Giangiacomo Mercatali (Haute Ecole de Gestion de Genève)
Constraining Generative Models: Conditioning, Structure, and Physics in Diffusion and Flows abstract
Abstract:
Diffusion and flow-matching models have become the default tools for generative modeling,but in scientific and structured domains their value depends on one ability: to generatenot just plausible samples, but samples that satisfy prescribed constraints and guidancesignals — known physics, structure, and target properties. Such requirements come inseveral distinct types, and a generative model has to be designed in a specific way toaccommodate each. This talk frames a line of work around that question — how do we builddiffusion and flow models that respect different kinds of constraints? — and presents onedesign per type.The first type is conditioning on target properties: a score-based diffusion withco-evolving processes that exchange information through loop guidance, steering generationtoward desired attributes. The second is structural: a continuous-time flow constrained bya causal dependency graph, learned jointly with the dynamics of interacting time series.The third is partial physics: when the governing equations are known only in part, agrey-box flow-matching model embeds the available physics while a structured latent absorbsthe unknown parameters and stochasticity. The fourth is hard physical constraints —conservation laws, boundary conditions — enforced at sampling time by projecting generationonto the constraint manifold.
14:00 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room F 26.5
Avi Wigderson (IAS, Princeton)
Optimization, Complexity and Math (or, can we prove P!=NP by gradient descent?) abstract
Abstract:
This talk aims to summarize a project I was involved in during the past decade, with the hope of explaining our most complete understanding so far, as well as challenges and open problems. The main messages of this project are summarized below; I plan to describe, through examples, many of the concepts they refer to, and the evolution of ideas leading to them. No special background is assumed. We extend the most basic tools of convex optimization in Euclidean space to a far more general setting of Riemannian manifolds that arise from the symmetries of noncommutative groups. We develop first-order and second-order algorithms, and analyze their performance in general. Invariant theory, which studies such group actions, plays an essential role in this development. The focus on symmetries exposes old and reveals new relations between the application problems below. These algorithms give exponential (or better) improvements in run-time for solving algorithmic many problems across CS, Math and Physics. In particular, these include problems in algebra (e.g. testing rational identities in non-commutative variables), in analysis (testing the feasibility and tightness of Brascamp-Lieb inequalities), in quantum information theory (to the quantum marginals problem), in algebraic geometry (to computing Kronecker coefficients), in computational complexity (to derandomizing new special cases of the PIT problem) and in optimization (to testing membership in large, implicitly described polytopes). Based on joint works with Zeyuan Allen-Zhu, Peter Burgisser, Cole Franks, Ankit Garg, Leonid Gurvits, Pavel Hrubes, Yuanzhi Li, Visu Makam, Rafael Oliveira and Michael Walter.REGISTER HERE : Lecture Prof. Avi Wigderson (IAS, Princeton) – Fill in form :forms.cloud.microsoft/Pages/ResponsePage.aspx?id=alXC9vvEsUqix54iDfEcQ-g_-oaFq4NMizPr-UXNEiNURExDNE9ORUhLOEs3QVc4U0U3R0hHVkg2Ri4u
15:30 • EPF Lausanne, BCH 2201