20 February 2021 • Jack Hirsch and Kevin Li and Jackson Petty and Christopher Xue
The hexagon is the least-perimeter tile in the Euclidean plane. On hyperbolic surfaces, the isoperimetric problem differs for every given area. Cox conjectured that a regular k-gonal tile with 120-degree angles is isoperimetric for its area. We prove his conjecture and more.
20 November 2020 • Robert Frank and Jackson Petty (Equal Contribution)
Reflexive anaphora present a challenge for semantic interpretation: their meaning varies depending on context in a way that appears to require abstract variables. We consider sequence-to-sequence architectures with recurrent units and show that such networks are capable of learning semantic interpretations for reflexive anaphora which generalize to novel antecedents.