Emergent Communication under Varying Sizes and Connectivities

1 Introduction . Communication plays a vital role for us humans to interact with one another [ Austin , 1975 , Allwood , 1976 , Linell , 2009 ] . We acquire new information about the environment and other people around us through communication , which further facilitates collaboration or competition and allows us to coordinate our future decisions and actions better . Over the past decades , numerous research outcomes have succeeded in mimicking human behavior and making artificial agents equipped with interactive communication abilities [ Batali , 1998 , Cangelosi and Parisi , 2002 , Christiansen and Kirby , 2003 , Steels , 2003 , Wagner et al. , 2003 ] . The communication in the artificial system is emergent in a way that there are no pre-specified usage rules , semantics , or syntax , all of which are formed by the artificial agents upon their necessities [ Lazaridou et al. , 2017 ] . Not only does empowering agents with their own communicative abilities set an important milestone in interactive AI systems , it also brings us steps closer to the world where machines cooperate with humans [ Mikolov et al. , 2016 , Crandall et al. , 2018 , Lazaridou and Baroni , 2020 ] . In human societies , hundreds of millions of people use the shared , agreed communication protocols to interact . As the group becomes more complex with increased size and connectivity , communication becomes more and more vital for us to coordinate with one another . Fortunately , we humans excel at using languages for large-group coordination and problem-solving [ Tomasello , 2010 , Lupyan and Bergen , 2016 ] . However , in the AI system counterpart , the question of how emergent communication will function under different group settings is understudied . As the group becomes more complex , will emergent communication become more effective for the system in promoting group coordination , as in human society , or will it lose its functionality ? Will the emergent communication still converge 35th Conference on Neural Information Processing Systems ( NeurIPS 2021 ) . to a shared , agreed language ? In the worst case , efficient interaction among agents through emergent communication can be hampered because different agents will start to use different languages to describe the same observation ( the left-most panel of Figure 1 ) . This research provides an analytical study on emergent communication in artificial groups of different sizes and connectivities . Our goal is to investigate the effect of emergent communication and analyze how agents ’ general agreement on the communication protocol changes under varying group settings . To study this question , we construct settings within which communication among agents is indispensable for achieving their shared goals . Communication is their only means to interact and compensate for their limited access to information from an environment . We divide agents into two groups and allow an agent to communicate with another agent in a different group through a bi-partite communication graph . To quantitatively evaluate the functional aspect of communication , we look at ( a ) the language similarity or message agreement of agents within the same group when describing the same referents and ( b ) the rate at which an arbitrary pair of agents in the bi-partite communication group succeed in communication and achieve the shared goal . To this end , our contributions and findings are as follows : ( 1 ) We find that as the size of the communication graph scales up to hundreds , the language used in the group becomes less similar amongst agents . However , the communication success rate is maintained . ( 2 ) We observe that when agents only get to communicate with nearby agents , a particular form of communication peculiar to agents ’ locality emerges . At the same time , distant pairs of agents that have not interacted during training can still communicate when a certain threshold for the maximal communication distance is reached . ( 3 ) We present and analyze the optimized communication graph in terms of overall communication success rate when ( a ) the node outdegrees are fixed or when ( b ) we penalize the formation of communication links between a distant pair of agents . Compared to the fully-connected all-to-all graph , the link density decreases by 81.25 % , but the communication success rate drops just by 5.89 % . With random , unoptimized communication links , the success rate drops by over 40 % with the same link density . Throughout the optimization process , we observe the emergence of hub nodes taking up a large share of the total communication channels and connecting the majority of other agent nodes , as we see in the real-world scale-free social networks [ Barabási and Albert , 1999 ] . 2 Related work . There have been successive attempts to let agents develop their own communication protocols through emergent communication [ Batali , 1998 , Cangelosi and Parisi , 2002 , Christiansen and Kirby , 2003 , Steels , 2003 , Wagner et al. , 2003 ] , followed by more recent approaches that are based on deep neural networks [ Foerster et al. , 2016 , Sukhbaatar et al. , 2016 , Hausknecht , 2016 , Havrylov and Titov , 2017 ] . 1 The idea is applied and extended to a variety of collaborative [ Lowe et al. , 2020 , Hu and Foerster , 2020 , Jaques et al. , 2019 , Kajić et al. , 2020 , Mordatch and Abbeel , 2018 ] and competitive [ Singh et al. , 2019 , Jaques et al. , 2019 ] environments . Recently , advances have been made for the emergent communication to be operationalized at scale ; to prevent agents from being `` lazy '' and let them generate meaningful signals [ Sunehag et al. , 2018 ] ; to effectively schedule 1The work by Lazaridou and Baroni [ 2020 ] surveys the nascent literature . the communication in a limited bandwidth [ Kim et al. , 2019 ] ; to foster conditions that encourage compositional and easier-to-teach languages [ Li and Bowling , 2019 ] ; to understand other agents ’ intention , belief , and point of view , i.e. , theory of mind [ Hu and Foerster , 2020 ] ; to win a combat against another group [ Singh et al. , 2019 ] . Orthogonally , there has been attempts to make the interactive communication more dynamic and more human-like by increasing the complexity of the environment [ Jaques et al. , 2019 , Das et al. , 2019 ] , making the communication span multiple turns [ Evtimova et al. , 2018 , Jorge et al. , 2016 ] . These lines of research focus on increasing the efficacy functionality of the emergent communication by suggesting more advanced perceptual , navigational , and generative AI capabilities . On the other hand , our work falls into the category of an analytical study of understanding the emergent communication from various perspectives . Recent studies find properties of emergent language that sets itself aside from [ Chaabouni et al. , 2019 , Kottur et al. , 2017 ] or are shared with [ Resnick et al. , 2020 , Baroni , 2020 ] natural human languages and seek for different possibilities to benefit existing NLP models [ Lee et al. , 2018 , Lazaridou et al. , 2020 ] . Bouchacourt and Baroni [ 2019 ] and Cao et al . [ 2018 ] studies various conditions under which the emerged language can be consonant and agreed as apposed to giving rise to idiolects or agent identity playing a crucial factor in interactive systems . The work of Graesser et al . [ 2019 ] is especially similar to ours in that it also studies the linguistic phenomena of emergent communication at a group ( community ) level . Specifically , the authors formulate one , two , or five artificial communities each of which comprising agents up to size 30 . By changing the inter and intra-community connection densities , the authors reproduce linguistic behaviors that can be observed in human communities . One of the findings is the emergence of the `` linguistic continuum '' , which to a great degree resembles our finding of `` dialects '' in section 5.4 . Our work is distinctive in a way that we do not assign agents into hard clusters of communities . Therefore , we observe finer granularities of linguistic continuums ( dialects ) at agent-levels rather than at community-levels . Finally , Dubova and Moskvichev [ 2020 ] , Dubova et al . [ 2020 ] , Tieleman et al . [ 2019 ] also studies emergent communications in group settings . 3 Game design . We design a communication game based on partial information . The purpose of the game is similar to that of the referential game [ Lazaridou et al. , 2017 ] , which is a variant of the signaling game [ Lewis , 1969 ] ; we test whether an artificial agent can perceive a given observation , speak through the emergent protocol about the observation according to the instruction , listen and make the right decision . Throughout the game , the message from the speaker agent should convey crucial information about the observation for the game to succeed . Compared to the referential game , the difference is : 1 ) agents only get to have partial , mutually exclusive information of the observations , so the communication should solely be about describing what information each agent has from their partial , limited observation , 2 ) The instruction information is symmetric for both listener and speaker : both agents have access to the instruction . In each game trial , two agents are presented with multiple pixel-based objects : a target , distractors , and instruction . The goal is to choose the correct target object for the description in the instruction . Crucially , communication is indispensable for the agents to correctly find the target since each of the two agents has its own limitation in the perception : One agent can only recognize different shapes , and the other can only differentiate colors . Therefore , the information of the object retrieved by the agents from their observations is mutually exclusive , but at the same time , is guaranteed to recover the complete state information when aggregated . Under this setting , the agents communicate based on their limited observations to compensate for their deficiencies and correctly choose the target object described in the instruction . In section 5.3 , we derive similar findings using the more conventional referential game as well . Agent and action Each of the two non-embodied agents is chosen from two distinctive groups . We denote agents that can only perceive colors ( i.e. , the color-only agents ) by c , and the corresponding group by Gc , such that c 2 Gc . Similarly , the shape-only agents and the corresponding group are denoted by s and Gs . The number of agents of both groups is set to be the same , i.e. , |Gc| = |G s | = N . We consider a situated environment , where the action space A is divided into the disjoint communication action space Am and decision-making action space Ae , such that Am [ Ae = A and A m \A e = ; . Of color-only and shape-only agents , one is randomly selected and act as a speaker ; it takes its observations , i.e. , objects and instruction , as inputs and sends a message m 2 Am to the other agent as an output , which can be either discrete or continuous . Next , the other agent is randomly selected and act as a listener . This agent takes the message along with the observations and makes a decision d 2 Ae . The decision is about choosing the position of the correct target object . Thus , the size of the decision making action space |Ae| is equal to the number of objects in the observation . Finally , the communication between agents ( c , s ) is successful if the decision d finds the target object . In the referential games , both speaker and listener agents get to observe the full information about the objects , i.e. , both shapes and colors , but only the speaker agent has an access to the instruction and the orders of the objects are shuffled for the listener agent . State and observation A state s is a 3-tuple s = ( ot , Od , w ) with the target object ot , the distractor objects Od , and the instruction w. Each object is of different colors and shapes 2 , and the instruction tells of choosing an object with certain color and shape . Therefore , for n and m different colors and shapes , there can be n ⇥m varying instructions . We represent the instruction using a fixed-sized vector by concatenating n and m-dimensional one-hot vectors . Observations comprise objects and instructions . In section 5.3 , we also conduct experiments using real-world images [ Krizhevsky , 2009 ] instead of the artificial shape and color observations . Communication graph A bipartite communication graph G is formed between Gc and Gs as multiple pairs ( c , s ) communicate , i.e. , form a set of directed communication links ( c , s ) , ( s , c ) 2 E , and establish communication protocols . Message agreement and communication success rate We introduce message agreement and communication success rates used to evaluate language convergence . First , let a and a0 be two agents randomly sampled from the same color-only or shape-only group , i.e. , a , a0 2 Gc or a , a0 2 Gs , and let ma and ma 0 be the messages generated by the agents from the same observation o 2 O . The message agreement of a certain group , which is either color-only or shape-only , in a communication graph is measured by the expected similarity between two messages ma and ma 0 : Ea , a0⇠G0 , o⇠O [ f ( ma , ma 0 ) |o ] , where f ( · , · ) is a similarity measure and G0 2 { Gc , Gs } . Next , the communication success rate of a communication graph is measured as : Ec⇠Gc , s⇠Gs , o⇠O [ r ( c , s , o ) ] with r being an identity function that returns 1 if agents successfully find the target object .

Summary: The paper studies the effect of population size and graph connectivity on the emergence of communication. The main questions studied in the paper were 1) how does the size of agents' population affect task success? and 2) when agents don't get to train directly, but through some other agents, how well they can communicate with each other when they put in contact? The game that was used in this paper to study the problem, was a referential game, and the task was discrimination task. The agents can take 2 roles of speaker and listener, such that speaker gets some observation and send a message to listener, and listener gets some other observation along with speaker's message, and it has to make a decision in a discriminative setup.