FPGA Implementations of Kernel Normalised Least Mean Squares Processors

Kernel adaptive filters (KAFs) are online machine learning algorithms which are amenable to highly efficient streaming implementations. They require only a single pass through the data and can act as universal approximators, i.e. approximate any continuous function with arbitrary accuracy. KAFs are members of a family of kernel methods which apply an implicit non-linear mapping of input data to a high dimensional feature space, permitting learning algorithms to be expressed entirely as inner products. Such an approach avoids explicit projection into the feature space, enabling computational efficiency. In this paper, we propose the first fully pipelined implementation of the kernel normalised least mean squares algorithm for regression. Independent training tasks necessary for hyperparameter optimisation fill pipeline stages, so no stall cycles to resolve dependencies are required. Together with other optimisations to reduce resource utilisation and latency, our core achieves 161 GFLOPS on a Virtex 7 XC7VX485T FPGA for a floating point implementation and 211 GOPS for fixed point. Our PCI Express based floating-point system implementation achieves 80% of the core’s speed, this being a speedup of 10× over an optimised implementation on a desktop processor and 2.66× over a GPU.