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This month, we sat down for a conversation with the newest member of our leadership team, Senior Scientist Jason Lee. Jason is an Associate Professor of EECS and Statistics at UC Berkeley. His research interests are in the theory of machine learning, optimization, and statistics. He has been participating in Simons Institute programs since we opened our doors in Fall 2013, when he was a graduate student.
In this talk, Alyosha Efros argues that models trained on surface (scraped) data will not transcend mimicry and pastiche. He suggests that to achieve full intelligence, we need deep data, mined by the models through curiosity-driven exploration, driven by intrinsic motivation rather than rewards.
Louis Golowich (UC Berkeley) shows how to perform classical and quantum computation in the presence of an almost-linear number of adversarial errors in every time step, and the utility of such schemes toward PCP constructions, both classical and quantum.
Shankar Balasubramanian (Caltech) presents research constructing a 3D Pauli stabilizer Hamiltonian whose ground-state space can encode a qubit for exponential time when coupled to a bath at nonzero temperature.
Hsin-Yuan (Robert) Huang asks whether there is a path forward for working with LLMs in a way that does not undermine the sacred human act of doing research.
Fan Chen (MIT) presents an algorithmic framework for high-accuracy sampling using unbiased stochastic queries.
Greetings from Berkeley! This has been a dizzying summer, one in which we witnessed an inflection point in AI’s capability to autonomously solve major open problems in math and theoretical CS. Like many of you, I feel a mix of amazement at this rapid acceleration and uncertainty about what it means for the future of TCS research as a profession. Scientifically, though, there is much to celebrate: the field has advanced by leaps and bounds this summer, whether done the old-school way, AI-assisted, or AI-driven.
Markov chains are important stochastic processes used ubiquitously to algorithmically solve high-dimensional sampling problems. In this minicourse, we present a powerful framework called spectral independence for upper bounding the rate of convergence to stationarity for discrete Markov chains. This framework has intimate connections with the theory of high-dimensional expanders (HDX), and since been generalized significantly via the theory of localization schemes, which also encompasses Eldan's stochastic localization. This minicourse is structured as follows:
Lecture 1: We begin by stating basic examples and applications of the theory. We then define spectral independence and prove that it implies rapid mixing.
Lecture 2: We describe several classes techniques for establishing spectral independence, using the monomer-dimer model on matchings as a running example. Time permitting, we will sketch the theory of localization schemes.