Forward and Backward Inference in Spatial Cognition

This paper shows that the various computations underlying spatial cognition can be implemented using statistical inference in a single probabilistic model. Inference is implemented using a common set of ‘lower-level’ computations involving forward and backward inference over time. For example, to estimate where you are in a known environment, forward inference is used to optimally combine location estimates from path integration with those from sensory input. To decide which way to turn to reach a goal, forward inference is used to compute the likelihood of reaching that goal under each option. To work out which environment you are in, forward inference is used to compute the likelihood of sensory observations under the different hypotheses. For reaching sensory goals that require a chaining together of decisions, forward inference can be used to compute a state trajectory that will lead to that goal, and backward inference to refine the route and estimate control signals that produce the required trajectory. We propose that these computations are reflected in recent findings of pattern replay in the mammalian brain. Specifically, that theta sequences reflect decision making, theta flickering reflects model selection, and remote replay reflects route and motor planning. We also propose a mapping of the above computational processes onto lateral and medial entorhinal cortex and hippocampus.Author Summary: The ability of mammals to navigate is well studied, both behaviourally and in terms on the underlying neurophysiology. Navigation is a well studied topic in computational fields such as machine learning and signal processing. However, studies in computational neuroscience, which draw together these findings, have mainly focused on specific navigation tasks such as spatial localisation. In this paper, we propose a single probabilistic model which can support multiple tasks, from working out which environment you are in, to computing a sequence of motor commands that will take you to a sensory goal, such as being warm or viewing a particular object. We describe how these tasks can be implemented using a common set of lower level algorithms that implement ‘forward and backward inference over time’. We relate these algorithms to recent findings in animal electrophysiology, where sequences of hippocampal cell activations are observed before, during or after a navigation task, and these sequences are played either forwards or backwards. Additionally, one function of the hippocampus that is preserved across mammals is that it integrates spatial and non-spatial information, and we propose how the forward and backward inference algorithms naturally map onto this architecture.