Structure-Aware Adaptive Nonconvex Optimization for Deep Learning and Scientific Computing (Minxin Zhang, UCLA)
2025-12-01 16:15 - 17:15 (America/Los_Angeles) | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: Modern machine learning and scientific computing pose optimization challenges of unprecedented scale and complexity, demanding fundamental advances in both theory and algorithmic design for nonconvex optimization. This talk presents recent advances that address these challenges by exploiting matrix and tensor structures, integrating adaptivity, and leveraging sampling techniques. In the first part, I introduce AdaGO, a new optimizer that combines orthogonalized momentum updates with adaptive learning rates. Building on the recent success of the Muon optimizer in large language model training, AdaGO incorporates an AdaGrad-type stepsize that scales orthogonalized update directions by accumulated past gradient norms. This design preserves the structural advantage of orthogonalized updates while adapting stepsizes to noise and the optimization landscape. We establish optimal convergence rates for smooth nonconvex functions and demonstrate improved performance over Muon and Adam on classification and regression tasks. The second part focuses on zeroth-order global optimization. We develop a theoretical framework for inexact proximal point (IPP) methods for global optimization, establishing convergence guarantees when proximal operators are estimated either deterministically or stochastically. The quadratic regularization in the proximal operator induces a concentrated Gibbs measure landscape that facilitates effective sampling. We propose two sampling-based algorithms: TT-IPP, which constructs a low-rank tensor-train (TT) approximation using a randomized TT-cross algorithm, and MC-IPP, which employs Monte Carlo integration. Both IPP algorithms adaptively balance efficiency and accuracy in proximal operator estimation, achieving strong performance across diverse benchmark functions and applications. Together, these works advance structure-aware adaptive first-order optimization for deep learning and zeroth-order global optimization in scientific computing.

A Signal Separation View of Classification (Ryan O'Dowd, CGU)
2025-11-17 16:15 - 17:15 | Estella 1021 (Emmy Noether Room), Pomona College, Claremont, CA, 91711, United States
Abstract: The problem of classification in machine learning has often been approached in terms of function approximation. In this talk, we propose an alternative approach for classification in arbitrary compact metric spaces which, in theory, yields both the number of classes, and a perfect classification using a minimal number of queried labels. Our approach uses localized trigonometric polynomial kernels initially developed for the point source signal separation problem in signal processing. Rather than point sources, we examine a convex combination of probability distributions representing the various classes from the machine learning classification problem. The localized kernel technique developed for separating point sources is then shown to separate the supports of these distributions. This is done in a hierarchical manner in our MASC algorithm to accommodate touching/overlapping class boundaries. The algorithm works in an active learning paradigm, deciding on points to query for their true class label and extending those labels to nearby points. We illustrate our theory on several simulated and real life data sets, including the Salinas and Indian Pines hyperspectral data sets and a document data set.

To Wait or Not to Wait? A Trade-off Between Population Externality and Signal Quality (Lan-Yi Liu, National Taiwan University)
2025-11-10 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: Transparency is vital for efficiency in social systems, yet individuals with critical information often strategically postpone disclosure, even when required, to benefit themselves.
To study this behavior, we introduce a multi-stage Chinese restaurant game with incomplete information that features system-recommended action rules and varying levels of player foresight. In our model, players initially receive a suggestion to join a queueing group based on their private signal, but can choose to switch groups. Following this, players sequentially select a final resource, balancing the desire to avoid congested externalities with the need to acquire more information.
We prove a closed-form solution for the players’ pure-strategy Nash equilibrium. Our key finding is that players with high-quality signals have no incentive to reveal their information to those with low-quality signals. This suggests that allowing players to strategically determine their decision timing, without further system design, leads to an inefficient equilibrium allocation.
Our results on congested externalities and system suggestions help explain the inherent trade-off between information quality and decision timing in various real-world scenarios, such as the challenges of vaccine distribution during a pandemic, the strategic crowding of factory location selection, and the decision-making faced by political candidates positioning themselves on the spectrum.

Convergence analysis of the Alternating Anderson-Picard method for nonlinear fixed-point problems (Xue Feng, UCLA)
2025-11-03 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: Anderson Acceleration (AA) has been widely used to solve nonlinear fixed-point problems due to its rapid convergence. This talk focuses on a variant of AA in which multiple Picard iterations are performed between each AA step, referred to as the Alternating Anderson-Picard (AAP) method. Despite introducing more `slow’ Picard iterations, this method has been demonstrated to be efficient and even more robust in both linear and nonlinear cases. However, there is a lack of theoretical analysis for AAP in the nonlinear context. In this work, we address this gap by establishing the equivalence between AAP and a multisecant-GMRES method that employs GMRES to solve a multisecant linear system at each iteration. From this perspective, we show that AAP actually “converges” the well-known Newton-GMRES method. These connections also help us understand the convergence behavior of AAP, especially the asymptotic convergence rate.

Estimating Shapley Values for Explainable AI via Richer Model Approximations (Teal Witter, CMC)
2025-10-27 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: Modern machine learning is ultimately a simple process: We iteratively update the weights of machine learning models to minimize a problem-specific loss. When it works well, we deploy the model in human-facing domains like healthcare, finance, or the justice system. But even though we know how models are trained, we don’t understand why they make decisions the decision they do. A particularly compelling approach to explaining AI predictions is the Shapley value, a game-theoretic quantity that measures how each input to the model affects its output. Mathematically, the ith Shapley value is the average change in the ith dimension of a particular function defined on the d-dimensional hypercube. Because the hypercube has 2^d points, exactly computing Shapley values is infeasible. In this talk, we will instead leverage algorithmic insights to develop state-of-the-art approximation methods.

Some New Advances in Similarity-Based Predictive Modeling (Joel A. Dubin, University of Waterloo)
2025-10-20 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: Earlier work has shown that similarity-based predictive models can improve upon predictive performance, as compared to using the entire training data to help build models, particular regarding model discrimination for binary responses. My collaborators and I have some updated results to share, regarding similarity-based modeling for joint consideration of model calibration and discrimination, as well as for dynamic prediction models. Properties of our methods will be investigated in comprehensive simulation studies, and we will demonstrate the methods through separate analyses of a publicly-available intensive care unit (ICU) database.

Modeling drug release for in vitro experiments (Minaya Villasana De Armas, Universidad Simon Bolivar)
2025-10-06 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: It is common to use adjuvants in immunotherapeutic regimens to strengthen the immune response. However, multiple dosages are required making it inconvenient for the patient. Hydrogels have been proposed as a vehicle to administer adjuvant and antigen in a sustained slow release thus reducing the need for re-administration.
In this instance, we use experimental data for stability studies on two different thermosensitive pentablock hydrogels as well as release of three adjuvants suspended in the hydrogels or in PLGA nanoparticles. The goal is to model this release and provide a framework by which these models can describe the various release profiles efficiently.

Bounds and Extremal Examples for the Hot Spots Ratio (Alex Hsu, University of Washington)
2025-09-29 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract: The shape of the fluctuations as heat approaches equilibrium in an insulated body are governed by the first Neumann eigenfunction of the Laplacian. Rauch’s hot spots conjecture states that the extrema of the first nontrivial Neumann Laplacian eigenfunction for a Lipschitz domain lies on the boundary. While this conjecture is false in general, its failure can be measured by the hot spots ratio, defined as the maximum over the entire domain divided by the maximum on the boundary. We determine the supremum of this quantity over all Lipschitz domains in every dimension $d$ and construct a sequence of sets for which the hot spots ratio approach this supremum. As $dto infty$, this maximal ratio converges to $sqrt{e}$, which matches the previously best known upper bounds.

LA City Council Reform: A Statistical Study of Alternatives (Evan Rosenman & Sarah Cannon, Claremont McKenna College)
2025-09-15 16:15 - 17:15 | Emmy Noether Room, Estella 1021, Pomona College,, 610 N. College Ave., Claremont, CA, 91711, United States
Abstract:
The 2022 Los Angeles City Council scandal intensified public demand for governance reform, leading to the creation of the Los Angeles Charter Reform Commission. The commission is now considering proposals from civic and academic groups. Major recommendations include: eliminating the automatic election of candidates who win a primary majority, expanding the size of the City Council, and adopting alternative electoral systems such as multimember districts and ranked-choice voting.
This project offers a rigorous, data-driven evaluation of these proposals, focusing on their implications for proportionality, racial representation, and electoral responsiveness. We combine methods from Statistics and Computer Science, including Bayesian ethnicity imputation, ecological inference, and advanced graph-sampling algorithms to explore district boundaries. This hybrid approach provides new insights into Los Angeles’s political geography and the challenges of building a fair, representative City Council. By providing empirical evidence on the strengths and weaknesses of various districting systems, our work aims to inform policymaking and advance democratic representation in Los Angeles.

The Shooting Method in the Analysis of Two-Point Boundary-Value Problems (Adolfo J. Rumbos, Pomona College)
2025-09-08 16:15 - 17:15
Abstract:
Two-point boundary-value problems (BVPs) appear frequently in applied mathematics. When looking for solutions of boundary-value problems for some partial differential equations (PDEs) in mathematical physics, two-point BVPs come up as a result of applying the method of separation of variables, for instance. In the case of linear PDEs, the resulting two-point BVPs fall into a class of problems known as Sturm-Liouville eigenvalue problems.
This presentation deals with the use of the shooting method to prove existence of solutions of two-point BVPs. The shooting method is a numerical technique used to estimate solutions of two-point BVPs once a solution is known to exist. In this talk we illustrate how the shooting method can be used to prove existence of eigenvalues of linear Sturm-Liouville problems. We also show how the shooting method can be applied to prove existence and uniqueness of solutions for some nonlinear, two-point BVPs, and existence of eigenvalues for some nonlinear eigenvalue problems.
The presentation describes research conducted with collaborators Vaidehi Srinivasan (Pomona College class of 2027) and Gavin Zhao (Pomona College class of 2029) in the summer of 2025 with the support of the Summer Undergraduate Research Program at Pomona College.
