\section{CONCLUSION}
\label{sec:conclusion}
We have introduced $\gamma$-CKL, a scale-free oracle model with a parameter $\gamma$ to control the power of the oracle.
$\gamma$-CKL yields embeddings that are competitive with commonly used choice models.
It scales favourably to high embedding dimensions, a key improvement over CKL.

In the context of interactive search, $\gamma$-CKL outperforms a state-of-the-art implementation based on the Probit model.
Our user study reproduces the existing results in a blind randomized trial and establishes statistically significant improvements for $\gamma$-CKL over {\em Probit}.
Interestingly, we observed not only a reduction in the number of search steps on average, but also a reduction in the average time our subjects took to answer queries.
This suggests a lower cognitive overhead, and provides further evidence that $\gamma$-CKL is well suited to model choices made by a human oracle.

At the same time, $\gamma$-CKL is only one representative of a large family of scale-free oracle models.
Any model that bases its decision only on the ratio of distances between the query points and the target shows scale-free properties.
We hope that our results motivate future researchers to study this type of oracle model.

In particular, a scale-free model enables a new class of efficient search schemes.
Framing the search process as a random walk enables us to construct a scheme with provably exponential convergence. 
We believe that the algorithm discussed in Section \ref{sec:search} would be particularly suitable for searching for procedurally generated content. %
In such a setting, viable parametrizations are often continuous. 
In our work, we have focused on a rigorous proof of the exponential convergence rate.
Future researchers can build on our insights by improving the query efficiency of the algorithm.
Introducing active learning to the stages of the exponential algorithm, for example by optimizing expected information gain, is a promising extension.
