Integrated Calendar

The central limit theorem (CLT) and related results for stationary weakly dependent sequences of random variables have been extensively studied in the past century, starting from a pioneering work of Berenstien (1927).  However, in many physical  phenomena there are external forces, measurement errors and unknown variables (e.g. storms, the observer effect, the uncertainty principle etc.). This means that the local laws of physics depend on time, and it leads us to studying non-stationary sequences. 

The asymptotic behaviour of non-stationary sequences have been studied extensively in the past decades, but it is still developing compared with the theory of stationary processes. In this talk we will focus on inhomogeneous Markov chains. For sufficiently well contracting Markov chains the CLT was first proven by Dobrushin (1956). Since then many results were proven for stationary chains. In 2021 Dolgopyat and Sarig proved local central limit theorems (LCLT) for inhomogeneous Markov chains. In 2022 Dolgopyat and H proved optimal CLT rates in Dobrusin's CLT. These results closed a big gap in literature concerning the non-stationary case. 

An open problem raised by Dolgopyat and Sarig in their 2021 book concerns limit theorems for Markov shifts, that is when the underlying sequence of functions that forms the partial sums depend on the entire path of the chain. Two circumstances where such dependence arises are products of random matrices and random iterated functions, and there are many other instances when the functionals depend on the entire path. 

In this talk we will present our solution to the above problem. More precisely, we prove CLT, optimal CLT rates and LCLT for a wide class of sufficiently well mixing Markov chains and functionals with infinite memory. Even though the inhomogeneous case is more complicated, our results seem to be new already for stationary chains.

Abstract: How voluntary, self-paced intentions emerge in the brain and translate into action remains one of the most fundamental open questions in neuroscience. Leveraging rare access to intracranial neuronal recordings from human motor cortex, we built a real-time, online closed-loop system that allowed us to study the formation of voluntary actions under competitive conditions.We show that participants have only limited capacity to voluntarily steer their motor-cortex activity when doing so is strategically advantageous-revealing tight constraints on intentional control at the neural population level. Yet the commitment to act can be decoded reliably from motor-cortex activity roughly 250 ms before movement onset, at a time point when participants report already being consciously aware of their decision. We also find that brain–computer interfaces trained in one cognitive context transfer seamlessly to another, despite substantial differences in neural trajectories and force profiles-suggesting a shared underlying representational structure for volitional actions in motor cortex.Offline analyses further uncovered the specific neural patterns that signal commitment to action, shedding new light on how early voluntary actions can be reliably predicted from motor-cortex activity. We will conclude by discussing how these and related results inform emerging efforts to track and interpret intentions in advanced AI systems (ai-intentions.org).

Glucose can enter the blood following a meal, and/or can be produced by the liver and kidneys at times of need such as fasting. An elevation in blood glucose beyond steady state levels leads to secretion of the hormone insulin, leading to increase in glucose uptake into muscle and adipose tissues. Diabetes Mellitus arises when insufficient levels of insulin are secreted into the blood, manifesting as a chronic elevation in blood glucose levels. A reduction in glucose levels can lead to secretion of a large number of hormones, such as glucagon, cortisol and adrenaline, which cause endogenous glucose production and secretion into the blood,  maintaining homeostasis of glucose levels. In this talk we will use mathematical modeling and biochemical measurements to study the dynamics of hormone secretion in healthy individuals and Diabetes patients, and (hopefully) provide an answer to a key question: does the "body" measure glucose levels and regulates glucose levels accordingly by secreting insulin/glucose, as expected by a standard negative feedback system, or does it estimate future glucose levels and secretes hormones/glucose in a feedforward mechanism?Students interested in meeting the speaker after the seminar may sign up here:LINKFOR THE LATEST UPDATES AND CONTENT ON SOFT MATTER AND BIOLOGICAL PHYSICS AT THE WEIZMANN, VISIT OUR WEBSITE: https://www.bio

Ensuring that AI systems behave as intended is a central challenge in contemporary AI. This talk offers an exposition of provable mathematical guarantees for learning and security in AI systems.

Starting with a classic learning-theoretic perspective on generalization guarantees, we present two results quantifying the amount of training data that is provably necessary and sufficient for learning: (1) In online learning, we show that access to unlabeled data can reduce the number of prediction mistakes quadratically, but no more than quadratically [NeurIPS23, NeurIPS25 Best Paper Runner-Up]. (2) In statistical learning, we discuss how much labeled data is actually necessary for learning—resolving a long-standing gap left open by the celebrated VC theorem [COLT23].

Provable guarantees are especially valuable in settings that require security in the face of malicious adversaries. The main part of the talk adopts a cryptographic perspective,  showing how to: (1) Utilize interactive proof systems to delegate data collection and AI training tasks to an untrusted party [ITCS21, COLT23, NeurIPS25]. (2) Leverage random self-reducibility to provably remove backdoors from AI models, even when those backdoors are themselves provably undetectable [STOC25].

The talk concludes with an exploration of future directions concerning generalization in generative models, and AI alignment against malicious and deceptive AI.

Much of the thinking about neural population codes was motivated in the past decades by reports on neurons with highly stereotyped tuning functions. Indeed, neurons are often observed to exhibit smooth, unimodal tuning to an encoded variable, centered around preferred stimuli that vary across the neural population. Recent experiments, however, have uncovered neural response functions that are much less stereotyped and regular than observed previously. Some of the most striking examples have been observed in the hippocampus and its associated brain areas. The classical view has been that hippocampal place cells are active only in a compact region of space and exhibit a stereotyped tuning to position. In contrast to this expectation, however, place cells in large environments typically fire in multiple locations, and the multiple firing fields of individual cells, as well as those of the whole population, vary in size and shape. We recently discovered that a remarkably simple mathematical model, in which firing fields are generated by thresholding a realization of a random Gaussian process, accounts for the statistical properties of place fields in precise quantitative detail. The model captures the statistics of field sizes and positions, and generates new quantitative predictions on the statistics of field shapes and topologies. These predictions are quantitatively verified in multiple recent data sets from bats and rodents, in one, two, and three dimensions, in both small and large environments. Together, these results imply that common mechanisms underlie the diverse statistics observed in the different experiments. I will discuss a mechanistic model, which suggests that the random Gaussian process statistics arise due to random connectivity within the CA3-CA1 hippocampal circuit. If time permits I will present another recent work, in which we uncover simple principles underlying the spatial selectivity in a new class of neurons in the medial entorhinal cortex, with tuning curves that are significantly less regular than those of classical grid cells. 

From rough sketches that spark ideas to polished illustrations that explain complex concepts, visual communication is central to how humans think, create, and share knowledge. Yet despite major advances in generative AI, we are still far from models that can reason and communicate through visual forms.

I will present my work on bridging generative models and visual communication, focusing on three complementary domains: (1) algorithms for generating and understanding sketches, (2) systems that support exploratory visual creation beyond one-shot generation, and (3) methods for producing editable, parametric images for design applications.

These domains pose unique challenges: they are inherently data-scarce and rely on representations that go beyond pixel-based images commonly used in standard models. I will show how the rich priors of vision-language models can be leveraged to address these challenges through novel optimization objectives and regularization techniques that connect their learned features with the specialized representations required for visual communication.

Looking ahead, this research lays the foundation for general-purpose visual communication technologies: intelligent systems that collaborate with humans in visual domains, enhancing how we design, learn, and exchange knowledge.

Bio:

Yael Vinker is a Postdoctoral Associate at MIT CSAIL, working with Prof. Antonio Torralba. She received her Ph.D. in Computer Science from Tel Aviv University, advised by Profs. Daniel Cohen-Or and Ariel Shamir. Her research spans computer graphics, computer vision, and machine learning, with a focus on generative models for visual communication. Her work has been recognized with two Best Paper Awards (SIGGRAPH 2022, SIGGRAPH Asia 2023) and a Best Paper Honorable Mention (SIGGRAPH 2023). She was selected as an MIT EECS Rising Star (2024) and received the Blavatnik Prize for Outstanding Israeli Doctoral Students in Computer Science (2024) as well as the VATAT Ph.D. Fellowship.