Dr Shubhendu Trivedi
Mentor
Shubhendu is a researcher interested in foundational problems in machine learning, especially those that incorporate geometric structure into neural networks, employ statistical physics-based approaches for neural network analysis, and develop conformal prediction methods for uncertainty quantification. Shubhendu has been a research associate at MIT and an NSF Institute Fellow in Computational and Experimental Mathematics at Brown University working on problems in algebraic machine learning. He received his PhD and MS degrees working at the Toyota Technological Institute at Chicago and the University of Chicago in 2018, with a thesis on group equivariant and symmetry-preserving neural networks. He also holds a MS with work on applications of the Szemeredi Regularity Lemma and a Bachelor's degree in Electrical Engineering. Apart from academic research, Shubhendu has also led multiple teams for industrial research on health analytics, equivariant models for relational data, knowledge graph engineering and zero-shot transfer learning. He has also been associated with a semi-conductors startup.
Project
Equivariant poset representations
Partially-ordered data is pervasive across a wide range of domains: from online user forums, to natural language understanding, to computer programs and, to bioinformatics. To develop successful applications in these domains, we need to learn representations mapping a hierarchy to a meaningful vector space. Partially ordered sets (posets) are combinatorial objects encoding such hierarchies. Despite the recent plethora of works on equivariant representations for other combinatorial structures, such as graphs and sets, posets have been consistently neglected in this context. In this project we will first discuss learning equivariant representations over combinatorial structures in general and then posets in particular. As a first model we will consider representing the poset as a Directed Acyclic Graph (DAG) and applying a Graph Neural Network (GNN) over it. We will then show how the DAG view does not explicitly encode all known aspects of a poset. Instead, we will consider applying a GNN over the poset zeta matrix (the analogous of the adjacency matrix for a poset). Finally, we will explore non-GNN-based equivariant architectures for representing posets. We will take inspiration from related notions of convolution over powersets to motivate the development of such a machinery.