\subsection{Conversation semantics}

Having ascertained that our agents are conducting bidirectional
conversations, we next try to decode what are the \emph{contents} of
such conversations. To do this, we train separate classifiers to predict, from the message exchanges in successful in-domain test game, what are Fruit, Tool 1, Tool 2 in the game.\footnote{We focus on
  the in-domain set as there are just 5 transfer fruit categories. We
  also tried predicting triples at once with a single classifier, that
  consistently reached above-baseline but very low accuracies.}
Consider for example a game in which fruit is \emph{apple} and tools 1
and 2 \emph{knife} and \emph{spoon}, respectively. If the
message-based classifiers are, say, able to successfully decode
\emph{apple} but not \emph{knife}/\emph{spoon}, this suggests that the
messages are about the fruit but not the tools. For each prediction
task, we train classifiers (i) on the whole conversation, i.e., both
agents' utterances (\emph{Both}), and (ii) on either Player's
utterances: Fruit (\emph{F}) or Tool only (\emph{T}). For comparison,
we also report accuracy of a baseline that makes guesses based on the
train category distribution (\emph{Stats}), which is stronger than
chance. We report  mean accuracy and SEM across successful training seeds. Supplementary Section \ref{suppsec:sem} provides further details
on classifier implementation and training.

\begin{table}[t]
\setlength{\tabcolsep}{2pt}
\small{
\begin{center}
\begin{tabular}{ |c|ccc| }
\hline
 Messages & Fruit & Tool 1 & Tool 2\\
\hline
Both& $37\pm1.70$& $31\pm1.21$& $24\pm1.07$\\
F& $37\pm1.75$& $23.3\pm0.66$& $16.7\pm0.51$\\
T& $14.1\pm0.79$& $32\pm1.17$& $25\pm1.04$\\
\hline
Stats. (\%)& $5.786\pm0.00$& $8.76\pm0.01$& $7.682\pm0.01$\\
\hline
\end{tabular}
\end{center}
}
\caption{Semantic classifier \% accuracy mean and SEM over successful training seeds.}
\label{tab:sem}
\end{table}
%
% \begin{table}[t]
% \setlength{\tabcolsep}{2pt}
% \begin{center}
% \begin{tabular}{ |c|ccc| }
% \hline
%  Messages & Fruit & Tool 1 & Tool 2\\
% \hline
% Both& $29\pm1.62$& $34\pm1.13$& $29\pm1.24$\\
% T& $12.4\pm0.90$& $35\pm1.19$& $29\pm1.27$\\
% F& $28\pm1.71$& $23.8\pm0.86$& $18.4\pm0.68$\\
% \hline
% Stats. (\%)& $5.787\pm0.01$& $8.78\pm0.02$& $7.686\pm0.01$\\
% \hline
% \end{tabular}
% \end{center}
% \caption{Semantic classifier \% accuracy mean and SEM over successful training seeds. Tool starts.}
% \end{table}

The first row of Table \ref{tab:sem} shows that the conversation as a whole carries information about any object. The second and third show that the agents are mostly conveying information about their respective objects (which is very reasonable), but also, to a lesser extent, but still well above baseline-level, about the other agent's input. This latter observation is intriguing. Further work should ascertain if it is an
artifact of fruit-tool correlations, or pointing in the direction of
more interesting linguistic phenomena (e.g., asking
``questions''). The asymmetry between Tool 1 and 2 would also deserve
further study, but importantly the agents are clearly referring to
both tools, showing they are not adopting entirely degenerate
strategies.\footnote{We experiment with single symbol messages (and multi-turn conversation) but using longer messages we could potentially witness interesting phenomena such as the emergence of compositionality. We leave this exploration for future work.}

We tentatively conclude that the agents did develop the expected
semantics, both being able to refer to all objects in the games. Did they
however developed \emph{shared} conventions to refer to them, as in
human language? This would not be an unreasonable expectation, since
the agents are symmetric and learn to play both roles and in both
positions. Following up on the idea of ``self-play'' of
\citet{Grasser:etal:2019}, after a pair of agents A and B are trained,
we replace at test time agent B's embedders and modules with those in
A, that is, we let one agent play with a copy of itself. If A and B
are speaking the same language, this should not affect test
performance. Instead, we find that with self-play average game
performance drops down to $67\%$ and $65 \%$ in in-domain and transfer test
sets, respectively. This suggests that the agents developed their own
idiolects. The fact that performance is still above chance could be
due to the fact that the latter are at least partially exchangeable,
or simply to the fact that agents can still do reasonably well by
relying on knowledge of average tool usefulness (self-play performance
is below that of the communication-less agents in Table
\ref{tab:perftable}). To decide between these interpretations, we
trained the semantic classifier on conversations where A is the Fruit
Player and B the Tool Player, testing on conversations about the same
inputs, but where the roles are inverted. The performance drops down
to the levels of the Stats baseline (Supplementary Table
\ref{tab:invres}), supporting the conclusion that non-random
performance is due to knowledge acquired by the agents independently
of communication, and not partial similarity among their codes.
