Research

List of publications (including preprints),

• Embedding Dimension Lower Bounds for Universality of Deep Sets and Janossy Pooling, with Ali Syed, and Jonathan Siegel
• We study the universality of the DeepSets and k-ary Janossy pooling approaches, in particular the important question of how large the embedding dimension must be to guarantee universality of the architecture. Specifically, using a novel technique, we prove new lower bounds on the required size of this embedding dimension for Deepsets and k-ary Janossy pooling (for n points in dimension d)
• Preprint available at https://arxiv.org/abs/2512.16074, submitted to NeurIPS 2026
• In-Context Multi-Operator Learning with DeepOSets, with Shao-Ting Chiu, Ali Syed, Jonathan Siegel, and Ulisses Braga-Neto
• In this paper, we show that the DeepOSets architecture, with the appropriate modifications, is a multi-operator in-context learner that can recover the solution operator of a new PDE, not seen during training, from example pairs of parameter and solution placed in a user prompt, without any weight updates. Furthermore, we show that DeepOSets is a universal uniform approximator over a class of continuous operators
• Preprint available at https://arxiv.org/abs/2512.16074, submitted to NeurIPS 2026