Predicting the future from the past in visual object motion: optimal representations of mixed stochastic/deterministic trajectories

Making predictions about the future state of the external world confers benefits to biological systems that can translate to increased fitness. This requires that sensory systems encode information about the stimulus in a manner suitable for prediction. However, physical constraints, such as finite metabolism and finite computing power, result in additional evolutionary pressures. These favor organisms that compress the representation of the input stimulus statistics along particular readout dimensions, creating an underlying tension between representing the statistics of a stimulus while preserving the information relevant to prediction. Here, we propose that the encoding scheme used by such biological systems can be predicted by the information bottleneck method. Using this technique, we can compute the optimal form of the encoding distribution for a variety of mixed stochastic and deterministic stimuli and demonstrate that these encoding distributions are optimized for prediction tasks at different timescales. We also consider the optimal encoding distribution when the underlying parameters of the stimulus evolve in time.