Emergent Communication of Generalizations

1 Introduction . The communication systems that emerge when two agents are trained to cooperate offer a window on the evolution of human language , as well as a promising avenue for improving the collaboration abilities of artificial agents . Much recent work studies Lewis-style [ 24 ] signaling games ( Figure 1a ) , where agents are trained to refer to a single object in a shared visual context . However , a general consensus of this work is that without careful environmental pressures , agents develop successful but uninterpretable communication schemes distinctly unlike human language [ 1 , 5 , 6 , 16 , 20 ] . We argue that the reference games typically used in these studies are ill-suited to drive linguistic systematicity for two reasons . One is perceptual : agents can exploit inscrutable patterns in single inputs , which leads to communication via spurious features [ 3 ] . The other reason is cognitive : human language can convey abstract ideas , such as kinds and causes , not only reference to specific objects . Simple reference games are unlikely to drive emergence of such abstract language . In particular , generalizations over categories are a crucial part of language [ 36 ] , helping us transfer knowledge that may be useful in the future . For example , we would like to teach our kin not just to avoid one specific lion , but to avoid all lions , including those that have not yet been seen . Some have even argued that language emerged precisely from this need to teach hard-won generalizations to others [ 19 ] . With this idea in mind , can we design an experimental setting that better catalyzes these abilities ? In this paper , we propose extensions of Lewis-style signaling games to sets . In the set reference ( setref ) game , a teacher must communicate to a student not just a single object , but rather a group of objects belonging to a concept ( Figure 1b ) . In the concept game , each agent sees different examples of the concept ( Figure 1c ) . Inspired by human teaching [ 9 ] , our core insight is that requiring generalization to combinatorially large sets of ( possibly unseen ) objects encourages agents to learn and communicate rich abstractions across inputs ( e.g . seagulls ) , instead of low-level features ( e.g . color # FDA448 ) . These tasks are more difficult than traditional reference games , and we will show with a variety of metrics that the learned languages are more systematic , compositional , and interpretable . Finally , the rich compositional space of concepts explored in these games allows us to probe for specific logical 35th Conference on Neural Information Processing Systems ( NeurIPS 2021 ) . Ref Setref Concept 9 Ref Setref Concept 9 Ref S tref Concept 9 Ref S tref Concept 9 operators in the emergent language . We propose a method for doing so , thereby demonstrating how the emergent languages reflect the compositional structure of their inputs . 2 Communication Games . First imagine a generic communication game between a teacher T and student S. Let G = ( c , XT , Y T , XS , Y S ) be a communication game , where c : X 7→ { 0 , 1 } is a latent concept to be communicated , XT = { xT1 , . . . , xTn } is a set of n inputs presented to the teacher , and Y T = { yT1 , . . . , yTn } is a set of labels for the teachers ’ inputs , defined as yTi = c ( xTi ) . We call xTi a target if yTi = 1 , which indicates that x T i is a member of the concept c ; otherwise x T i is a distractor and yTi = 0 . X S and Y S are defined similarly for the student . Given its targets and distractors ( but not the latent concept c ) , the teacher must send a message m to a student that allows them to correctly identify their own targets , where m = ( m1 , . . . , mn ) is a discrete sequence over a fixed alphabet mi ∈M . Now we can define variants of this communication game as follows : Reference game . In basic reference games , the teacher and student see the same examples ( XT = XS , Y T = Y S ) and there is a single ( repeated ) target : xTi = x T j for all i , j where y T i = y T j = 1 . 1 Set reference ( setref ) game . Now we extend our game to sets : the teacher and student see the same examples , but there are multiple target images encoding the concept ( e.g . different red triangles ) . Concept game . Finally , we propose the more abstract concept game , where the teacher and student see different examples ( XT 6= XS , Y T 6= Y S ) of the same concept . When XT and Y T contain a single positive and negative example , this is a reference game with separate inputs for each agent , a setup which has been shown to encourage linguistic systematicity in some settings [ 8 , 21 , 22 ] . 3 Models . Now we will formalize our models of the teacher and student . Given a communication game G , a teacher is defined as a distribution over messages given inputs pT ( m | XT , Y T ) , and a student is a distribution over targets given a message : pS ( Y S | XS , m ) = ∏ i p S ( ySi | xSi , m ) . Teacher . The teacher encodes all inputs with a convolutional neural network ( CNN ) fTθ ; embeddings for targets and distractors are averaged to form target and distractor prototype embeddings [ 33 ] ,2 which then conditions a recurrent neural network ( RNN ) used to produce the message . Let XT+ and X T − denote the sets of targets and distractors in X T ; then define a prototype embedding 1For the most consistent comparison across games , our reference game has multiple identical targets and student target decisions made independently for each input , instead of the single-target forced-choice setting . Appendix E shows results with traditional games trained with cross entropy loss ; conclusions are the same . 2Note that the teacher ’ s job is one of representation learning for sets [ 42 ] and thus one can use any set representation learning method beyond the prototypical networks explored here . As a more advanced implementation , we tried a variant of Set Transformers [ 23 ] , but this did not give any tangible performance benefit . NOT yellow AND circle ( Laysan Albatross ) bill : hooked AND wing : black AND ... wing-shape : long blue OR rectangle [ 0 1 … 1 0 ] [ 0 1 … 0 1 ] [ 1 0 … 1 0 ] bill : cone AND breast : red AND ... [ 1 0 … 1 ] [ 1 0 … 1 ] [ 0 1 … 0 ] bill : cone breast : red bill : hook Figure 2 : Example games , with targets ( red border ) and distractors for the ShapeWorld concept blue OR rectangle ( left ) and the Birds concept painted bunting ( right ) . Concepts are represented as intensional logical formulas ( top ) or extensional sets of boolean input features ( bottom ) , where each vector is the binary representation of an individual member of the concept ( e.g . blue rectangle , or the labeled attributes of one particular bird ) . See Figure S1 in Appendix A for additional game examples . xT+ = 1 |XT+ | ∑ xi∈XT+ fTθ ( xi ) ( analogously for x T − ) . Then p T ( m | XT , Y T ) = pRNN-DECODE ( m | proj ( [ xT+ ; x T − ] ) ) where proj is a linear projection to the RNN hidden state . Student . The student takes a message and makes predictions about the labels ŷSi independently for each input xSi . Given the teacher message and an input image , define p S ( ySi | xSi , m ) = σ ( RNN-ENCODE ( m ) · fSφ ( xSi ) ) , where fSφ is a separate CNN for the student . We jointly train a teacher-student pair , including the vision modules and communication protocol , via stochastic gradient descent to maximize the student likelihood of selecting the correct target images . Formally , the loss for a single game is L ( T , S , G ) = − ∑ i log pS ( ySi | xSi , m̂ ) , m̂ ∼ pT ( m | XT , Y T ) . ( 1 ) To maintain backwards differentiability , we use the straight-through Gumbel-Softmax [ 14 ] trick with τ = 1 , simulating samples from the teacher distribution over tokens via softmax and discretizing in the forward pass only . For full model and training details and a link to code , see Appendix A . 4 Tasks . We examine the languages developed for our proposed communication games over two datasets : first , an artificial shape dataset which allows us to evaluate communication over cleanly defined logical concepts ; second , a dataset of birds to test agents ’ ability to learn concepts from realistic visual input . ShapeWorld . We use the ShapeWorld visual reasoning dataset [ 18 ] ( Figure 2 , left ) . For reference games , target images are a single object , defined by a conjunction of a shape and a color ( e.g . red triangle , green square ) ; of the 30 possible shapes , we hold out 20 % for testing . For setref and concept games , concepts include the conjunctions tested in reference games , but also primitive concepts ( e.g . blue shapes ) and arbitrary disjunctions or conjunctions of ( possibly negated ) shapes and/or colors . This produces 312 concepts , 20 % of which are held out for testing . These more general concepts can not be tested in reference games , since a single object is always identified by a shape and color . This rules out disjunctive concepts like red OR blue that only make sense across multiple objects . Similarly , since reference game targets must necessarily have both color and shape , we can never guarantee that a message for a reference game only carries the semantics blue and not , for example , blue circle , if the target is a blue circle . By looking at sets , setref and concept games allow us to more precisely control the semantics of the concepts in each game . Each game consists of 10 targets depicting shapes satisfying the concept , and 10 distractors . We specifically sample “ hard ” targets and distractors to test understanding of conjunctions or disjunctions ( see Appendix B for details ) . Finally , we specify an agent vocabulary of 14 tokens and maximum length 5 , so that the communication channel has the same bandwidth as the true concept formulas ; 3 see Appendix C for experiments varying these parameters for both this dataset and the next one . Birds . We next use the Caltech-UCSD Birds dataset [ 40 ] which contains 200 classes of birds with 40–60 images ( Figure 2 , right ) . As before , reference games involve a single target ; setref and concept 3In the true concept formulas there are 5 shapes , 6 colors , and the 3 AND/OR/NOT operators , i.e . 14 tokens ; and the longest concept formulas have the form NOT x AND NOT y , i.e . length 5. game targets are members of a specific bird class . We use 100 classes at train and 50 at test , sampling 5 targets and 5 distractors per game . The dataset contains boolean attributes ( e.g . beak , size ) for individual birds and classes.4 Thus , we represent reference game concepts as the feature vector of the target bird , and setref/concept game concepts as the feature vector of the class . In our evaluation , we will measure how well the languages capture these features . As there is no reference language for this task , we set the vocabulary size to 20 and the message length to 8 ( though again see Appendix C ) .

Summary: In the referential game setup that is widely used in the emergent communication literature, this paper proposes expanding the target into a target set, and studies the effects of different choices for the distractor and target sets. The authors find that choosing suitable sets leads to more consistent communication protocols and higher topographic similarity between concept and message spaces, but at the same time causes a drop in communicative success.  The other contribution of the paper is a composition-based evaluation of the protocols that emerge from the set-based training. Small transformers are trained to mimic operators such as ‘AND’ and ‘NOT’. Evaluating the listener performance on the messages produced by those operator models shows a non-trivial communication performance, albeit significantly reduced relative to the original speaker models. The authors conclude that there is limited evidence for compositionality in the communication protocols based on this experiment.