RT @latzplacian: Andrea Bertozzi, Nadejda Drenska, Matthew Thorpe, and I have guest edited a theme issue on “Partial differential equations….

RT @LucaAmb: 1/4) I am very happy to share our latest work on the information theory of generative diffusion:. "Entropic Time Schedulers fo….

RT @KempnerInst: 4/26 at 3pm:. 'Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groups'. Zakhar Shumaylov ·….

RT @pfau: Imagine if, in the 1890s, Eastman Kodak had created an entire research team devoted to figuring out if film cameras actually did….

If you are coming to #ICLR2025 come say hello. We will be presenting on how to turn Neural Operators equivariant even when all you know is the lie algebra!. Generally happy to chat all things #geometry and #optimization in deep learning!. 🔗

RT @yaringal: Hot take: I think we just demonstrated the first AI agent computer worm 🤔. When an agent sees a trigger image it's instructed….

Check out the full works on this and learn how we construct symplectic networks in the preprints! This was the work with the team @CamImaging: @dademurari, @FerdiaSherry, @caromitreka and @pasullet! . ➡️➡️

If you were to look at the energy under the learned flow, the dissipation closely mimics the kind of error accumulation you expect to get from classical symplectic integrators. Theoretically, however, we were only able to show linear growth - so showing why remains open!

But what if you were approximating the flow using a neural network? .Well you can do a sorta a-posteriori analysis - if you know the Hamiltonian, you find the errors and make sure they aren’t too big during training! Here’s what a good and a bad approximate Hamiltonian look like.

For example, for symplectic Euler on a separable Hamiltonian, this gives the shadow Hamiltonian which is close to the true one for a small enough step size. Or generally preserves the *shadow* Hamiltonian.

In some sense this is the basis for constructing classical symplectic integrators. This lets you do backward error analysis to show conservation of a *shadow* Hamiltonian.

I recently learned about a very cool fact: if you compose flows of two Hamiltonians, this is also Hamiltonian. What is more - you can write down the exact Hamiltonian!

RT @CamImaging: Fantastic talk from @Zakobian at today's CIA seminar! 🚀 He shared insightful work on the Future of Synthetic Data, coverin….

RT @dohmatobelvis: "Much of the point of a model like o1 is not to deploy it, but to generate training data for the next model. Every probl….

RT @docmilanfar: overcoming scarcity with synthetic data

RT @MLStreetTalk: A few months ago @iliaishacked wrote a paper in @Nature "AI models collapse when trained on recursively generated data".….

RT @yaringal: I'm looking for PhD applicants who have expertise in Gaussian processes and/or Transformers for an exciting PhD project. If t….

RT @erturklab: Our new study shows that SARS-CoV-2 spike protein accumulates & persists in the body for years after infection, especially i….

RT @mweber_PU: A postdoc position is available in my group at Harvard @hseas to perform research at the intersection of Geometry & Machine….

RT @tarantulae: New article: "The geometry of data: the missing metric tensor and the Stein score" (. I show how yo….