Learning Structure and Dynamics from Neural Data: Nonstationarity, Causality, and Brain-Wide Coordination

Abstract

Neural activity exhibits rich structure across space, time, and scales, arising from interactions among local circuits, distributed brain-wide networks, and external stimuli. At the same time, neural systems exhibit substantial trial-to-trial variability and nonstationarity in connectivity, posing fundamental challenges for understanding, predicting, and ultimately controlling neural dynamics. This thesis develops data-driven methods for learning structure and dynamics from large-scale neural recordings, organized around three themes: nonstationarity, causality, and brain-wide coordination. The first part of the thesis investigates the contribution of shared brain-wide dynamics to trial-to-trial variability in sensory responses. In collaboration with the Steinmetz Lab at the Department of Neurobiology and Biophysics, I developed a Poisson reduced-rank regression framework to quantify this contribution in the mouse visual cortex. Applied to simultaneous electrophysiology and cortex-wide calcium imaging recordings, the model revealed that a substantial fraction of response variability is explained by low-dimensional activity distributed across the cortex. These brain-wide dynamics accounted not only for variability associated with spontaneous behavior but also for additional fluctuations beyond what behavioral measurements alone could explain, demonstrating that the seemingly local sensory responses are strongly shaped by coordinated brain-wide population dynamics. The next two parts of the thesis focuses on identifying functional interactions between neurons. During an internship at Oak Ridge National Laboratory, I developed a transformer-based framework that connects attention mechanisms with Granger causality to infer time-averaged directed interactions from neural activity. Building on this work, in collaboration with colleagues at the Allen Institute, I co-developed NetFormer, an interpretable transformer architecture for learning nonstationary time-varying functional connectivity between neurons. NetFormer combines a linearized attention mechanism with a dynamical systems interpretation, enabling efficient inference of evolving network structure. Across simulated and experimental datasets, the model successfully recovered biologically meaningful connectivity patterns, including spike-timing-dependent plasticity, task-driven network structure, and experimentally measured cell-type-level connectivity, demonstrating the potential of interpretable deep learning models for studying dynamical neural circuits. The final part of the thesis investigates probabilistic forecasting of large-scale neural activity as a step toward future model-based control of neural systems. Using widefield calcium imaging recordings from multiple mice, I benchmarked fourteen probabilistic forecasting models spanning classical statistical methods, modern deep learning architectures, and pre-trained foundation models. Overall, deep learning–based forecasting methods outperformed classical statistical approaches, producing more accurate forecasts over longer prediction horizons. These results establish a benchmark for probabilistic forecasting of large-scale neural activity and provide new insight into the predictability of spontaneous cortical dynamics. Together, these studies demonstrate how advances in mathematical modeling, statistical inference, machine learning, and large-scale neural recordings can be integrated to better characterize trial-to-trial variability, infer functional interactions, and predict neural dynamics. More broadly, they provide a foundation for future work on causal discovery and model-based control of neural systems.