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This was actually a note I wrote way back in grad school, but never published or even posted to arXiv. After proving the result, I couldn't find a prior reference, but it seemed so basic that I figured it must have been done already. So I posted it on my website and moved on.

But then a weird thing happened...people found it anyway, and actually started citing it like it was a novel result! I guess I accidentally made the top Google result for "Bregman bias-variance" or something.

So I reached out to Frank Nielsen, who helpfully pointed me to the relevant literature. I meant to set the record straight, but by this point I'd actually lost the original LaTeX for the notes, and just never had the time to rewrite them...

Until one day recently, I dropped the notes into an LLM and...got the raw LaTeX right back out. In theory I could have done it myself in a few hours, but this was enough to get me over the "activation energy" to finally do it. So thank you, Frank and Gemini! (Please don't hate me, Bluesky)

13/11/25, 8:45 pm0 reposts7 likes

@echostatements.bsky.social

I will say, it is a very odd feeling to finally tick something off your to-do list after 12 years...satisfying, but odd.

Danny Wood

I'm really glad to see this on arXiv after all these years!

People keep coming out of the woodwork (no pun intended) to tell me that this three-page note is behind the best work of their careers and I am blown away.