hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final
((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3, has jacobian determinant -2, and sends (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0)
Mathematical Foundations of AI:
The Erlangen AI Hub Conference 2026
๐ Venue: Mathematical Institute, University of Oxford ๐ Date: 1โ3 September 2026
๏ฟฝ๏ฟฝ๏ฟฝ Poster submissions are now open
๐๏ธ Early Bird tickets are available for a limited time
๐ Register below
@UniofOxford
๐ข"The Erlangen AI Hub is an asset to @UniofOxford , to its academic, commercial and institutional collaborators; and to the UK, which must succeed within aย global, competitive, community." Great piece by Peter Grindrod, Professor at @OxUniMaths - ๐
Can LLMs reason in superposition? We introduce MUX, a method that turns text CoT into latent continuous reasoning.
Instead of one-hot vectors as in CoT, the model now learns to predict weighted averages of several one-hot vectors, that we call multiplexed tokens. These multiplexed tokens can be designed to be lossless, so by predicting them one is essentially doing multi-token prediction (MTP) in superposition.
MUX is the best latent reasoning method across 32 math settings spanning 1-8B LLaMA base models, reducing CoT length by 3-6x. Furthermore, it is able to perform parallel search, harnessing a core strength of superposed reasoning.
In collaboration with @alperen_gozeten , @mmbronstein, @ismaililkanc, and @jw9730.
1/๐งต
As AI advances rapidly, our understanding struggles to keep pace. Mathematics plays a critical role in closing this gap.
Erlangen AI Hub founding director @mmbronstein will speak at our annual conference Mathematical Foundations of AI on September 1-3. See link below:
Mathematical Foundations of AI:
The Erlangen AI Hub Conference 2026
๐ Venue: Mathematical Institute, University of Oxford ๐ Date: 1โ3 September 2026
๐ Poster submissions are now open
๐๏ธ Early Bird tickets are available for a limited time
๐ Register below
@UniofOxford
โMany of todayโs most transformative technologies rest on mathematical ideas that once seemed abstract or esoteric.โ
Why maths is pivotal for all AI technologies, and how future leadership will depend on investing in numerical disciplines.
Find out moreโฌ๏ธ
... We will next explore how the foundations of AI are unlocking the next generation of AI systems.
๐ Venue: Mathematical Institute, University of Oxford
๐ Date: 1โ3 September 2026
๐๏ธ Some Early Bird tickets still available
๏ฟฝ๏ฟฝ Register here: https://t.co/kcyqGpgP3L
Stronger mathematical foundations lead to more reliable AI and a new community is forming around these ideas, centred on the work of the Erlangen AI Hub, with partners at 8 universities across the UK. After a very successful first annual conference ...(1/2) @mmbronstein