  In this paper, we consider contention resolution algorithms that are
augmented with predictions about the network. We begin by studying the natural
setup in which the algorithm is provided a distribution defined over the
possible network sizes that predicts the likelihood of each size occurring. The
goal is to leverage the predictive power of this distribution to improve on
worst-case time complexity bounds. Using a novel connection between contention
resolution and information theory, we prove lower bounds on the expected time
complexity with respect to the Shannon entropy of the corresponding network
size random variable, for both the collision detection and no collision
detection assumptions. We then analyze upper bounds for these settings,
assuming now that the distribution provided as input might differ from the
actual distribution generating network sizes. We express their performance with
respect to both entropy and the statistical divergence between the two
distributions -- allowing us to quantify the cost of poor predictions. Finally,
we turn our attention to the related perfect advice setting, parameterized with
a length $b\geq 0$, in which all active processes in a given execution are
provided the best possible $b$ bits of information about their network. We
provide tight bounds on the speed-up possible with respect to $b$ for
deterministic and randomized algorithms, with and without collision detection.
These bounds provide a fundamental limit on the maximum power that can be
provided by any predictive model with a bounded output size.
