The Bounded-Cache Transformer uses a fixed-size key-value memory updated by outer-product writes, claiming constant memory and preserved quality without providing experimental data.
Threshold solutions for the intercritical inhomogeneous NLS
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We consider the focusing inhomogeneous nonlinear Schr\"odinger equation in $H^1(\mathbb{R}^3)$, \begin{equation} i\partial_t u + \Delta u + |x|^{-b}|u|^{2}u=0,{equation} where $0 < b <\tfrac{1}{2}$. Previous works have established a blowup/scattering dichotomy below a mass-energy threshold determined by the ground state solution $Q$. In this work, we study solutions exactly at this mass-energy threshold. In addition to the ground state solution, we prove the existence of solutions $Q^\pm$, which approach the standing wave in the positive time direction, but either blow up or scatter in the negative time direction. Using these particular solutions, we classify all possible behaviors for threshold solutions. In particular, the solution either behaves as in the sub-threshold case, or it agrees with $e^{it}Q$, $Q^+$, or $Q^-$ up to the symmetries of the equation.
fields
cs.CL 1years
2024 1verdicts
REJECT 1representative citing papers
citing papers explorer
-
A Method for Building Large Language Models with Predefined KV Cache Capacity
The Bounded-Cache Transformer uses a fixed-size key-value memory updated by outer-product writes, claiming constant memory and preserved quality without providing experimental data.