  We automate the process of machine learning correlations between knot
invariants. For nearly 200,000 distinct sets of input knot invariants together
with an output invariant, we attempt to learn the output invariant by training
a neural network on the input invariants. Correlation between invariants is
measured by the accuracy of the neural network prediction, and bipartite or
tripartite correlations are sequentially filtered from the input invariant sets
so that experiments with larger input sets are checking for true multipartite
correlation. We rediscover several known relationships between polynomial,
homological, and hyperbolic knot invariants, while also finding novel
correlations which are not explained by known results in knot theory. These
unexplained correlations strengthen previous observations concerning links
between Khovanov and knot Floer homology. Our results also point to a new
connection between quantum algebraic and hyperbolic invariants, similar to the
generalized volume conjecture.
