Simons Foundation Lectures

The observation of 1D localization of ultra-cold atoms in a correlated disorder produced by laser speckle allowed us to observe an effective mobility edge in excellent agreement with theoretical calculations. Beyond qualitative observations, similar experiments in 3D and comparison to theory raise major problems. I will describe our experimental efforts for modifying our experiment to be able to release in the disorder atoms with well-defined energies. I will then present the first success with the improved experimental scheme. Firstly, we achieve direct measurements of the mobility edge with an unprecedented accuracy. Moreover, when releasing atoms with a narrow energy distribution below the mobility edge, in the localized regime, we observe patterns that we are tempted to interpret as localized wave-functions. This opens the perspective to directly test the landscape theoretical description, when we can engineer precisely our disorder, a goal that seems within our reach.Uploaded 28-02-25For more information, please visit: https://www.simonsfoundation.org/event/simons-collaboration-on-the-localization-of-waves-annual-meeting-2025/

Over the last decade, tremendous advances in sequencing technology have allowed scientists to study the full spectrum of human genetic variation and its relationship to disorders associated with mental health. In this lecture, Evan Eichler will present his laboratory’s recent work studying specific forms of both inherited and sporadic mutations to identify new genes underlying autism and developmental delay. He will also discuss promising paths forward for understanding more complex genetic forms of these disorders. More details: https://www.simonsfoundation.org/event/rare-variants-and-the-genetics-of-autism/Uploaded 05-11-20

Despite the fact that experimental neural scaling laws have substantially guided empirical progress in large-scale machine learning, no existing theory can quantitatively predict the exponents of these important laws for any modern LLM trained on natural languages. It is also unclear whether they can be beaten by training with other objectives. Matthieu Wyart will review the efforts of the collaboration in studying this phenomenon, including the first such theory in the case of data-limited scaling laws. Wyart will then introduce synthetic languages displaying a hidden hierarchy (a central notion in both linguistics and computer vision), and discuss how these languages are learnt by deep, but not shallow, nets. Scaling laws in these synthetic languages follow from the same principle as in natural languages when trained at the token level, but these languages can be learnt much more efficiently by machines predicting in an abstract space — justifying the success of joint embedding predictive architectures (JEPA) and other machines learning from their own latents.Uploaded 06-11-26For more information please visit: https://www.simonsfoundation.org/events/simons-collaboration-on-the-physics-of-learning-and-neural-computation-annual-meeting-2026/

How do modern neural networks evolve from randomly initialized weights toward a useful representation of the data? How does this proceed layerwise, and what role does the structure of attention play in the case of language models?Uploaded 06-11-26Collaboration progress on this central problem draws from diverse methods including dynamical mean field theory, spectral methods, tractable toy models, symmetry analysis, and stochastic dynamics. Eva Silverstein will review several inter-related results exhibiting explicitly how interpretable representations emerge. These encompass multiple stages of learning: the escape from an initially uninformative regime, the emergence of structured directions during training, and, in simplified hierarchical models, the layer-by-layer construction of increasingly useful features. The structured directions that emerge during the learning dynamics include novel ones introduced via symmetry breaking in attention, enabling models to amplify or suppress meaningful token and representation classes. For more information please visit: https://www.simonsfoundation.org/events/simons-collaboration-on-the-physics-of-learning-and-neural-computation-annual-meeting-2026/

Virtual Fibring of Manifolds and GroupsOne can learn a lot about a compact manifold if one can show that it fibres over the circle - in essence, this allows us to view a static n-dimensional manifold as a manifold of dimension n-1 that evolves in time.Being fibred (over the circle) is a relatively rare property. It is much more common to be virtually fibred, that is, to admit a finite cover that is fibred. For example, it was the content of a conjecture of William Thurston, now two theorems by Ian Agol and Dani Wise, that all finite-volume hyperbolic 3-manifolds are virtually fibred; in fact, this property is extremely common among irreducible 3-manifolds.The situation is less clear in higher dimensions. On the obstruction side, we know that virtually fibred manifolds must have vanishing Euler characteristic. This immediately shows that compact hyperbolic manifolds in even dimensions will not be virtually fibred. A more involved obstruction comes from L2-homology: virtually fibred manifolds must be L2-acyclic.The motivation behind the research I will present lies in trying to find situations in which the vanishing of L2-homology is is not only necessary, but also sufficient for virtual fibring. It turns our that a lot more can be said if we replace aspherical manifolds by their homological cousins: Poincare duality groups. Concretely, if G is an n-dimensional Poincare-duality group over the rationals, and if G satisfies the RFRS property, then G is L2-acyclic if and only if there is a finite-index subgroup G0 of G and an epimorphism from G0 onto the integers such that its kernel is a Poincare-duality group over the rationals of dimension n-1. (This last theorem is joint with Sam Fisher and Giovanni Italiano.)The RFRS property was introduced in Agol's work on Thurston's conjecture. A countable group is RFRS if and only if it is residually {virtually abelian and poly-Z}. All compact special groups in the sense of Haglund-Wise satisfy this property, so there is a ready supply of RFRS groups, also among fundamental groups of hyperbolic manifolds in high dimensions.Uploaded 05-10-26