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Given a dynamical system which admits chaos, its possible equilibria are studied through the collection of its invariant measures (i.e the probability of an event does not change under time-evolution). This collection may be very large, and we often wish to single out measures of importance. In particular, physical measures are a sought-after object, as they describe an observable equilibrium. In this talk we will define what are physical measures (in a broad sense, including SRB measure), and list a few recent results and open questions regarding their existence for smooth dynamical systems. In particular, finding “testable” conditions for the existence of physical measures is an on-going and active field of research.

Generative models, such as ChatGPT and DALL-E, are used by millions of people daily for tasks ranging from programming and content creation to resume filtering. These models often create the impression of being “intelligent,” which can incentivize careless use in critical applications. While generative models are empowering, they appear to be black boxes, and their misuse can result in harmful or unlawful outcomes.

In this talk, I will present algorithms and tools for dissecting and analyzing generative models using holistic, causal, and data-centric approaches.

By applying these methods to state-of-the-art models, we can foster trust in these technologies by uncovering human-interpretable concepts that underpin their behavior, scrutinizing their extensive training data, and evaluating their learning processes.

Finally, I will reflect on how generative models have transformed the field of AI and discuss the challenges that remain in ensuring their responsible development and use.

Nanophotonics is at the forefront of research and development in scalable quantum technologies,ranging from quantum sensing to quantum computing. Traditionally, inherently weak photon-photonand photon-atom interactions in dielectric materials pose significant challenges to fully exploiting thepotential of these platforms. However, recent advances in the fabrication of nonlinear microresonatorswith nanometric features have allowed for the enhancement of all-optical interactions,necessitating new approaches to generating, controlling, and measuring quantum light.In this seminar, I will delve into unexplored regimes at the intersection of nonlinear and quantumoptics. I will begin by showcasing our latest advancements in developing integrated microresonatorsin thin-film 4H-Silicon Carbide. This innovation enables nonlinear photonics, quantum optics, andcollective quantum emitter excitations on the same platform. Following this, I will present ourexperimental demonstration of quadrature lattices of the quantum vacuum. This work shows howpulses that spontaneously emerge in microresonators can generate lattice dynamics of the quantumvacuum and how we can exert control over these dynamics.I will then discuss the broader implications of our findings, including enhanced interactions withquantum emitters, and ultrafast nonlinear quantum nanophotonics, which enable nonlinearinteractions at the single photon level. These outcomes pave the way toward new regimes of lightmatterinteractions that are enabled on scalable photonic microchips, with transformativeimplications for fundamental physics and quantum applications.

Machine Learning (ML) systems are increasingly integrated into society, but challenges arise when human incentives and expectations are overlooked. In this talk, I will present frameworks for aligning ML with society, focusing on strategic classification and personalization in decision making.
Strategic classification models scenarios where individuals, aware of the deployed classifier, manipulate their observable attributes to achieve favorable outcomes. For example, individuals might apply for additional credit cards to boost their credit score just so they can qualify for a loan, even though it doesn’t impact their ability to repay the loan. The learning goal is to find a classifier robust against strategic manipulations. I will answer a fundamental question: Does learnability imply strategic learnability?

In addition, I will discuss multi-objective Markov Decision Processes (MDPs), which involve multiple, potentially conflicting objectives. In classic reinforcement learning and MDPs, policies are evaluated with scalar reward functions, implying that every optimal policy is optimal for all users. However, real-world scenarios involve multiple, sometimes conflicting objectives, necessitating personalized solutions. I will present an MDP framework that accommodates different user preferences over objectives, where preferences are learned via policy comparisons, and the goal is to efficiently compute a near-optimal policy for a given user.

Suppose a finite group satisfies the following property: If you take two random elements, then with probability bigger than 5/8 they commute. Then this group is commutative. Starting from this well-known result, it is natural to ask: Do similar results hold for other laws (p-groups, nilpotent groups...)? Are there analogous results for infinite groups? Are there phenomena specific to the infinite setup? We will survey known and new results in this area. New results are joint with Gideon Amir, Maria Gerasimova and Gady Kozma.

This talk will explore advances in 3D scene reconstruction, focusing on approaches to estimate camera poses and scene structures in challenging multiview and dynamic content scenarios. First, I will outline foundational aspects of my earlier work, where we characterized the algebraic structure of fundamental and essential matrices in multiview settings and developed deep learning methods for joint recovery of camera parameters and sparse 3D scene structures. The main part of the talk introduces TracksTo4D (NeurIPS 2024), a novel, efficient method for reconstructing dynamic 3D structures and camera motion from casual videos. TracksTo4D leverages a dedicated encoder, trained in an unsupervised way on a dataset of casual videos, that uses 2D point tracks as input to infer dynamic 3D structures and camera motion. Our architecture takes into account symmetries in the problem, enforces the reconstruction to be of low rank, and models both static and dynamic scene components. Our model demonstrates strong generalization to unseen videos from new categories, achieving accurate 3D reconstruction and camera localization through a single feed-forward pass while drastically reducing running times.

Bio:

Yoni Kasten is a senior research scientist at NVIDIA Research in Tel Aviv, on Prof. Gal Chechik’s team. His research in 3D computer vision focuses on algebraic characterizations of multi-camera systems and deep neural models for surface reconstruction, dynamic scene modeling, and 4D scene reconstruction. Yoni earned his PhD from the Weizmann Institute, where his work on structure from motion estimation using algebraic characterizations, supervised by Prof. Ronen Basri, received the John F. Kennedy Prize for Outstanding Doctoral Research. He also completed his M.Sc. in Computer Science at the Hebrew University of Jerusalem under the supervision of Prof. Shmuel Peleg and Prof. Michael Werman.

Mechanical force is a critical feature for most physical processes, and remote measure of mechanical signals with high force sensitivity and spatial resolution is crucial for progress in fields as diverse as robotics, biophysics, civil engineering, and medicine. Existing nanoscale remote force sensors, however, are very limited in the dynamic range of forces they can detect, and are rarely compatible with subsurface operation, restricting sensor applicability [1]. In this talk, I will describe how we leverage the extreme optical nonlinearity offered by photon-avalanche [2], and its susceptibility to steep change due to minute changes in the environment – to create nanoscale force sensors that can be addressed remotely by continuous-wave, deeply-penetrating, infrared light, and can detect picoNewton to microNewton forces with a dynamic range spanning more than four orders of magnitude [3]. Using atomic force microscopy coupled with single-nanoparticle optical spectroscopy, we characterize the mechano-optics of different Tm3+-doped avalanching upconverting nanoparticles on a single particle level, to rationally design force sensors with different modalities of force-dependent optical readout, including mechanobrightening and mechanochromism. By manipulating the interionic distances and hence energy transfer pathways within the nanosensors by application of force, we demonstrate exceptional mechanical sensitivity coupled with high single-particle brightness, over multiple scales of force. The adaptability of these nanoscale optical force sensors, along with their multiscale sensing capability, enable operation in the dynamic and versatile environments present in diverse, real-world structures spanning biological organisms to nanoelectromechanical systems.

Particle systems that can be described macroscopically via free boundary problems (FBP) include the $N$-branching Brownian motion (branching Brownian particles on the line with removal of the leftmost particle upon each branching), and the Atlas model (Brownian particles on the line where the leftmost particle is equipped with a positive drift). The regularity of the free boundary plays a crucial role in proving the particle system -- FBP relation, but does not hold in some natural generalizations of these models. I will describe a weak FBP formulation where control over free boundary regularity is not required in order to achieve this relation in the two cases above. I will also describe an analogous weak formulation of a ``free obstacle’' problem aimed at a branching Brownian motion with removals occurring at the most densely populated areas.

This is partly based on joint works with Amarjit Budhiraja and with Leonid Mytnik and Gershon Wolansky.

The ESCRT membrane remodeling complex, found across all life forms, exhibits a versatility that transcends evolutionary boundaries. From orchestrating the constriction of micron-wide tubes in cell division to facilitating the budding of 50 nm vesicles in receptor degradation, ESCRTs perform diverse functions in animal cells. In recent years, ESCRT homologs were identified in prokaryotes, highlighting a role for this protein machinery in the ancient world.  We seek to understand the mechanistic principles underlying the functional diversity of the ESCRT system across evolution. Specifically, we focus on understanding how the ESCRT complex orchestrate in cells to constrict and cut membranes in eukaryotes, focusing on its role in cell division, and in prokaryotes, focusing on the recently discovered Asgard archaea. By combining high-resolution imaging with biochemical and structural studies we aim to unlock the secrets of this fundamental membrane remodeling machinery and its potential role in evolution.