeed, they had very recent work introducing this unifying perspective (but without the conditional information density perspective).

https://arxiv.org/abs/2004.09148 

Hello, @giuseppe_durisi. Is the student on Twitter?

I think the boundedness assumption we make is not so important to highlight. It's trivial to extend this. The thing to highlight is the generality of your perspective as it includes single draw, PAC-Bayes, etc. I suspect our advances over the SZ bounds are complementary to yours.

@shortstein I believe this answers your recent question. They call the log RN derivative the information density and so its evaluation at a point drawn from the measuring being dominated should likely be called something similary... instantaneous information density?