Thesis Central

Language acquisition and reasoning, two skills fundamental to human intelligence, both require internalizing and applying a collection of rules and structures derived from a limited set of examples. Crucially, this requires not only the ability to identify important structures in those examples, but also the ability to systematically combine learned structures in novel combinations, or systematicity. Interestingly, despite recent successes in the sphere of language generation, statistical learners like today's foundation models still fail to consistently reason systematically, suggesting a possible incompatibility between the current learning paradigm or model architectures and the acquisition of systematicity. We aim to develop a better understanding of the extent to which statistical learners are capable of generalizing to novel combinations, which we call compositional generalization, in systematic tasks. To that end, we identify some ways in which model architecture or optimization choices can encourage the inductive biases needed for models to generalize compositionally, as well as challenges in more realistic task settings.

Asteroseismology is an important tool for probing the fundamental characteristics of pulsating stars. Stellar oscillations are influenced by internal pressure, temperature gradients, and the structure of convective zones. Therefore, studying these oscillations enhances our understanding of stellar interiors. Research has shown that high mass main sequence stars exhibit strong pulsations. Theoretical models predict that low mass stars including M dwarfs can also pulsate at shorter periods and lower amplitudes. However, previous Kepler and K2 missions failed to detect convincing pulsations in M dwarfs likely due to a combination of instrumental limitations and the intrinsic faintness of the signals. In this work, we aim to identify solar like pulsations in low mass stars, particularly M dwarfs, using the Transiting Exoplanet Survey Satellite (TESS) 20 second cadence data. The high cadence and improved photometric precision of 20 second cadence data provide our best current opportunity to detect these faint pulsations especially in the low frequency, low amplitude regime where they are expected to occur. We extracted and analyzed light curves from our target stars to identify and characterize noteworthy signals. After processing the data, we used Lomb Scargle periodograms, power spectrum, and threshold analysis to investigate the nature of these signals. Our analysis revealed a variety of phenomena, including stellar flares, eclipsing binaries, variable stars, previously uncatalogued pulsations from nearby higher mass stars, and strong rotational modulation signatures in many of our targets.

This collection of poems writes into history my family's own story, one centered around the coming together of my Korean-Lithuanian background and the lessons of love I've derived from those who came before me.