Learning Hadamard
2 PM, 28 Oct 2026
Justin Tan describes how learned search may be deployed to find new record-breaking matrices for the Hadamard maximal determinant problem.
The Hadamard maximal determinant problem seeks binary matrices with the highest possible determinant at every order. Its simplicity belies subtle number-theoretic constructions required at n ≡ 3 (mod 4). Dr Justin Tan presents collaborative work combining these ideas with reinforcement learning to set new records in six orders, and argues that similar problems in extremal combinatorics may be resolved in this way.
Mr Justin Tan is a Cognia Junior Research Fellow at LIMS. He studied mathematical physics at the University of Melbourne, followed by a PhD at Cambridge. He works on string theory, computational geometry, and reinforcement learning for interesting problems in pure mathematics.
