Research

Research Interests #

I am deeply interested in exploring a wide range of mathematical concepts, understanding connections between diverse topics, and applying the rigorous study of abstract structures (e.g., algebra, geometry) to data science and machine learning. Below, I outline some of the areas I am currently exploring and am passionate about. If you share an interest in these topics, I would be delighted to connect.

• Any-dimensional Learning: Developing neural network architectures that can be trained on inputs of small sizes and generalize effectively to larger sizes, ideally with theoretical guarantees on asymptotic performance.

  • On one hand, I am keen to understand the implicit inductive biases of existing neural networks in relation to their size generalization capabilities, to determine which tasks they are most suitable for. On the other hand, I am interested in designing neural networks capable of solving specific any-dimensional problems, such as those encountered in combinatorial optimization and probabilistic/statistical modeling.
  • I am particularly interested in the concept of “learning an algorithm”: investigating whether a learned algorithm generalizes to input dimensions outside the training range, whether the learned algorithm can be interpreted to derive useful insights, and whether theoretical limits exist on the performance achievable by a learned algorithm.
  • This area relates to topics such as graph neural networks (GNNs) for combinatorial optimization, the transferability and size generalization of GNNs, length generalization in large language models (LLMs), and neural algorithmic reasoning.

• Symmetries in Machine Learning: Investigating how to effectively leverage symmetries in various learning tasks and design equivariant neural networks—architectures that incorporate symmetry constraints—for mathematical applications.

  • Within this area, I aim to understand the expressive power, size generalization behavior, and other properties associated with different parameterization choices for equivariant networks.