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Danny Wood
Danny Wood
@echostatements.bsky.social
AI Research Scientist || PhD in machine learning || Ensembles, probabilistic machine learning, recurrent neural networks || https://echostatements.net
160 followers315 following67 posts
The answer in rot13: Onpxebbzf rot13.com The construction is a bit cheeky (pun intended) but I think worth it for the surface reading #cryptic #crypticcrossword
Danny Wood reposted
Danny Wood reposted
Every summer I repost this article on how to spot drowning. Please read it and pass on. In the last few years I’ve had SIX messages from people who saved a kid’s life after clicking on the link from my feed. slate.com/technology/2...
I'd never heard of disappearing polymorphs until watching this video. It's mildly terrifying but well worth a watch www.youtube.com/watch?v=ksn5...
Danny Wood reposted
A nice article by Nicholas Carlini on writing great papers. A lot of the advice you can find elsewhere but the sections on collaborations and conclusions both had new insights for me. It also helps that I've really liked the papers of his that I've read nicholas.carlini.com/writing/2026...
A simple command line tool combining a crossword solver and anagram finder. A lot of online crossword solver tools felt unnecessary cumbersome to me, so I've tried to make this as lightweight and simple to use as possible github.com/EchoStatemen...
Danny Wood reposted
Replying to @astrokatie.com
You know that thing where the farther something is, the smaller it looks? That doesn’t quite work in an expanding universe. It’s true for a while but after a certain point, more distant things (of the same size) start to look BIGGER because their light has been traveling since the cosmos was small 🙃
Can we get LLMs to generate text that is perfectly typeset down to the very last character? In a new blog post, I show how using a constrained beam search, LLMs can efficiently generate perfect blocks of monospace text echostatements.net/posts/2026/0...
This post was inspired by a video by @tomvii.bsky.social, where he uses paraphrasing by large language models as part of an entirely new typesetting system based around his own programming language I highly recommend checking it out: www.youtube.com/watch?v=Y65F...
The library is open source, so feel free to play with it: github.com/EchoStatemen...
Danny Wood reposted
TIL if you do Miller-Rabin with the first 12 prime bases, you have a fast, exact primarily test for all 64-bit integers. Cf. oeis.org/A014233 which gives the upper bound on the two-sided correctness of Miller-Rabin given that you tested on the first k bases.
This result was one of the foundational ideas built upon by what has since become by far my most cited paper, so I'm really happy to see a version on arXiv where it can hopefully be preserved for posterity
New (sort of) preprint on arXiv today: a generalized bias-variance decomposition for Bregman divergences! arxiv.org/abs/2511.08789
Danny Wood reposted
I published a new post on my rarely updated personal blog! It's a sequel of sorts to my Quanta coverage of the Busy Beaver game, focusing on a particularly fearsome Turing machine known by the awesome name Antihydra.
I'm a big fan of when counterexamples to intuitive sounding theorems are so convoluted that outside of mathematics, the kind of rules-lawyering needed to construct them would be considered pedantic or even rude youtu.be/pLgcZLysOFk?...
The video is a fun watch but if you don't check it out, the counterexample I'm referring to is the Alexander horned sphere en.wikipedia.org/wiki/Alexand...
How do you make Minecraft spherical? A really fun read about all the problem solving that goes into transferring Minecraft gameplay onto a spherical world www.bowerbyte.com/posts/blocky...
Really nice primer on double-descent and the bias-variance trade-off I'm impressed by the depth that Welch Labs consistently manages to pack into their videos without sacrificing the storytelling for a popular science audience www.youtube.com/watch?v=z64a...
Since @spmontecarlo.bsky.social shared a post about Crinkled Arcs a couple of weeks ago, I've spent a fair bit of time digging into them This new blog post attempts to collect what I found into an interactive introduction to crinkled arcs and their relationship to Brownian Motion
A surprisingly intuitive and practical use for limit ordinals (assuming you have an infinite chess board handy) youtu.be/CQ4Ap5itTX4?...
Danny Wood reposted
Danny Wood reposted
Both the blog post and paper are cited in the GPT-OSS model card here: openai.com/index/gpt-os...
This idea seems to have originated in a blog post by Evan Miller, which is a really nice read and suggests that just adding +1 to the denominator of the softmax could solve the extreme value issue: www.evanmiller.org/attention-is...
This turns out to be a special case of the attention sink as implemented in the new GPT models, as explained in this paper: arxiv.org/pdf/2309.174...
It looks like they're designed to solve a problem raised in this paper (amongst others), that when an attention head wants to not add additional information, it will give the vast majority of its attention probability mass to non-informative tokens... arxiv.org/abs/2306.12929