Integrated Calendar

Alex Furman (University of Illinois)

Title: Picking out arithmetic rank-one locally symmetric manifolds among negatively curved ones

Abstract: The definition of an arithmetic locally symmetric manifold uses the language of algebraic groups and number theory. It turns out that in the world of negatively curved manifolds the arithmetic locally symmetric ones can be detected using abstract commensurators and coarse-geometry. Based on a joint work with Yanlong Hao.

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Balint Virag (University of Toronto)

Title: Random plane geometry: a gentle introduction

Abstract: Assign a random length of 1 or 2 to each edge of the square grid based on independent fair coin tosses. The resulting random geometry, first passage percloation, is conjectured to have a scaling limit.  Most random plane geometric models (including hidden geometries) should have the same scaling limit. I will explain the basics of the limiting geometry, the "directed landscape", the central object in the class of models named after
Kardar, Parisi and Zhang.

 

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Emmanuel Breuillard (University of Oxford)

Title: Undecidable problems in linear groups.

Abstract: The Skolem problem asks to determine whether or not a linear recurrence sequence over the integers has a zero. No algorithm is known to answer this simple question. In this talk I will discuss recent joint work with G. Kocharyan, where we consider a wider class of problems, dealing with finitely generated subgroups of matrices,  and show their undecidability.

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Omer Angel (University of British Columbia)

Title: Interacting Polya urns.

Abstract: The classical Polya urn has counters X_t,Y_t that are incremented with probability proportional to their current value. I will discuss some of the many generalizations possible when multiple
Polya urns are coupled.

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Shmuel Weinberger (University of Chicago)

Title: How existential is topology?


Abstract:  Topology proves many things exist

A distribution is k-incompressible, Yao [FOCS ’82], if no efficient compression scheme compresses it to less than k bits. While being a natural measure, its relation to other computational analogs of entropy such as pseudoentropy (Hastad, Impagliazzo, Levin, and Luby [SICOMP 99]), and to other cryptographic hardness assumptions, was unclear.

We advance towards a better understating of this notion, showing that a k-incompressible distribution has (k-2) bits of next-block pseudoentropy, a refinement of pseudoentropy introduced by Haitner, Reingold, and Vadhan [SICOMP ’13]. We deduce that a samplable distribution X that is (H(X) 2)-incompressible, implies the existence of one-way functions.

Joint work with Iftach Haitner and Jad Silbak.

The dominant paradigm in generative modeling consists of two steps: i) pre-training on a large-scale but unsafe dataset, ii) aligning the pre-trained model with human values via fine-tuning. This practice is considered safe, as no current method can recover the unsafe, pre-fine-tuning model weights. In this paper, we demonstrate that this assumption is often false. Concretely, we present Spectral DeTuning, a method that can recover the weights of the pre-fine-tuning model using a few low-rank (LoRA) fine-tuned models. In contrast to previous attacks that attempt to recover pre-fine-tuning capabilities, our method aims to recover the exact pre-fine-tuning weights. Our approach exploits this new vulnerability against large-scale models such as a personalized Stable Diffusion and an aligned Mistral.

Bio:

Eliahu Horwitz is a PhD candidate in Computer Science at the Hebrew University of Jerusalem, working under the supervision of Prof. Yedid Hoshen. His research area is computer vision, with a focus on representation learning and generative models. Currently, his work revolves around reversing the training trajectories of neural networks.

A recipient of the KLA Scholarship for Outstanding Graduate Students and a CIDR (Center for Interdisciplinary Data Science Research) fellow, Eliahu’s academic achievements are complemented by his practical experience. Before transitioning to research, he honed his skills as a self-taught software developer, working with diverse technologies across the tech stack at both startups and large-scale companies. His latest research can be found on his website: pages.cs.huji.ac.il/eliahu-horwitz.

While cognitive neuroscientists have uncovered principles of perceptual decision-making by analyzing choices and neuronal firing across thousands of trials, we do not yet know the behavioral or neuronal dynamics underlying one SINGLE choice. For instance, why might a subject judge a given stimulus in category A 70% of the time but in category B 30%? Until we can work out precisely what determines single-decisions – this choice, right now – the mechanisms of real-world decision-making will remain unknown. In tactile psychophysical tasks with rats and humans, we are trying to sort out factors that explain the variability in judgments (across trials) to the identical stimulus input. We identify four factors: (i) trial-to-trial fluctuations in sensory coding, (ii) temporal context, namely, the history of preceding stimuli and choices, (iii) attention, and (iv) bias (predictions originating in beliefs about the environment’s probabilistic structure). The strategy is to bring these factors under experimental control, rather than leaving them to vary according to uninterrogated states within the subject. Psychophysics from rats and humans show that large chunks of variability are accounted for by these factors; evidence from cortical neuronal populations in rats provides some mechanistic grounding.