Speaker: Assistant Prof. Andrea Agazzi from Università di Pisa, Italy

Title: Convergence and optimality of neural networks for reinforcement learning

Abstract: Recent groundbreaking results have established a convergence theory for wide neural networks in the supervised learning setting. Under an appropriate scaling of parameters at initialization, the (stochastic) gradient descent dynamics of these models converge towards a so-called “mean-field” limit, identified as a Wasserstein gradient flow. In this talk, we extend some of these recent results to examples of prototypical algorithms in reinforcement learning: Temporal-Difference learning and Policy Gradients. In the first case, we prove convergence and optimality of wide neural network training dynamics, bypassing the lack of gradient flow structure in this context by leveraging sufficient expressivity of the activation function. We further show that similar optimality results hold for wide, single layer neural networks trained by entropy-regularized softmax Policy Gradients despite the nonlinear and nonconvex nature of the risk function.

**Keller 303**

Speaker: Isaac Goldbring, UC Irvine.

Title: The Connes Embedding Problem, MIP*=RE, and the Completeness Theorem

Abstract: The Connes Embedding Problem (CEP) is arguably one of the most famous open problems in operator algebras. Roughly, it asks if every tracial von Neumann algebra can be approximated by matrix algebras. In 2020, a group of computer scientists proved a landmark result in complexity theory called MIP*=RE, and, as a corollary, gave a negative solution to the CEP. However, the derivation of the negative solution of the CEP from MIP*=RE involves several very complicated detours through C*-algebra theory and quantum information theory. In this talk, I will present joint work with Bradd Hart where we show how some relatively simple model-theoretic arguments can yield a direct proof of the failure of the CEP from MIP*=RE while simultaneously yielding a stronger, Gödelian-style refutation of CEP. No prior background in any of these areas will be assumed.

Keller 403.* Title:* Non-deterministic Automatic Complexity of Fibonacci words

**Abstract***Automatic complexity rates can be thought of as a measure of how random words can be for some given automaton (machine). By creating a scale between 0 and 1 that ranges from predictable to complex, if the rate of a given word is strictly between 0 and 1/2 then we call it indeterminate. In this paper we show that for an infinite Fibonacci word the non-deterministic automatic complexity can be no greater than 1/Φ^2.*

**:**Kuykendall Hall 210

Title: Low($\Pi^0_1$-IM) = $\Delta^0_1$

Abstract: My dissertation investigated $\Pi^0_1$-immune sets, i.e. those

that have no co-enumerable subset. This talk continues that work, first

connecting it to modern notions of computability-theoretic lowness. Then

I settle (in the affirmative) a conjecture that my dissertation left

open: only the computable sets fail to co-enumerate a $\Pi^0_1$-immune

set.

Watanabe 112