Many knot invariants in knot theory are discovered by finding a property of knot diagrams which is invariant under the three Reidemeister moves. Now in principle, any knot invariant can be described in a diagram-independent way, that is, as a property of the three-dimensional knot itself without reference to diagrams of the knot. But in practice, it can take years between the development of a knot invariant and the discovery of a diagram-independent description of it.

So my question is, for what knot invariants is a diagram-independent description not yet known?