Tensors in artificial intelligence

The nervous system acts as a state machine, taking an input vector at time t1 and a state vector (memory) at time t1 and generating an output vector and state vector at time t2.  Since the input vector and state vector at t1 are typically not parallel to the output vector and state vector at t2 one is led to consider tensors in order to perform the calculations of output and state at t2 from the input and state at t1.  There has been a limited amount of work along these lines; the papers by Pellionisz and Llinas (for example, Neuroscience, vol. 16, pg 245, 1985) and the PhD thesis of C. P. Dolan, UCLA, 1989.