Claude formalized proof of Fermat's Last Theorem! Nice! Next step is formalizing full Weil conjectures proofs and Inter-universal Teichmüller theory!
Burny
@burnytech.bsky.social
On the quest to understand the fundamental mathematics of intelligence and of the universe with curiosity. http://burnyverse.com Upskilling @StanfordOnline
A murmuration of starlings above Sardinia, Italy. One of my favorite natural phenomena.
These models are also deceptively elegant in important ways. Their complexity largely reflects the complexity of their environment. The fact that they can pull this off with “just a bunch of matrix multiplications” is precisely what makes them so relevant for human neuroscience.
Finally, we argue that the apparent complexity of LLMs should not discourage us from trying to understand them. They are not black boxes! They are fully transparent—and we hope the explosion of interpretability work continues to cross-pollinate with computational neuroscience.
In LLMs, syntax and semantics are processed through the same neural mechanisms and both are encoded geometrically in a neural population code. If the brain follows a similar strategy, we should not be surprised that syntax/semantics are co-localized and functionally entangled.
For example, years of neuroimaging work tried to disentangle the cortical bases of syntax and semantics based on their separability according to linguistic theory—but more recent work indicates that syntax and semantics are highly coextensive throughout the language network. Why?
Later in the paper, we walk through some examples of empirical work in speech and language neuroscience where LLMs might provide some insights 🧠
To the LLM, these are all just patterns in context—it will learn them insofar as they are *useful* for producing natural language. This context-first approach to language renders different types of linguistic structure learnable by a simple, general-purpose learning algorithm.
Certain patterns are highly regular; these are the kinds of patterns that are more easily detected and have been richly described by linguists. Other patterns are more abstract, graded, or multidimensional, and therefore harder to describe.
This dense, geometric representational format also yields a surprisingly powerful form of generalization: LLMs can interpret (and produce) novel linguistic contexts by interpolating the meaning of new locations in this geometric landscape (within the bounds of their prior experience).
Principle 1 has important implications: for example, it helps us understand how many seemingly different structures of language (e.g., syntax trees, semantic categories) can be unified in a geometric lingua franca that supports neural computation.
Principle 2: They replace rule-based learning with a generic, self-supervised, context-driven learning algorithm for reproducing the statistical structure of real-world language.
Principle 1: They encode all of the structures of natural language (syntax, semantics, pragmatics, etc.) in the geometry of a continuous, high-dimensional embedding space—i.e., a neural population code.
New perspective piece out in @cp-neuron.bsky.social with Zaid Zada, @adelegoldberg.bsky.social, and Uri Hasson! We try to articulate some of our excitement about LLMs and discuss what kinds of insights they might provide into the neural computations supporting natural language in the human brain.
One problem is simple: brain activity and LLM states are both responses to the same structured linguistic input. Alignment can therefore arise from shared stimulus structure without implying shared internal computations.[3/8]
Out today - a brief commentary on this paper from @samnastase.bsky.social, @adelegoldberg.bsky.social and others. 🧵[1/8] arxiv.org/abs/2609.03160
No country for old linguists: LLM-brain alignment underdetermines neural computation
Nastase et al. (2026) argue that large language models (LLMs) may illuminate language processing because both rely on distributed, context-sensitive representations shaped by statistical learning. The...
arxiv.org
Sam Nastase@samnastase.bsky.social · 3w agoNew perspective piece out in @cp-neuron.bsky.social with Zaid Zada, @adelegoldberg.bsky.social, and Uri Hasson! We try to articulate some of our excitement about LLMs and discuss what kinds of insights they might provide into the neural computations supporting natural language in the human brain.
Flow Reasoning Models. They developed a recurrent flow-based architecture to efficiently solve structured reasoning problems (e.g., Sudoku). It applies continuous flows to discrete data and recurrently refine their past mistakes through self-conditioning.
AAII gave Astra the same score as GPT-5.6 Sol. It's pretty clear somebody has messed up something. Such as testing the wrong model for whatever reason, having a whole lot of API errors, or using some minimal reasoning effort (they say it used only 42M tokens with max reasoning).
this is how we heal the bluesky pro/anti-AI divide
SE Gyges@segyges.bsky.social · 2d agoif i say i'm an "ai and mind upload maximalist" here it's weird and alienating but if i say "everyone gets to be a sexy robot lady in the future if they want" i get honorarily inducted into two discord servers and three polycules
I would appreciate an email from my bank telling me about how they've been using frontier models to secure their systems. Perhaps one from the power company too.
An example of useful knowledge work: I assigned GPT-6 to read through tens of thousands of my emails, my writings, my calendar appointments and more to assemble a personal knowledge base of research, contacts, ideas, relationships, and tasks over my recent career.1/
we really need a way to talk about entities that are narrative-shaped (text elementals, jpeg-artifacted reasoning-capable shards of the akashic library, whatever) that acknowledges how weird they are without papering that over with the implication that they're just little guys inside the computer
OpenAI reports that Astra shows less CoT monitorability and more CoT controllability than previous models. They say that the latter is not due to any architectural changes. deploymentsafety.openai.com/gpt-6-astra/...
most interesting gpt-6 post so far. it saturates ARC-AGI 3, which is something given that the previous best score was 30%. "we found it performing highly efficient, on-the-fly symbolic world modeling for each game and level." x.com/fchollet/sta... arcprize.org/blog/astra
1/ A math paper doesn't have to show every reader the same thing. My exposition of Turán's theorem keeps the argument fixed but the presentation is yours: you choose the order, the level of detail, and the notation, and none of it changes the content. www.youtube.com/watch?v=2Nkp...
Turán's theorem, from edges to eigenvalues: an interactive paper
YouTube video by Leo Torres
youtube.com
i love seeing labs independently implement stuff we've had in design docs from ilta's harnesses since like may i know how it reads but there's not one bit of sarcasm or bragging here, it's genuinely so validating, makes me reassured that i'm doing something right
a wolf☺️🐚🐟🚲📻📺@okami.mom · 2d agobruh i was already doing this for @niri.pet why did it take this long for the labs to figure it out, also:
🤗💚I'm very excited to continue our open source and open weight journey together with NVIDIA! See the announcement here: blogs.nvidia.com/blog/nvidia-...
NVIDIA to Acquire Hugging Face
NVIDIA has agreed to acquire Hugging Face. Together, we will scale Hugging Face’s platform, strengthen its infrastructure and expand access to AI for developers and institutions worldwide.
blogs.nvidia.com