August 28 - Organizational Meeting
Speaker: Addie DuncanTitle: Explainability and Interpretability in Machine LearningAbstract: Machine learning models can make accurate predictions very quickly. However the most powerful models types such as ensemble models or deep neural networks are effectively black boxes, mixing together millions of parameters to make a prediction. Even when the behavior of our models appear to be reasonable for the task assigned, we are left wondering: why did my model make ~this~ prediction? Interpreting and explaining the decisions made by machine learning models is an important part of an ethical and comprehensive implementation. And while some models are inherently easier to understand, our most accurate models often fail to provide a route towards interpretation. In this talk we will discuss several different mathematical methods for applying model-agnostic explainability algorithms to typical black box models. We will emphasize state-of-the-art interpretability algorithms and demonstrate the triumphs and pitfalls of explainability.Speaker: Ziheng ChenTitle: Don't Put All Your Eggs In One Basket; Put Them In A HashtableAbstract: It's well known that eggs in a basket are fragile. What is the alternative choice then? In a hashtable! In this talk, we'll introduce one of the most fundamental data structures in computer science. We'll begin with the typical applications and then move on to practical construction and performance analysis. As a particular example of a random algorithm, the hashtable has a few exciting properties and generalizations.October 2 - Invited Speaker
Speaker: Axel Turnquist Title: Computing Freeform Optics Inverse Problems via Optimal TransportAbstract: We introduce two freeform optics inverse problems. The first is known as the reflector antenna problem and it consists of finding the shape of a reflector that redistributes a source (directional) intensity distribution to a desired far-field target intensity distribution. The second is known as the lens refractor problem, where the goal is to find the shape of a lens, with a given refractive index (relative to ambient space), that redistributes a source (directional) intensity distribution to a desired far-field target intensity distribution. Theoretically, it turns out that these problems differ considerably. We will discuss their PDE formulations, their connections with Optimal Transport, the differences in the problems, and different approaches for how one can perform numerical computations for these problems.Speaker: Paulina HoyosTitle: An Overview of Manifold Learning AlgorithmsAbstract: Manifold learning addresses the problem of recovering information about a nonlinear low-dimensional manifold from data sampled from that manifold, which is embedded in a higher-dimensional ambient space. Although there are different methods and algorithms for this task, all approaches boil down to extracting the top or bottom few eigenvalues and associated eigenvectors of certain large and sparse matrices to perform a spectral embedding of the data. In this talk, we'll review the existing manifold learning algorithms and show their strengths and weaknesses.Speaker: Will PorteousTitle: ChatGPT and LLMs Explained (Like Any Other Algorithm)Abstract: ChatGPT and LLMs Explained (Like Any Other Algorithm)abstract: There are plenty of popular science articles describing ChatGPT and Large-Language-Models (LLMs), but most ML researchers don't know what's happening behind the scenes. How are strings passed to a neural network? What is the probabilistic model of language that ChatGPT is using? How does it know U.S. Federal law but can only sometimes handle 5th grade math? We eschew soft analogies about "attention mechanisms" and "tokens" and instead introduce large-language models as if they were any other algorithm: we'll discuss the inputs, outputs, the probabilistic modeling used, training algorithms involved, and everything in-between.
Speaker: Liangchen LiuTitle: Study deep learning from the loss landscape perspectiveAbstract: In our recent journey into the realm of deep learning, we were led by Will to explore the fascinating world of Large Language Models and gain insights into their operational pipelines. However, it turns out, or I should say everyone knows that, we are pretty bad at understanding what’s happening behind deep learning models, even the more traditional ones. In this talk, I will first talk about why traditional learning theory doesn’t work with deep learning, then try to provide some hints to suggest that the key to the magic of deep learning may be concealed within its loss landscape. Through some empirical observations and theoretical derivations, we will see how the flatness of this landscape empowers the “AI" (Flat Earthers are you hyped?) Some familiarity with deep learning is preferred but not necessary, as we will start everything from the basics and from a more math-y perspective. No complex neural network architectures or engineer's tricks involved.October 30 - Talk Rescheduled
November 6 - Talk Rescheduled
Speaker: Isaac Martin and Andrew MooreTitle: Implementing logic on Ising machinesAbstract: Ising machines are a form of quantum-inspired processing-in-memory computer which has shown great promise for overcoming the limitations of traditional computing paradigms while operating at a fraction of the energy use. The process of designing Ising machines is known as the reverse Ising problem. Unfortunately, this problem is in general computationally intractable: it is a nonconvex mixed-integer linear programming problem which cannot be naively brute-forced except in the simplest cases due to exponential scaling of runtime with number of spins. In this talk, we'll define Ising machines, discuss methods which make this horrible optimization problem a little more tractable and explore some of the mathematics/algorithms that have proven useful in this area.November 20 - Thanksgiving Break
Speaker: Julia LindbergTitle: Invariants of SDP Exactness in Quadratic Programming Abstract: In this talk I will discuss a specific convex relaxation of quadratic polynomial optimization problems, called the Shor relaxation. We study this relaxation by fixing a feasible set and considering the space of objective functions for which the Shor relaxation is exact. I will give conditions under which this region is invariant under the choice of generators defining the feasible set. I will then describe this region when the feasible set is invariant under the action of a subgroup of the general linear group. I will conclude by applying these results to quadratic binary programs and give an explicit description of objective functions where the Shor relaxation is exact, then use this knowledge to design an algorithm that produces candidate solutions for binary quadratic programs.Speaker: Patrícia Muñoz EwaldTitle: RG and RBMs, or “Is deep learning a renormalization group flow?”Abstract: That’s the title of an actual paper published in 2020. Renormalization group (RG) flow in physics is a formal way of looking at physical systems at different scales and with varying degrees of freedom. Because of the coarse-graining, dimension reducing, perhaps feature extracting (?) nature of deep learning, physicists have been trying to tie these two things together. One candidate for a simple comparison is a restricted Boltzmann machine (RBM), a type of one layer generative neural network. We will give a very basic overview of these two concepts, and explore their relation.