andLearning

Broadly speaking, compression eitherinvolvesquantization [33,50,27,26,28-31,15, 32]to reduce the precision of transmitted information, or biased sparsification [24,25,35,34,51, 52, 49, 53] to transmit only a few components of a vector with the largest magnitudes. TheDIANAtechnique was further generalized in [31]to account for avariety of compressors. For0 < η 1 L+β < 1 Li+β, i S, we have0 < 1 η(λi +β) < 1, and hence,D is asymmetric positive-definite matrix. In this section, we will compile some results that will proveto be useful later in our analysis. Wedosotosetupthebasic proof structure that we will later build on for analyzing more involved settings.