Neural Computation and Time

Time is not only the fundamental organizing principle of the universe, it is also the primary organizer of information about the world we perceive. Our brain encodes these perceptions in sequential patterns of spiking activity. But different stimuli lead to different information encoded on different timescales; sometimes the same stimulus carries information pertaining to different perceptions on different timescales. The orders of time are many and the computational circuits of the brain must disentangle these interwoven threads to decode the underlying structure. This thesis deals with solutions to this disentanglement problem implemented not at the network level, but in smaller systems and single neurons that represent the past by clever use of internal mechanisms. Often, these solutions involve the intricate tools of the neural dendrite or other peculiar aspects of neural circuits that are well known to physiologists and biologists but disregarded in favor of more homogeneous models by many theoreticians. It is at the intersection of the diverse biological reality of the brain and the difficulty of the computational problem to disentangle the threads of temporal order that we find new and powerful computational principles: Symbolic computation on the level of single neurons via dendritic plateau potentials, embedding history in delayed feedback dynamics or consecutive filter responses, or the idea that learning a generalized differential description of a systems can largely forgo the need to remember the past – instead, patterns can freely be generated. Together, the different challenges that information ordered in different, asynchronous times present require a diverse palette of solutions. At the same time, computation and the structure imposed by time are deeply connected