Thomas Ahle
@thomasahle.bsky.social
Head of AI @ NormalComputing. Tweets on Math, AI, Chess, Probability, ML, Algorithms and Randomness. Author of tensorcookbook.com
Added a new symbols menu - let me know if I missed any of your favourite LaTeX commands!
November 11, 2025 at 12:02 AM
Added a new symbols menu - let me know if I missed any of your favourite LaTeX commands!
I needed an easy way to make high resolution equations to post on Bluesky, so I made this: thomasahle.com/latex2png
LaTeX to Image
Effortlessly convert LaTeX math equations into high-quality images (PNG, JPEG, SVG).
thomasahle.com
March 16, 2025 at 10:15 AM
I needed an easy way to make high resolution equations to post on Bluesky, so I made this: thomasahle.com/latex2png
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.
Turns out it generalizes to _every distribution_ using cumulant tensors!
That's higher order variance, skewness, kurtosis, etc.
February 19, 2025 at 9:15 PM
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.
Turns out it generalizes to _every distribution_ using cumulant tensors!
That's higher order variance, skewness, kurtosis, etc.
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.
Hopefully it can also be a way to help people become familiar with tensor diagrams.
February 18, 2025 at 8:01 AM
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.
Hopefully it can also be a way to help people become familiar with tensor diagrams.
Now live in a new Functions chapter in tensorcookbook.com
February 9, 2025 at 11:24 AM
Now live in a new Functions chapter in tensorcookbook.com
Some sketches for the next chapter
February 6, 2025 at 10:28 AM
Some sketches for the next chapter
I added code execution to tensorcookbook.com so you can try tensorgrad's automatic tensor algebra without installing anything.
February 4, 2025 at 3:58 PM
I added code execution to tensorcookbook.com so you can try tensorgrad's automatic tensor algebra without installing anything.
🎉 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/english/news...
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...
di.ku.dk
January 28, 2025 at 4:35 PM
🎉 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/english/news...
Tensor Product Attention illustrated with Tensor Diagrams
January 18, 2025 at 2:00 PM
Tensor Product Attention illustrated with Tensor Diagrams
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...
(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...
December 18, 2024 at 12:37 PM
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...
(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...
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 🌻
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 🌻
December 12, 2024 at 11:41 PM
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 🌻
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 🌻
"Central Limit Theorem" for the Poisson Distribution
December 11, 2024 at 10:45 AM
"Central Limit Theorem" for the Poisson Distribution
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.
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...
thomasahle.com
December 3, 2024 at 8:54 AM
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.
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
AlphaZero generalized and simplified most of the tricks in chess engines like Stockfish, but one category is missing: history heuristics...
1/5
Test-Time Training Boosts AI Reasoning
Test-Time Training (TTT) enhances AI models' abstract reasoning, achieving 53% accuracy on ARC—a 25% improvement over prior methods.
http://ekinakyurek.github.io/papers/ttt.pdf
#AI #AbstractReasoning #Innovation
Test-Time Training (TTT) enhances AI models' abstract reasoning, achieving 53% accuracy on ARC—a 25% improvement over prior methods.
http://ekinakyurek.github.io/papers/ttt.pdf
#AI #AbstractReasoning #Innovation
December 3, 2024 at 5:42 AM
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
AlphaZero generalized and simplified most of the tricks in chess engines like Stockfish, but one category is missing: history heuristics...
1/5
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).
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).
November 29, 2024 at 4:27 PM
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).
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).