Date/Time : 09 May 2025 14:00
Venue : S17 #04-04 (SR3)
Speaker : Emmanuel Bengio ,

In this talk I will share some recent progress on training GFlowNets and applying them to scientific problems, as well as speculate on the bigger picture; using GFNs to be good Bayesians. I will start the talk with a quick tutorial/refresher on GFlowNets to set the stage, and hope to finish with an open discussion of next steps and open problems. Interruptions, debates, and clarifications will be welcome throughout.

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Date/Time : 08 May 2025 11:00
Venue : S17 #04-04 (SR3)
Speaker : Tianqi Wang, Yale University

We construct an example of discrete, faithful and simple-stable representation of a closed hyperbolic surface groups into $SO^+(4,1)$ that is not convex-cocompact but deforms to a Fuchsian one continuously. Therefore the simple-stable characters forma domain of discontinuity for the mapping class group action on the character variety, who has a connected component strictly containing the convex-cocompact characters. We further talk about some general notions of ending currents in the study of discrete faithful representations into $SO^+(4,1)$.

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Date/Time : 30 Apr 2025 16:30
Venue : S17 #04-06 (SR1)
Speaker : Grigorios Chrysos , University of Wisconsin-Madison

Activation functions play a pivotal role in deep neural networks, enabling them to tackle complex tasks like image recognition. However, activation functions also introduce significant challenges for deep learning theory, network dynamics analysis, and properties such as interpretability and privacy preservation. In this talk, we revisit the necessity of activation functions across various scenarios. Specifically, we explore expressing network outputs through high-order interactions among input elements using multilinear algebra. This approach allows us to attain the necessary expressivity via these high-order interactions. Yet, the question remains: Is this expressivity alone sufficient for effective learning? Our recent research, presented at ICLR’24, unveils meticulously designed networks, which achieve strong performance even in demanding tasks, such as ImageNet image recognition.

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Date/Time : 30 Apr 2025 14:00
Venue : S17 #04-04 (SR3)
Speaker : Lin Shu, Peking University

There are a variety of interesting chaotic dynamical systems in negatively curved spaces. Entropies related to these systems are important quantities for understanding not only the complexities of their dynamics but also the complexities of the underlying spaces. This partially explains why the study of entropies in negatively curved spaces has always been a vibrant topic in dynamical systems. In this talk, we will give a biased introduction to this heavy topic by focusing on some natural diffusions (for instance, foliated Brownian motion) associated with the geodesic flow in a negatively curved space. We will mention some of our results (joint with F. Ledrappier) on stochastic entropies of these diffusions, in an attempt to use these quantities to characterize the geometry of the underlying space, to find connections between classical dynamical measures, and to understand the linear response theory for heat conduction, etc.

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Date/Time : 30 Apr 2025 15:00
Venue : S17 #04-05 (SR2)
Speaker : Liu Jinpeng, Tsinghua University

Nonlinear dynamics play a prominent role in scientific computation and artificial intelligence. Whereas previous quantum algorithms for general nonlinear equations have been severely limited due to the linearity of quantum mechanics, we gave the first efficient quantum algorithm for nonlinear differential equations with sufficiently strong dissipation. This is an exponential improvement over the best previous quantum algorithms, whose complexity is exponential in the evolution time. Furthermore, we design the first quantum algorithm for training classical sparse neural networks with end-to-end settings. We benchmark instances of ResNet with sparse pruning applied to Cifar-100 dataset and DPM-Solver for U-ViT applied to ImageNet-100 dataset, and we find that a quantum enhancement is possible at the early stage of learning. Our work shows that fault-tolerant quantum computing can contribute to the training and inference processes of most state-of-the-art large language models and diffusion models.

References:
[1]Efficient quantum algorithm for dissipative nonlinear differential equations. Proceedings of the National Academy of Science 118, 35 (2021).
[2]Towards provably efficient quantum algorithms for large-scale machine learning models. Nature Communications 15, 434 (2024)
[3]Towards efficient quantum algorithms for diffusion probability models. arXiv:2502.14252

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Date/Time : 30 Apr 2025 16:00
Venue : S17 #04-05 (SR2)
Speaker : Silu Yin, Hangzhou Normal University

In this talk, we investigate the ill-posedness of the non-strictly hyperbolic compressible ideal MHD (IMHD) system in two dimensions，which exhibits multiple propagation speeds. For scalar quasilinear wave equation, Smith-Tataru showed its local well-posedness in $H^{11/4+}(R^2)\times H^{7/4+}(R^2)$. Here, we construct a counterexample to the local existence of low-regularity solutions to the IMHD system in the borderline space $H^{7/4}(R^2)$. Our proof is based on a coalition of a carefully designed algebraic approach and Christodoulou’s geometric approach. We give a complete description of solutions’ dynamics up to the earliest singular event, when a shock forms. This talk is based on a joint work with Xinliang An and Haoyang Chen.

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Date/Time : 30 Apr 2025 15:15
Venue : S17 #04-04 (SR3)
Speaker : Fabrizio Bianchi, University of Pisa

For a rational map, the classical Mané-Manning formula relates the entropy, the Lyapunov exponent, and the Hausdorff dimension of any invariant measure. I will describe a generalisation of this formula valid for invariant measures for endomorphisms of P^k(C) in any dimension with strictly positive Lyapunov exponents. This is joint work with Y. M. He.

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Date/Time : 30 Apr 2025 14:00
Venue : S17 #04-05 (SR2)
Speaker : Zak Shumaylov,

In the last five years, neural solvers have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). Paralleling the central role of symmetries in classical numerical analysis – where they guide the development of stable and structure-preserving algorithms, these principles are now proving equally vital in machine learning. Incorporation of symmetries often leads to faster learning, better generalization, with solutions respecting fundamental physical laws. This talk explores how similar principles can be be integrated into modern neural PDE solvers, focusing on Lie point symmetries, generalized symmetries, and Hamiltonian structures. These approaches demonstrate how revisiting classical symmetry ideas leads to more robust, data-efficient, and physically consistent learning frameworks

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Date/Time : 29 Apr 2025 15:00
Venue : S17 #04-05 (SR2)
Speaker : Federico Pasqualotto, University of California San Diego

In this talk, I will first review the singularity formation problem in incompressible fluid dynamics, describing how particle transport poses the main challenge in constructing blow-up solutions for incompressible fluids. I will then outline a new mechanism that allows us to overcome the effects of particle transport, leveraging the instability seen in the classical Taylor–Couette experiment. Using this mechanism, we construct the first swirl-driven singularity for the incompressible Euler equations in R^3. This is joint work with Tarek Elgindi (Duke University).

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