Events

A common theme in mathematics is that limits of finite objects are well behaved. This allows one to prove many theorems about finitely approximable objects, while leaving the general case open --- examples for this are Gottschalk's conjecture, Kaplansky's direct finiteness conjecture, and many more. When the topology of the space is somewhat coarse, it becomes very hard to decide whether every object is approximable by finite ones, or whether there exist non-approximable objects. Some of the more famous problems in various fields of mathematics can be framed this way; this includes Connes' embedding problem (CEP) in functional analysis, the Aldous--Lyons conjecture in probability theory, the soficity problem of Gromov--Weiss in group theory, and more. 

In 2019, Ji--Natarajan--Vidick--Wright--Yuen resolved CEP in the negative, namely, they showed that there are non-approximable characters of the free group. The amazing thing about their result is that it is deduced from complexity theory, and specifically from undecidability in certain (quantum) interactive proof systems. Inspired by their work, we suggest a novel interactive proof system which is related to the Aldous--Lyons conjecture in the following way: If the Aldous--Lyons conjecture was true, then every language in this interactive proof system is decidable. A key concept we introduce for this purpose is that of a Subgroup Test, which is our analogue of a Non-local Game. By providing a reduction from the Halting Problem to this new proof system, we refute the Aldous-Lyons conjecture.

In this first talk we introduce the main concepts, motivate the conjecture and give a high level description of the proof strategy. No special mathematical background will be assumed.

This talk is based on a joint work with Lewis Bowen, Alex Lubotzky and Thomas vidick.

A common theme in mathematics is that limits of finite objects are well behaved. This allows one to prove many theorems about finitely approximable objects, while leaving the general case open — examples for this are Gottschalk's conjecture, Kaplansky's direct finiteness conjecture, and many more. When the topology of the space is somewhat coarse, it becomes very hard to decide whether every object is approximable by finite ones, or whether there exist non-approximable objects. Some of the more famous problems in various fields of mathematics can be framed this way; this includes Connes' embedding problem (CEP) in functional analysis, the Aldous–Lyons conjecture in probability theory, the soficity problem of Gromov–Weiss in group theory, and more. 

In 2019, Ji–Natarajan–Vidick–Wright–Yuen resolved CEP in the negative, namely, they showed that there are non-approximable characters of the free group. The amazing thing about their result is that it is deduced from complexity theory, and specifically from undecidability in certain (quantum) interactive proof systems. Inspired by their work, we suggest a novel interactive proof system which is related to the Aldous--Lyons conjecture in the following way: If the Aldous–Lyons conjecture was true, then every language in this interactive proof system is decidable. A key concept we introduce for this purpose is that of a Subgroup Test, which is our analogue of a Non-local Game. By providing a reduction from the Halting Problem to this new proof system, we refute the Aldous-Lyons conjecture.

In this first talk we introduce the main concepts, motivate the conjecture and give a high level description of the proof strategy. No special mathematical background will be assumed.

This talk is based on a joint work with Lewis Bowen, Alex Lubotzky and Thomas vidick.

In the previous talk we defined Subgroup Tests and the interactive proof system induced by them. In addition, we showed that if the Aldous--Lyons conjecture was true, then this interactive proof system contains only decidable languages. In this talk, we describe why the Halting Problem can be decided in our interactive proof system, which in turn refutes the Aldous--Lyons conjecture. This is done in two steps: The first relates Subgroup Test to a new subclass of non-local games which we term Tailored Games. The second shows that the techniques of MIP*=RE can be refined so that all the games in it are tailored, or in acronym fashion, that Tailored-MIP*=RE.

This talk is based on a joint work with Lewis Bowen, Alex Lubotzky and Thomas vidick.

The growing success of machine learning across a wide range of domains and applications has made it appealing to be used also as a tool for informing decisions about humans. But humans are not your conventional input: they have goals, beliefs, and aspirations, and take action to promote their own self-interests. Given that standard learning methods are not designed to handle inputs that "behave", it is natural to ask: how should we design learning systems when we know they will be deployed and used in social environments?

As a starting point, I will present the problem of strategic classification, in which users can modify their features (at a cost) in response to a learned classifier in order to obtain favorable predictions. I will then describe some of our work in this field, demonstrating how even mild forms of strategic behavior can dramatically transform the learning problem, and the role game theory can play in addressing some of the new challenges that arise. Finally, I will argue for strategic classification as a framework that can be useful for formally reasoning about learning under user behavior in general, and which holds potential for weaving more elaborate forms of economic modeling into the learning pipeline.

Arithmetic Topology, first pioneered by Mazur in 1963, draws analogies between number theory and low dimensional topology, primes and knots, and surface and p-adic fields.

On one hand, quantum field theory can be expressed in terms of the geometry and topology of low-dimensional manifolds, on the level of states (via the Atiyah-Segal) and on the level of observables (via the Beilinson–Drinfeld). Thus, as first proposed by Minhyong Kim (in his Arithmetic Chern-Simons Theory), one can try and find arithmetic versions of quantum field theoretic ideas.

In the talk, I will introduce a new general framework for (d+1)-dimensional arithmetic TQFT.

I will explain the classification of such TQFTS for the (1+1)-dimensional case, in terms of Frobenius algebras with some extra structure, this enables us to study pro-p cobordisms and TQFTs for p-adic fields and surfaces at the same time. 

If time permits, I will outline how we use the above to compute a Dijkgraaf-Witten like invariants for G, a finite p-group, to get formulas for counting covers of Surfaces/p-adic fields with Galois group G (these formulas are similar to the ones given by Mednykh for surfaces using TQFTs, and by Masakazu Yamagishi using a more algebraic approach).

The talk is based on joint work with Oren Ben-Bassat.

No prior knowledge of Topological Quantum Field Theory or Arithmetic Topology will be assumed.

Objects play an important role in vision. Much of human vision is centered around objects and there is evidence we develop a basic understanding of what objects are from a very young age.
Learning about objects without supervision has been a focus of much research in recent years. Many models have been suggested with different structures, assumptions and inductive biases
and while impressive progress has been achieved in some limited domains we have yet to obtain a general system that can learn about objects unsupervised from real-world data.

In this talk I argue that there is a fundamental mismatch between some of the assumptions made by most "object centric" models and real-world data, and that this mismatch prevents such models from learning
meaningful representations at scale - ultimately making the problem setting ill-posed. Following that I will present some of our current work which attempts to address some of these issues.

Bio: Daniel Zoran is a research scientist at Google DeepMind in London working on problems in computer vision, attention and visual representation learning.
He completed his PhD under the supervision of Prof. Yair Weiss at the Hebrew University of Jerusalem and was a postdoc at Bill Freeman's group at MIT.

Do we live in a simulation? Perhaps we should consider the possibility. Replicating real-world observations into a digital twin offers numerous potential benefits. For instance, in autonomous navigation, one could recreate safety-critical scenarios to test an agent's behavior more efficiently and without risking human lives. True-to-life simulations can enable counterfactual analysis, aiding in the interpretability of AI decision-making. Furthermore, they allow us to relive captured experiences for immersive entertainment.

In my research, I develop tools that enable these capabilities through the reconstruction of scene properties, such as geometry and color, and through perception methods like 3D scene segmentation and 3D object detection. This also includes the controllable generation and manipulation of content. To ensure scalability, my focus is particularly on representations that respect the symmetries in the data, such as rotation equivariance, and that can leverage large datasets at scale by minimizing the need for supervision.

Among these topics, in this talk, I will specifically highlight several of my recent papers. These include studies on 3D object detection from single images [1], neural fields for dynamic outdoor scene reconstruction [2], and piecewise equivariant representations [3].

[1] 3DiffTection: 3D Object Detection with Geometry-Aware Diffusion Features. Chenfeng Xu, Huan Ling, Sanja Fidler, Or Litany. CVPR 2024

[2] Zero-to-Hero: Enhancing Zero-Shot Novel View Synthesis via Attention Map Filtering, Ido Sobol, Chenfeng Xu, Or Litany. NeurIPS 2024

[3] EmerNeRF: Emergent Spatial-Temporal Scene Decomposition via Self-Supervision. Jiawei Yang, Boris Ivanovic, Or Litany, Xinshuo Weng, Seung Wook Kim, Boyi Li, Tong Che, Danfei Xu, Sanja Fidler, Marco Pavone, Yue Wang. ICLR 2024

Bio: Or Litany is a Senior Research Scientist at the NVIDIA Toronto AI research team, and an Assistant Professor at the Technion where he leads the LIT-Lab specializing in 3D computer vision and generative AI. He is an Azrieli Faculty Fellow and a Taub Fellow. Previously, he conducted postdoctoral research at Stanford University under the guidance of Prof. Leonidas Guibas, and at Meta AI Research (FAIR), where he was hosted by Prof. Jitendra Malik.

In this talk, we examine the benefits of semantic vector representations for computer vision, highlighting their advantages over pixel-space representations in various applications. We first consider the problem of human motion anomaly detection and demonstrate the advantage of doing that over human poses. Then, we introduce a novel category-agnostic approach, termed GraphCape, that enables pose estimation across any category. Finally, we will explore further improvements for structure-based CAPE networks, dynamically predicting useful connections.

Bio: Or Hirschorn is a PhD candidate at Tel Aviv University, advised by Prof. Shai Avidan. His research interests are in developing methods for learning semantic vector representations of images and their applications for a variety of vision tasks. His MSc work won him the Weinstein scholarship for outstanding signal processing research.