Scale-invariant temporal history (SITH): optimal slicing of the past in an uncertain world

In both the human brain and any general artificial intelligence (AI), a representation of the past is necessary to predict the future. However, perfect storage of all experiences is not feasible. One possibility, utilized in many applications, is to retain information about the past in a buffer. A limitation of this approach is that, although events in the buffer are represented with perfect accuracy, the resources necessary to represent information at multiple time scales go up rapidly. Here we present a neurally-plausible, compressed, scale-free memory representation we call Scale-Invariant Temporal History (SITH). This representation covers an exponentially large period of time at the cost of sacrificing temporal accuracy for events further in the past. The form of this decay is scale-invariant and can be shown to be optimal, in that it is able to respond to worlds with a wide range of relevant time scales. We demonstrate the utility of this representation in learning to play video games at different levels of complexity. In these environments, SITH exhibits better learning performance than both a fixed-size buffer history representation and a representation with exponentially decaying features. Whereas the buffer performs well as long as the temporal dependencies can be represented within the buffer, SITH performs well over a much larger range of time scales with the same amount of resources. Finally, we discuss how the application of SITH, along with other human-inspired models of cognition, could improve reinforcement and machine learning algorithms in general.