The emergence of human language has always been an important and controversial
issue. This problem attracts attentions from a broad range of communities,
including philology~\cite{}, biology~\cite{}, and computer
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@@ -26,6 +27,11 @@ compostionality). In this example, each shape is represented by a unique value
of symbol $s_0$ and each color is represented by symbol $s_1$. Figure1(b) shows a
language with low compostionality. Colors and shapes are ambiguous if only we
extract information from a single symbol.
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The emergence of human language has always been an important and controversial issue. This problem attracts attentions from a broad range of communities, including philology, biology and computer science. In computer science, researchers induce and analyze the emergent language in multi-agent systems by setting up communication scenarios, such as referential games and communication-action policies.
Compositionality is a widely used metric to evaluate the emergent language. It is a concept in the philosophy of language [1], which describes and quantifies how complex expressions can be assembled out of simpler parts [2]. For example, Figure1(a) shows a perfect compositional language (with maximum compostionality). In this example, each shape is represented by a unique value of symbol s_0 and each color is represented by symbol s_1. Figure1(b) shows a language with low compostionality. Colors and shapes are ambiguous if only we extract information from a single symbol.
>>>>>>> 4ed7826846e80d0c69ee5244e0e20fc563300e19
\begin{figure}[t]
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@@ -39,65 +45,22 @@ low compostionality.}
\label{fig:symbols}
\end{figure}
Prior studies focus on investigating how to affect the compositionality of the
emergent language. Researchers have found that various environmental pressures
would affect compositionality, e.g., small vocabulary sizes[3], memoryless[4],
carefully constructed rewards[5] and ease-of-teaching[6]. However, these works
only consider \emph{nurture} [7] (i.e., environmental factors), rather than
\emph{nature} (i.e., hereditary factors from agents), when inducing or exploring
the emergent language without exception. Moreover, some environmental pressures,
like regrading the entropy as an item of additional rewards, may be too ideal to
exist in the real world.
In contrast to prior work, we investigate the compositionality of emergent
language from a new perspective, i.e., the agent capacity. Different from
previous work that only considers external environmental factors, we study the
impact of agent internal capacity on the compositionality of emergent
language. Specifically, we first analyze the correlation between agent capacity
and compositionality theoretically, and propose a novel metric to evaluate
compostionality quantitatively. Then, on the basis of the theoretical analysis
and the metric proposed, we verify the relationship between agent capacity and
compostionality experimentally.
Theoretically, on the basis of mutual information theory[8], we analyse the
correlation between compostionality of the emergent language and complexity of
the semantic information carried by a symbol. Such semantic information can be
characterized in neural network-based agents and requires the certain capacity
(i.e., the count of neural nodes in the hidden layer). Specifically, we use the
MSC (Markov Series Channel)[9] to model the language transmission process and
use the probability distribution of symbols and concepts to model policies of
agents. After modelling, we use the mutual information matrix $MRI^B$ to
quantitatively represent the semantic information, and each column of $MRI^B$
correspond to information carried by one symbol. We find that each column of the
matrix should be an one-hot vector for a perfectly compositional language, cause
a symbol only transmit information of a certain concept exclusively. Therefore,
the average similarity between the columns of $MRI^B$ and a one-hot vector is
higher, indicating that the emergent language is more compostional (i.e., the
compostionality is higher). We propose the metric \emph{MIS} to measure
compositionality by calculating such average similarity
quantitatively. Moreover, MIS comes lower indicates that the emergent language
tends to delivery semantic information about more concepts in each symbol, so
that the complexity of semantic information carried by one symbol tend to be
higher. As a result, higher agent capacity is required to characterize the more
complex semantic information when MIS (i.e., compositionality) is lower.
Experimentally, we verify the relationship between agent capacity and
compostionality in a
Then with experiments we show that a low-bilateral (i.e. low-compositionality)
language needs higher capacity of the model to emerge. We build a
listener-speaker referential game as experimental framework, and train agents
with the correctness of forecast output from the listener as the only
criterion. The criterion does not imply any environmental pressures on the
agents. Therefore, we can study the impact of capacity on the compositionality
without any environmental pressures’ affection. Moreover, to study the impact of
capacity on the compositionality under a more ‘natural’ environment, the speaker
and listener are individual agents, i.e. disconnected models without sharing
parameters. The conclusion suggests that by restricting the number of neurons in
a model the emerging languages attend to have higher bilaterality, thus higher
compositionality.
Prior studies focus on investigating how to affect the compositionality of the emergent language. Researchers have found that various environmental pressures would affect compositionality, e.g., small vocabulary sizes[3], memoryless[4], carefully constructed rewards[5] and ease-of-teaching[6]. However, these works only consider \emph{nurture} [7] (i.e., environmental factors), rather than \emph{nature} (i.e., hereditary factors from agents), when inducing or exploring the emergent language without exception. Moreover, some environmental pressures, like regrading the entropy as an item of additional rewards, may be too ideal to exist in the real world.
In contrast to prior work, we investigate the compositionality of emergent language from a new perspective, i.e., the agent capacity. Different from previous work that only considers external environmental factors, we study the impact of agent internal capacity on the compositionality of emergent language. Specifically, we first analyze the correlation between agent capacity and compositionality theoretically, and propose a novel metric to evaluate compostionality quantitatively. Then, on the basis of the theoretical analysis and the metric proposed, we verify the relationship between agent capacity and compostionality experimentally.
Theoretically, on the basis of mutual information theory[8], we analyse the correlation between compostionality of the emergent language and complexity of the semantic information carried by a symbol. Such semantic information can be characterized in neural network-based agents and requires the certain capacity (i.e., the count of neural nodes in the hidden layer). Specifically, we use the MSC (Markov Series Channel)[9] to model the language transmission process and use the probability distribution of symbols and concepts to model policies of agents. After modelling, we use the mutual information matrix MRI^B to quantitatively represent the semantic information, and each column of MRI^B correspond to information carried by one symbol. We find that each column of the matrix should be an one-hot vector for a perfectly compositional language, cause a symbol only transmit information of a certain concept exclusively. Therefore, the average similarity between the columns of MRI^B and a one-hot vector is higher, indicating that the emergent language is more compostional (i.e., the compostionality is higher). We propose the metric \emph{MIS} to measure compositionality by calculating such average similarity quantitatively. Different from other metrics, such as \emph{topographic similarity}[10] and \emph{posdis}[11], \emph{MIS} is a bilateral metric because it takes both listener and speaker's understanding of semantics into account. Moreover, \emph{MIS} comes lower indicates that the emergent language tends to delivery semantic information about more concepts in each symbol, so that the complexity of semantic information carried by one symbol tend to be higher. As a result, higher agent capacity is required to characterize the more complex semantic information when \emph{MIS} (i.e., compositionality) is lower.
Experimentally, we verify the relationship between agent capacity and compostionality. We build a listener-speaker referential game as experimental framework, and train agents of Stochastic Policy Gradient Algorithm[12] with the correctness of forecast output from the listener as the criterion (i.e., reward). The criterion does not imply any environmental pressures on the agents. Therefore, we can study the impact of capacity on the compositionality without any environmental pressures’ affection. Moreover, to study the impact of capacity on the compositionality under a more ‘natural’ environment, the speaker and listener are disconnected models without sharing parameters. Our first experiment is to verify that agent need higher capacity to master an artificial language with lower compositionality under a scenario of language teaching. Specifically, we fabricate the speaker to output preassigned languages with different compostionality respectively, and train the listener to interpret the preassigned language. For all artificial language, we compare the accuracy curve during training process of the listener with different capacity, and show how capacity affect learning languages with different compostionality. Our second experiment is to verify that lower agent capacity would facilitate higher compostionality of the emergent language under a scenario of language inducing. Specifically, we training a speaker and a listener to create a communication protocol (i.e., emergent language), so that the listener can select the same object which is received by the speaker. By adjusting capacity and comparing the compositionality of emergent language, we show that the emergent language attend to have higher compositionality when agent capacity is restricted more stringently. As a result, these two experiments verify the negative correlation between agent capacity and compostionality both in language teaching and language inducing.
This paper makes the following contributions:
We propose a ‘bilateral’ metric \emph{MIS}, which takes both listener and speaker's understanding of semantics into account. Compare to previous ‘unilateral’ metrics, \emph{MIS} can handle situations where the semantics of the listener and the speaker are not exactly the same (, we discuss the problem in next section).
We analyse the relationship between compostionality and agent capacity theoretically.
We verify the negative correlation between agent capacity and compostionality both in language teaching and language inducing.
