Research

Reliable empirical machine learning as scientific computation.

I build reproducible computational systems for model evaluation, scientific inference, and uncertainty-aware decision-making. The work sits between applied mathematics, ML, and research infrastructure: controlled numerical experiments, explicit assumptions, artifact provenance, calibrated uncertainty, numerical stability checks, and statistically valid comparisons.

Research Interests

Four research directions.

Mathematical Machine Learning

I study how learning systems can be compared, calibrated, and trusted under distribution shift and imperfect benchmarks.

statistical learning theory
calibration
conformal prediction
robustness
model selection
representation learning
graph learning
distribution shift
benchmark validity

Optimization and Numerical Computation

I am interested in optimization as a computational lens on stability, approximation, constraints, and scientific inverse problems.

stochastic approximation
adaptive first-order methods
mirror descent
momentum
preconditioning
constrained optimization
inverse problems
PDE-constrained learning

Scientific Computing and AI for Science

I want ML systems for science to preserve structure, expose uncertainty, and remain numerically testable.

numerical linear algebra
Krylov methods
state-space inference
differentiable simulation
surrogate modeling
uncertainty quantification
active experimentation
structure-aware neural systems

Reliable AI Systems

I treat AI evaluation as an experimental system whose claims need provenance, statistical comparison, and failure analysis.

LLM evaluation
tool-use and retrieval benchmarks
agent reliability
artifact lineage
dataset/version control
inference orchestration
auditability
observability
failure-mode analysis

Research Statement Preview

Modern ML systems should be treated as scientific instruments.

Modern ML systems should be calibrated, auditable, stress-tested, falsifiable, and reproducible, not merely ranked by benchmark scores. I am interested in mathematical structure that makes these systems stable and reliable, and in computational practice that can test those claims at scale.

My research direction spans reliable AI for science, robust optimization, uncertainty quantification, graph-structured inference, differentiable simulation, and evaluation methods for foundation models.

Current Questions

Questions I am currently thinking about.

Stochastic approximation and empirical ML behavior

How can stochastic approximation and optimization theory better explain the empirical behavior of modern learning systems?

Spectral structure and graph learning

How can numerical linear algebra and spectral structure improve graph learning, retrieval, and representation learning?

Reproducibility under evolving pipelines

What does reproducibility mean for complex ML pipelines where datasets, prompts, models, tokenizers, and evaluation logic all evolve?

Evaluation as controlled scientific practice

How can evaluation systems be designed so that empirical ML behaves more like a controlled scientific discipline?

Preparation

Why the engineering background belongs in the research story.

My systems work has repeatedly centered on the same concerns that matter in computational research: whether an experiment can be replayed, whether a metric is measuring what it claims to measure, whether a model comparison is contaminated by leakage, and whether a numerical or statistical procedure remains trustworthy when scaled.

I now want to make that computational maturity serve a more mathematical research path: optimization, stochastic modeling, numerical computation, graph methods, and reliable AI systems.