Research
Theoretical foundations for in-context learning and geospatial artificial intelligence.
In-Context Learning Theory
Rigorous characterization of when transformer architectures can efficiently perform in-context learning. We establish the ICL-Easy/ICL-Hard dichotomy through the framework of Sufficient Statistic Complexity (SSC) and Attention-Computable SSC (AC-SSC): function classes admitting additive sufficient statistics computable by attention layers achieve sample complexity matching empirical risk minimization, while classes with combinatorial statistics require super-polynomial resources. Our work provides matching upper and lower bounds, connects to circuit complexity theory via Håstad's theorem, and demonstrates how chain-of-thought reasoning can break computational hardness barriers.
Geospatial Artificial Intelligence (GeoAI)
Application of in-context learning theory to foundation models across the geospatial sciences. We establish domain-specific dichotomy theorems characterizing ICL complexity for climate prediction (Climate Prediction Dichotomy Theorem), remote sensing analysis (Remote Sensing Dichotomy Theorem), and navigation systems (Navigation Dichotomy Theorem). Our work spans multi-modal geo-foundation models integrating optical imagery, SAR, and spatiotemporal data; climate models for temperature/precipitation forecasting versus extreme event prediction; and GNSS-based navigation distinguishing continuous state estimation from discrete fault identification. Each domain receives rigorous theoretical treatment with explicit ICL-Easy/Hard classification and sample complexity analysis.
Quantum Geodesy
Theoretical analysis of quantum-enhanced measurement systems for Earth's gravitational potential field estimation. We prove the geopotential function class is ICL-Easy and quantify the advantage of Heisenberg-limited quantum gravimeters over classical sensors: for realistic parameters, sample complexity reduces by a factor of 10¹² when using cold atom interferometry with entangled states. Our framework establishes tight bounds for both classical and quantum measurement regimes, connects geodetic inverse problems to computational hardness via sparse parity reductions, and provides the complete Geodetic Dichotomy Theorem distinguishing tractable forward estimation from intractable inverse recovery.
Geospatial Intelligence (GeoINT)
Theoretical foundations for intelligence analysis using geospatial data and foundation models. We develop rigorous frameworks for understanding when transformer architectures can efficiently perform GeoINT tasks—from imagery analysis and object detection to change detection and threat assessment. Our work establishes complexity bounds for intelligence-relevant learning problems, characterizes the role of multi-modal fusion (optical, SAR, hyperspectral), and provides principled guidance for deploying foundation models in operational intelligence contexts.