Commit 8a40dae5 by YZhao

..

parent f40a1f4e
......@@ -36,5 +36,12 @@ MIS_0 = \frac{1}{M}\sum_{j=0}^{M-1}\frac{\max_{i\in[0,N-1]}RI\left(c_i,s_j\right
MIS = \frac{N\cdot MIS_0 - 1}{N-1}
\end{equation}
\begin{figure}[t]
\centering
\includegraphics[width=0.9\columnwidth]{fig/occupy}
\caption{An emergent language that the unilateral metrics cannot measure its non-compositionality. Notice that when $s_1 = \mathrm{a}$, the listener can neither determine the shape nor the color without the knowledge about $s_0$.}
\label{fig:unilateral}
\end{figure}
MIS is a bilateral metric. Unilateral metrics, e.g. \emph{topographic similarity (topo)}\cite{} and \emph{posdis}\cite{}, only take the policy of the speaker into consideration. We provide an example to illustrate the inadequacy of unilateral metrics, as shown in Figure~\ref{fig:unilateral}. In this example, the speaker only uses $s_1$ to represent shape. From the perspective of speaker, the language is perfectly compositional (i.e. both topo and posdis are 1). However, the listener cannot distinguish the shape depend only on $s_1$, showing the non-compositionality in this language. The bilateral metric MIS addresses such defect by taking the policy of the listener into account, thus MIS < 1.
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment