A new generation of manycore processors is on the rise that offers dozens and more cores on a chip and, in a sense, fuses host processor and accelerator. In this paper we target the efficient training of generalized linear models on these machines. We propose a novel approach for achieving parallelism which we call Heterogeneous Tasks on Homogeneous Cores (HTHC). It divides the problem into multiple fundamentally different tasks, which themselves are parallelized. For evaluation, we design a detailed, architecture-cognizant implementation of our scheme on a recent 72-core Knights Landing processor that is adaptive to the cache, memory, and core structure. Our library efficiently supports dense and sparse datasets as well as 4-bit quantized data for further possible gains in performance. We show benchmarks for Lasso and SVM with different data sets against straightforward parallel implementations and prior software. In particular, for Lasso on dense data, we improve the state-of-the-art by an order of magnitude.