Not really. Lots of neurons in this part of the brain modulate their activity to movement in heterogeneous ways. The algorithm details vary, but at some level you’re trying to find a 2d x/y velocity signal encoded in the 200d neural signals. This decoder is a bit more sophisticated (using deep learning style approaches), but a Kalman filter was state of the art for a long time.

For the adaptation, there’s a rich literature of neuroscientists in this field studying how the participant adapts to the control characteristics of the decoder, and how the decoding algorithm can be designed to adapt after seeing more data during use. Here’s one paper if you’re interested http://www.stat.columbia.edu/~liam/research/pubs/merel-fox-c...