Flatness is really an algebraic notion with a subtle geometric interpretation. It is best explained in terms of modules and illustrated by morphisms. De nition 1 Let A be a ring and M an A-module. Then M is …

We design a specialized dataflow, Fused Logit Attention Tiling (Flat), targeting the two memory BW-bound operators in the atten-tion layer, L and A. Flat includes both intra-operator dataflow and a …

We say that N is flat if ⌦ N is exact, or equivalently if. M1 ⌦ N ! M2 ⌦ N. is injective for every sequence. = 0. (There other equivalent formulations in the literature but we won’t use them.) …

057N In this chapter, we discuss some advanced results on flat modules and flat mor- phismsofschemesandapplications. Mostoftheresultsonflatnesscanbefound …

Various problems of geometry, topology and dynamical systems on sur-faces as well as some questions concerning one-dimensional dynamical systems lead to the study of closed surfaces endowed with a …

Equational criterion). An A module M is flat if and only if every relation in M is trivial, i.e., for every relation Í i fixi 0 in M there are elements yj 2 M and elements aij Í 2 A such that xi j aij yj for all i a

Denote by A(P) the set of connections on P, and Aflat(P) the set of flat connections. Let G(P) denote the gauge group. This is defined as the space of maps u : P ! G that are equivariant: for all p 2 P, g 2 G. …