המטריקה המקפצת: שימוש חוזר כמסגרת רוחב-אופטימלית לפיצול סטרוקטורלי בלמידה רציפה

תקציר מקורי באנגליתarXiv:2603.15412v2 Announce Type: replace Abstract: The mammalian brain, most extensively studied in rodents and bats, solves an enormous variety of non-spatial cognitive tasks using neural circuitry, including grid cells, place cells, and hippocampal indexing, that originally evolved for physical navigation. We formalize the above observation within the local Urysohn width (LUW) framework for continual learning. The central construct is the \emph{metric slingshot}: a learned embedding $\phi: X \to Z$ that maps an arbitrary learning problem into a navigational latent space $Z$ where pre-evolved contraction maps (grid cells) already provide the metric machinery, so that only the topological indexing subproblem must be solved de novo. We prove three results. First, the optimal spacing of mul