Optimal prediction with resource constraints using the information bottleneck

Author summary From catching a ball to building immunity, we rely on the ability of biological systems to incorporate past observations to make predictions about the future state of the environment. However, the success of these predictions is limited by environmental parameters and encoding capacities of the predictors. We explore these trade-offs in three systems: simple intertial motion, more complex motion with long-tailed temporal correlations, and mutating viral strains. We show that the velocity and position of a moving object should not be equally well-remembered in the biological systems internal representation, and identify the flexible "best-compromise" representations that are not optimal but remain predictable in a wide range of parameters regimes. In the evolutionary context, we find that the optimal predictive representations are discrete, reminiscent of immune strategies that cover the space of potential viruses. Responding to stimuli requires that organisms encode information about the external world. Not all parts of the input are important for behavior, and resource limitations demand that signals be compressed. Prediction of the future input is widely beneficial in many biological systems. We compute the trade-offs between representing the past faithfully and predicting the future using the information bottleneck approach, for input dynamics with different levels of complexity. For motion prediction, we show that, depending on the parameters in the input dynamics, velocity or position information is more useful for accurate prediction. We show which motion representations are easiest to re-use for accurate prediction in other motion contexts, and identify and quantify those with the highest transferability. For non-Markovian dynamics, we explore the role of long-term memory in shaping the internal representation. Lastly, we show that prediction in evolutionary population dynamics is linked to clustering allele frequencies into non-overlapping memories.