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Thomas Ahle

@thomasahle.bsky.social
284 followers 379 following 33 posts

Head of AI @ NormalComputing. Tweets on Math, AI, Chess, Probability, ML, Algorithms and Randomness. Author of tensorcookbook.com

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Thomas Ahle @thomasahle.bsky.social · 6h
Thanks Rasmus! We also made this website where you can try it for yourself: thomasahle.com/fast-polynom...
thomasahle.com
Fast Polynomial Evaluation — chain compiler
Evaluate a degree-n polynomial with about n/2 multiplications. Type a polynomial, pick ℚ, ℝ, ℂ, a Mersenne prime or a binary field, and get the preprocessed evaluation chain as math, C code or a circu...
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Reposted by Thomas Ahle
Rasmus Pagh @rasmuspagh.net · 14/09/2026
In a new result published on arXiv, former BARC PhD students @thomasahle.bsky.social and Jakob Bæk Tejs Houen make great progress on this question: floor(n/2)+1 multiplications suffice for any n. Great to see progress on a classic problem with such a clean result! arxiv.org/abs/2609.06022
arxiv.org
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Thomas Ahle @thomasahle.bsky.social · 31/05/2026
Open training also requires open data. It seems all top (open and closed) models right now train on each other's output. But a truly open model would get sued for this
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Thomas Ahle @thomasahle.bsky.social · 31/05/2026
Open models currently depend on big (mostly Chinese) companies being willing to sink tons of money in training. What is the best model right now that's trained distributed, like folding@home or Leela chess?
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Thomas Ahle @thomasahle.bsky.social · 31/05/2026
The charitable reading is "the industrial revolution was a net good, but some people lost a lot, e.g. tailors. Don't be the tailor of the next revolution." But this could go a lot harder than the industrial revolution...
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Reposted by Thomas Ahle
Clément Canonne @ccanonne.github.io · 11/01/2026
Mathematical writing is my passion.
The "kombucha girl" meme, where the left panel (with her frowning) stating "According to the proposition" and the right one (showing her interested face) stating "Lemma tell you"
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Thomas Ahle @thomasahle.bsky.social · 12/11/2025
like this?
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Thomas Ahle @thomasahle.bsky.social · 11/11/2025
Added a new symbols menu - let me know if I missed any of your favourite LaTeX commands!
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Thomas Ahle @thomasahle.bsky.social · 24/04/2025
I can't tell how much interest there is. But messages like this definitely encourage me to continue it!
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Thomas Ahle @thomasahle.bsky.social · 16/03/2025
I needed an easy way to make high resolution equations to post on Bluesky, so I made this: thomasahle.com/latex2png
thomasahle.com
LaTeX to Image
Effortlessly convert LaTeX math equations into high-quality images (PNG, JPEG, SVG).
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Thomas Ahle @thomasahle.bsky.social · 19/02/2025
> If NATO hadn't been trying to expand there, there would have been no war. There would. > If NATO stops trying to expand into Ukraine, the war ends. It wouldn't. > If the US stops sending weapons and fomenting anti-Russian sentiment, the war ends. This war is about territory not sentiment.
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Thomas Ahle @thomasahle.bsky.social · 19/02/2025
You can play around with expectations of higher order Gaussians using the new tensorcookbook.com/playground
tensorcookbook.com
Tensorgrad Playground
The Tensor Cookbook is a comprehensive guide to tensors, using the visual language of tensor diagrams. It closely follows the legendary 'Matrix Cookbook' while pr...
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Thomas Ahle @thomasahle.bsky.social · 19/02/2025
Isserlis' (or Wick's) theorem is one of the strongest tools to handle High Dimensional Gaussians. Turns out it generalizes to _every distribution_ using cumulant tensors! That's higher order variance, skewness, kurtosis, etc.
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Thomas Ahle @thomasahle.bsky.social · 18/02/2025
I added a Playground to tensorcookbook.com for when you need that Matrix or Tensor Derivative in a hurry. Hopefully it can also be a way to help people become familiar with tensor diagrams.
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Thomas Ahle @thomasahle.bsky.social · 12/02/2025
Now we're just waiting for a ZkiT model
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Thomas Ahle @thomasahle.bsky.social · 09/02/2025
Now live in a new Functions chapter in tensorcookbook.com
tensorcookbook.com
The Tensor Cookbook
The Tensor Cookbook is a comprehensive guide to tensors, using the visual language of tensor diagrams. It closely follows the legendary 'Matrix Cookbook' while pr...
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Thomas Ahle @thomasahle.bsky.social · 06/02/2025
Some sketches for the next chapter
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Thomas Ahle @thomasahle.bsky.social · 04/02/2025
I added code execution to tensorcookbook.com so you can try tensorgrad's automatic tensor algebra without installing anything.
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Thomas Ahle @thomasahle.bsky.social · 28/01/2025
🎉 Congratulations to Rasmus Pagh @rasmuspagh.net, the inventor of Cuckoo Hashing, and my PhD advisor, for becoming an ACM fellow! 🎉 di.ku.dk/english/news...
di.ku.dk
Professor Rasmus Pagh Receives International Recognition as ACM Fellow
Professor Rasmus Pagh has been named a 2024 Fellow of the Association for Computing Machinery (ACM), a prestigious honor awarded to leading researchers in computing. This recognition highlights his si...
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Thomas Ahle @thomasahle.bsky.social · 18/01/2025
Tensor Product Attention illustrated with Tensor Diagrams
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Thomas Ahle @thomasahle.bsky.social · 18/12/2024
Neat one-page proof of "Stirling's bound" (n/e)ⁿ√{2π n} ≤ n! ≤ (n/e)ⁿ(√{2π n}+1) Inspired by the discussion on mathoverflow.net/a/458011/5429. Just had to keep hitting it with logarithmic inequalities...
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Thomas Ahle @thomasahle.bsky.social · 13/12/2024
Yes please!
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Thomas Ahle @thomasahle.bsky.social · 12/12/2024
Poisson Probability Puzzle: Let X ~ Poisson(𝜇); Z = (X - 𝜇)/√𝜇; Y ~ Normal(0, 1). How close is E[|X|^k] is to E[|Y|^k]? Say we connect 𝜇 and k by 𝜇 = c k³, what is now the limit E[|X|^k]/E[|Y|^k] as k → ∞? This was harder to solve than expected, but the answer was surprisingly pretty 🌻
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Thomas Ahle @thomasahle.bsky.social · 11/12/2024
"Central Limit Theorem" for the Poisson Distribution
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Thomas Ahle @thomasahle.bsky.social · 03/12/2024
A while ago Twitter removed the option of embedding your timeline on your website. Luckily, with Bluesky, I'm now able to put it back on thomasahle.com. Good to be back.
thomasahle.com
Thomas Dybdahl Ahle
Thomas Dybdahl Ahle is a researcher in the theoretical foundations of machine learning and massive data, including similarity search, high dimensional geometry, kernel methods, sketching and derandomi...
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Thomas Ahle @thomasahle.bsky.social · 03/12/2024
Can you refer me to the openai forum?
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Thomas Ahle @thomasahle.bsky.social · 03/12/2024
For more information on history heuristics in chess, see www.chessprogramming.org/History_Heur...
chessprogramming.org
History Heuristic - Chessprogramming wiki
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Thomas Ahle @thomasahle.bsky.social · 03/12/2024
near future. Time will tell if they'll update the entire network, or a smaller LoRA or side network. Even chatbots like o1 could use TTT as an alternative to in context learning. 5/5
chessprogramming.org
History Heuristic - Chessprogramming wiki
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Thomas Ahle @thomasahle.bsky.social · 03/12/2024
while searching. If two subtrees are conceptually similar, it has to do all the work twice. Test Time Training fixes this! If AlphaZero updated its weights while searching, it could transfer learnings between the subtrees! I'm sure we'll start seeing a lot of TTT architectures in the near... 4/5
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Thomas Ahle @thomasahle.bsky.social · 03/12/2024
Obviously having a pretrained cnt[from][to] array wouldn't be helpful at all in chess, as moves may be good or bad entirely dependent on the position. But because the butterfly table is reset at every search, it encodes "local information". AlphaZero meanwhile doesn't learn anything while... 3/5
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Thomas Ahle @thomasahle.bsky.social · 03/12/2024
Chess engines like Stockfish will keep a so-called butterfly board, keeping track of how often a move was chosen in the search tree. _Independently of the position_. This is data is considered elsewhere in the search tree to decide how much time to spend considering the move. Why do this? 2/5
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Thomas Ahle @thomasahle.bsky.social · 03/12/2024
Test Time Training promises to finally unify learning and search. As always, chess is a good place to study such ideas: AlphaZero generalized and simplified most of the tricks in chess engines like Stockfish, but one category is missing: history heuristics... 1/5
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Thomas Ahle @thomasahle.bsky.social · 30/11/2024
Your o1 supports images?
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Thomas Ahle @thomasahle.bsky.social · 30/11/2024
Making a wiki style website is a good way to do this, while encouraging others from. The community to contribute and keep it updated. In fact, writing good Wikipedia articles for your field might be the best way to spread this knowledge.
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Thomas Ahle @thomasahle.bsky.social · 29/11/2024
Clever use of the KV-cache: Writing in the margins (arxiv.org/abs/2408.14906) at Neurips next week. By "taking notes" as you read, ypu reduce the complexity from N^3 (N tokens at N^2 cost) to N^3/3 (1+4+9+...+N^2).
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