Theory-Focused Research

Foundations of ML, GNN theory, generative modeling theory, and complexity under dependence

My theory-focused work studies the foundations of machine learning under dependence, with emphasis on statistical complexity, minimax analysis, lower bounds, and structure-aware learning theory. A recurring goal is to identify regimes where classical i.i.d.-based intuition breaks down, prove sharp lower and upper bounds in those regimes, and derive algorithmic consequences for learning and sampling.

Current themes

  • Minimax learning theory for graph-structured learning (GNNs): I study how graph topology, dependence, and mixing properties affect the effective sample complexity of message-passing neural architectures. My recent ICLR 2026 paper develops minimax lower bounds and structural regime characterizations for ReLU message-passing GNNs, showing that realistic slowly mixing graphs can induce significantly harder structure-driven rates than classical sample-size scaling would suggest.

  • Structure-aware complexity in generative modeling: I am extending this line of work toward the science and theory of generative modeling, especially:
    • complexity of score estimation in diffusion-based models
    • error propagation from score estimation to sampling quality

    • statistical-computational tradeoffs in sequence-structured settings

      A central theme is that dependence structure (e.g., graph topology or sequence dependence) can govern both statistical and algorithmic difficulty.

  • Efficient inference and compute-quality tradeoffs: I also study how inference-time budget constraints interact with estimation and decision quality in large models, including confidence-guided stopping and adaptive computation. This provides a practical bridge between complexity theory and deployment-time behavior.

Representative papers

  • ICLR 2026 (accepted): Minimax Sample Complexity of Graph Neural Networks: Lower Bounds and Structural Effects
  • CGES (under review / arXiv): Confidence-Guided Early Stopping for Efficient Inference

Methodological perspective

I combine rigorous theorem development with theory-grounded empirical diagnostics designed to distinguish between competing scaling laws and structural regimes.