4 papers
A Hierarchical Language Model with Predictable Scaling Laws and Provable Benefits of Reasoning
Jason Gaitonde, Frederic Koehler, Elchanan Mossel +2
We introduce a family of synthetic languages with hierarchical structure -- generated by a broadcast process on trees -- for which the role of context length and reasoning in autor…
Rotationally invariant first passage percolation: Breaking the variance barrier
Riddhipratim Basu, Vladas Sidoravicius, Allan Sly
For first passage percolation (FPP) on Euclidean lattices with , it is expected that the variance of the first passage time between two points grows sublinea…
Rotationally invariant first passage percolation: Concentration and scaling relations
Riddhipratim Basu, Vladas Sidoravicius, Allan Sly
For rotationally invariant first passage percolation (FPP) on the plane, we use a multi-scale argument to prove stretched exponential concentration of the first passage times at th…
Coalescence of Geodesics in Exactly Solvable Models of Last Passage Percolation
Riddhipratim Basu, Sourav Sarkar, Allan Sly
Coalescence of semi-infinite geodesics remains a central question in planar first passage percolation. In this paper we study finer properties of the coalescence structure of finit…