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: The current manuscript proposes to study the emergence of language when agents communicate with each other about generalizations over a set of objects, as part of a referential game. Experiments with object sets yield improved and more interpretable language that evolves between the agents. Additionally, the work also explores finding approximate logical operators in the emergent language.