One-to-Many Communication and Compositionality in Emergent Communication (2024)

Abstract: Compositional languages leverage rules that derive meaning from combinations of simpler constituents. This property is considered to be the hallmark of human language as it enables the ability to express novel concepts and ease of learning. As such, numerous studies in the emergent communication field explore the prerequisite conditions for emergence of compositionality. Most of these studies set out one-to-one communication environment wherein a speaker interacts with a single listener during a single round of communication game. However, real-world communications often involve multiple listeners; their interests may vary and they may even need to coordinate among themselves to be successful at a given task. This work investigates the effects of one-to-many communication environment on emergent languages where a single speaker broadcasts its message to multiple listeners to cooperatively solve a task. We observe that simply broadcasting the speaker’s message to multiple listeners does not induce more compositional languages. We then find and analyze two axes of environmental pressures that facilitate emergence of compositionality: listeners of *different interests* and *coordination* among listeners.

## introduction the field of emergent communication studies the core environmental factors in language emergence and the characteristics of emergent languages in relation to those of humans. the recent developments in artificial neural networks have spurred research on the field utilizing communication simulations of neural agents @xcite . this has served as a crucial testbed for studying evolution of language @xcite , which often lacks concrete physical trace. the field has also demonstrated promising application possibilities in numerous domains leveraging language's desirable properties @xcite @xcite . @xcite is one of the most prominent features of human languages. compositional languages can express complex meaning with combinations of simpler attributes leveraging systematic rule structures. this enables the ability to express novel concepts by combining familiar attributes. compositionality is also attributed to enhancing languages' learnability @xcite and gives rise to robustness to noisy communication channel @xcite . determining the prerequisite environmental pressures for emergence of compositionality has been extensively studied in the field. these factors include language's learnability @xcite @xcite , agents' capacity @xcite , reliability of communication channel @xcite , task difficulty @xcite @xcite @xcite , and communication channel capacity @xcite . recently, populations of agents have been investigated as a driving force for emergence of compositionality @xcite following prior sociolinguistic findings that larger population sizes tend to derive more structured languages @xcite . most of these studies take one-to-one communication regime where only a single speaker-listener pair interacts with each other during an instance of game play. even when there are multiple listeners in the system, a speaker's message is only sent to a single listener @xcite @xcite @xcite . consequently, they fail to model the effects of one-to-many communication in emergent languages. this work investigates the effects of one-tomany communication regime on the compositional-ity of emergent languages. in real-world communications, a single message often concerns multiple parties: an advertisement of a product, a sergeant's command to a squad, etc. in these scenarios, there are more than one interested entity for a given message. this environment opens two interesting aspects of communication, and we find that these aspects each introduce a new environmental pressure that facilitates emergence of compositionality. first, the listeners may not share the same interests. in the case of the advertisement of a product, some of the viewers of the advertisement may only be interested in certain characteristics of the product such as colors and sizes, while others may only care about the price and brand name. while it is still the case that the advertisement must contain all of the relevant information for the product, we argue that it introduces a new pressure that forces the message to be easier to understand for listeners that are only interested in certain parts of the attributes. we hypothesize that these listeners would prefer messages that are easily interpretable, without the need to understand other details corresponding to attributes that they are not concerned with. second, listeners may need to coordinate among themselves to be successful at the task at hand. in the case of the sergeant's command to a squad, coordination among the squad may be required for them to have successfully carried out the mission. hence, a misinterpretation of the command from a single listener may result in failure for the entire squad. we argue that the pressure that the language be simultaneously understood by multiple listeners forces the language to be more compositional. intuitively, it is plausible that one listener may develop a compositionally inferior language, but it is less likely to be shared by other listeners in the group due to its inferior compositionality. extensive experiments confirm the hypotheses that agents of different interests and coordination among agents are crucial environmental pressures for emergence of compositionality. we find that simply broadcasting a speaker's message to multiple listeners does not enhance compositionality of induced languages. we observe emergence of compositionality when listeners of different interests are introduced or coordination pressures are injected to the environment. we then analyze what kinds of compositionality structures are derived from these pressures with various compositionality measures. ## one-to-many communication game we analyze emergent languages of agents playing a variant of lewis reconstruction game @xcite . the process of the game is as follows. speaker π θ observes an object @xmath0. an object contains k attributes and each attribute can take one of |x | possible values. a message @xmath1. the game contains a set of n listeners {π ϕ i } n @xmath2. each listener π ϕ i is concerned with k i attributes, where for each round of game play, the set of listeners are randomly partitioned into m groups {g upon receiving message m, listener π ϕ i outputs its prediction for the object as let g (i) denote the indices of listeners in the group that listener π ϕ i belongs to. listener π ϕ i receives a reward of 1 if all of the listeners' predictions in its group are correct, i.e., r l i (x) = 1 if ∀@xmath3, x @xmath4. the speaker receives the average reward of all listeners as a reward, which is equal to the fraction of successful listeners: r s (x) = 1 n n @xmath5. see appendix a for graphical illustrations. ## experimental setup dataset we represent each attribute's value with one-hot encoding. the number of attributes, k, is set to 4, and the number of values, |x |, is set to 10. we set aside 10% of all attribute-value combinations as test set and use the rest as train set. speaker architecture one-hot encoded object x passes through a linear layer and initializes a single-layer gru @xcite of hidden size 500. it recurrently processes the input in total of @xmath6. in each time step, the output is fed to a linear layer and then goes through softmax activation to produce a vocabulary distribution of dimension |w| = 10. listener architecture a listener π ϕ i is a singlelayer gru of hidden size 500. the listener sequentially processes the speaker's message m, the last output of which is then passed to k i linear layers corresponding to the number of attributes the listener is interested in. they each go through softmax activation and produce a distribution of size |x | corresponding to the number of possible values an attribute can take. optimization we maximize each of the listeners' and speaker's expected reward with the rein-force algorithm @xcite . the expected reward for listener π ϕ i is written as reporting we report average scores over 10 random seeds unless stated otherwise. throughout the paper, we use error bars to indicate 95% confidence interval @xmath7. bold and underline indicate the best and second best results. ## evaluation metrics topographic similarity (topsim) let d obj : x k ×x @xmath8: w t ×w @xmath9, respectively. topographic similarity @xcite ) is spearman's rank correlation of d obj and d msg over the joint uniform object, message distribution. high topsim scores indicate that similar objects are mapped to similar messages. for d obj and d msg , we use cosine distance and levenshtein distance @xcite , respectively. positional disentanglement (posdis) let m i denote the symbol in the i-th position of message m. let a i 1 denote the attribute that has the highest mutual information with m i , i.e., a i 1 = arg max a i(m i ; a). similarly, let a i 2 denote the attribute that has the second highest mutual information with m i , i.e., a i 2 = arg max a̸ =a i 1 i(m i ; a). positional disentanglement @xcite bag-of-symbols disentanglement (bosdis) let n i denote the number of occurrences of the i-th symbol from vocabulary w in a message. other notations follow from positional disentanglement. bag-of-symbols disentanglement @xcite ## experiments with raw images we expand our study to more realistic scenarios employing datasets that consist of raw pixel images.