Graduate Students Seminar

Session Chair:  Abhisek Chatterjee
Discussant:        Dr. Nguyen

Speaker 1:  Paul Luongo

Title The Big Data Paradox in the Age of Intelligent Machines

Abstract
More data need not yield more accurate conclusions. This talk introduces Xiao-Li Meng’s data defect correlation, which relates realized error in a finite population mean estimate to the association between data selection and the quantity being measured. A controlled machine behavior experiment with a small transformer language model illustrates how a small selection defect in a large text training corpus can propagate into learned behavior even in a relatively sophisticated, context-aware network, allowing the same model trained on a smaller but more representative subcorpus to approximate the target distribution more faithfully. We then extend Meng's scalar mean estimation perspective to the more general setting of estimating equations, using ordinary least squares regression to illustrate how such selection effects can cancel or amplify during fitting, with potential implications for model selection under nonrandom sampling regimes. We conclude by discussing connections to anticipated LLM training data scarcity and the problem of AI alignment: What must our data faithfully represent for a model to learn the behavior we intend?

Speaker 2: Dinesh Ekanayaka

Title Multiple Stable Oscillations in Chemical Reaction Networks

Abstract
Limit cycles are isolated periodic orbits that arise in nonlinear dynamical systems and play a central role in the modeling of oscillations in chemistry, biology, and engineering. Determining the number of limit cycles remains an unsolvable problem, suggested by Hilbert’s 16th problem. In this presentation, we discuss limit cycles and their appearance in chemical reaction networks and biochemical oscillator models. We focus on systems that exhibit birhythmicity, where two stable limit cycles coexist and produce distinct oscillatory behaviors. We then examine a recently proposed family of planar ordinary differential equations that can generate arbitrarily many stable limit cycles. Numerical examples are presented to illustrate systems with neighboring limit cycles and systems with nested limit cycles.