Uniform $\mathcal{C}^k$ Approximation of $G$-Invariant and Antisymmetric Functions, Embedding Dimensions, and Polynomial Representations

no code implementations • 2 Mar 2024 • Soumya Ganguly, Khoa Tran, Rahul Sarkar

For any subgroup $G$ of the symmetric group $\mathcal{S}_n$ on $n$ symbols, we present results for the uniform $\mathcal{C}^k$ approximation of $G$-invariant functions by $G$-invariant polynomials.

Mathematical conjecture generation using machine intelligence

no code implementations • 12 Jun 2023 • Challenger Mishra, Subhayan Roy Moulik, Rahul Sarkar

Finally, we propose a pipeline of mathematical discovery in this space and highlight the importance of domain expertise in this pipeline.

An improvement to a result about graph isomorphism networks using the prime factorization theorem

no code implementations • 2 May 2022 • Rahul Sarkar

The unique prime factorization theorem is used to show the existence of a function on a countable set $\mathcal{X}$ so that the sum aggregator function is injective on all multisets of $\mathcal{X}$ of finite size.