Luca Ambrogioni

1/2) I am very happy to finally share something I have been working on and off for the past year: "The Information Dynamics of Generative Diffusion" This paper connects the entropy production, divergence of vector fields and spontaneous symmetry breaking in a unified framework

Mathematical Foundations of Deep Learning arxiv.org/abs/2603.18387

Someone once asked me what my single favorite physics textbook was. Hard question really - as I only rarely go back to my undergrad textbooks, so there is some distance that makes the evaluation hard. But if I had to pick just one, it would be this. Any other suggestions?

@VergaraLautaro I make it clear in the acknowledgement section

How many researchers working and producing papers with AI are telling the audience its use?

Update: #Aletheia has now powered 8 math research papers! 📈 Our most recent success, “The Simplicity of the Hodge Bundle,” was solved fully autonomously. It’s at Level 2 “Publishable research” per our categorization. More in thread!

@CodveAi @mandylu It isn't

@mandylu honestly the harder question is "when does it start mattering?" - if the output is indistinguishable, the origin becomes philosophical

remember when everything was human-generated?

@aryehazan That's how you win a war nowadays

highest level defector gets to stay alive and maybe rule as an added bonus

@RoyEyono @EliSennesh Pretty cool

Why you may ask? It turns out that layer normalization actually implicitly normalizes back-propagated error signals "under the hood" !

How do neural circuits in the brain implement normalization? 🧠 In our new paper, we show that just normalizing sensory input isn't enough. Crucially, we must also normalize the error signals! 🧵👇 Paper: arxiv.org/abs/2603.17676

@WKCosmo The good thing is that this kind of attitude is probably strongly negatively correlated with Darwinian fitness

Something we really need to get away from is flattening things down to the point where there is zero distinction made between Cesar Chavez being a serial child molester and a 26-year-old assistant professor going on a date with an undergrad.

@JCJesseLai @mittu1204 @StefanoErmon @MoleiTaoMath Thank you for casting some clarity on this. Like with flow matching, people often rush to the conclusion that new approaches are more conceptually novel than they actually are.

[1/D] 🤔 What are drifting models really connected to? 📢 Our new paper, A Unified View of Drifting and Score-Based Models, shows that the bridge to score-based models is clear and precise (w/ team and @mittu1204, @StefanoErmon, @MoleiTaoMath)! ✍️ Main takeaway: drifting is more closely connected to score-based (diffusion) modeling than it may first appear! 🔗 arxiv.org/abs/2603.07514 🎯 Here’s why: Drifting’s mean-shift moves a sample toward the kernel-weighted average of nearby samples. Score function points toward regions of higher density. So both describe local directions that push samples toward where data is denser. We show that this link is exact for Gaussian kernels (Section 4.1): 📌drifting’s mean-shift = a rescaled score-matching field between the Gaussian-smoothed data and model distributions — the vector field underlying score matching (Tweedie!). 📌This also clarifies the bridge to Distribution Matching Distillation (DMD): both use score-based transport directions, but only differ in how the score is realized—drifting does so nonparametrically through kernel neighborhoods, whereas DMD relies on a pretrained diffusion teacher. 🤔 So what happens for the default Laplace kernel used in drifting models? Let’s look below 👇

@norpadon In general I think that the importance of belif in religion is overestimated

@LucaAmb Imo morality is orthogonal to belief. You can believe in Jesus but reject him

Trying to get a basic grasp of Christianity (e.g. God is postulated to be stateless, but Jesus was fully God and yet he changed states, wtf), and it feels like medieval theologists were just trying to do reasonable philosophy but were sandbagged by the silly book canon

If you want to make AI really stupid, make it only work on fully formalize systems If you want to make it actually smart, make it write a good book

Ai is the crystallization of thought, it does not work without a seed

@norpadon I do because I do not think that this can be fully explained rationally and the paradox is unavoidable when touching the topic of God seriously I think that the rational God becomes sterile without its connection with the world.

@LucaAmb I am aware of this explanation, but I don’t find it satisfactory. I feel like it just hides the issue under the rug of Trinity

@TradeTexasBig but gates was sharing his own money, we are talking about shareholder money here. In any case you are completely right that he didn't fail fast enough, honestly this all debacle was obvious since the beginning

@LucaAmb I think u r missing the multi layered thinking my tweet doesn't capture. No I dont expect him to deploy his capital now that he has written off. What I said is he didnt fail fast enough and when all done , he could ve shared this 80 bill like gates

The issue is its not misallocated capital ..issue is zuck is incapable of allocating capital for greater good. The worst successful founder in history

@TradeTexasBig It was a very bad buseness decision, but do you expect a CEO to donate 80bills to cancer research? Thst's not how capitalism work

@LucaAmb That refers to 80 bill he could have just given to a good cause vs metaverse , a what if.

'Finite Neural Networks as Mixtures of Gaussian Processes: From Provable Error Bounds to Prior Selection', by Steven Adams, Andrea Patanè, Morteza Lahijanian, Luca Laurenti. jmlr.org/papers/v27/24-… #gaussian #approximation #approximate

It's time to bring 3D meshes into modern machine learning properly! 🛸 Our work solves the non-differentiability of the Exp map on meshes, enabling gradients to flow directly through geodesics. It’s differentiable, GPU-fast, and fully parallelised. circle-group.github.io/research/DSG