Catalytic Role Of Noise And Necessity Of Inductive Biases In The Emergence Of Compositional Communication

1 Introduction . In emergent communication studies , one often considers agents who can share information about a set of objects described by the common features . Such a situation is common in multi-agent systems with partial observation ( Foerster et al . ( 2016 ) , Lazaridou et al . ( 2016 ) , Jaques et al . ( 2018 ) , Raczaszek-Leonardi et al . ( 2018 ) ) and it is the major theme in signaling games ( Fudenberg et al . ( 1991 ) , Lewis ( 1969 ) , Skyrms ( 2010 ) , Lazaridou et al . ( 2018 ) ) . In a signaling game , one agent ( a sender ) conveys information about an object to another agent ( a receiver ) , which then has to infer the object ’ s features . Typically , agents are rewarded if some of the features are correctly identified . During this process , the agents develop a communication protocol . A recent line of work has studied conditions under which compositionality emerges ( Batali ( 1998 ) ; Kottur et al . ( 2017 ) ; Choi et al . ( 2018 ) ; Korbak et al . ( 2019 ) ; Li and Bowling ( 2019 ) ; Słowik et al . ( 2020b , a ) ; Guo et al . ( 2020 ) ) . Compositionality is a crucial feature of natural languages and it has been investigated extensively in cognitive science ( see e.g . Chomsky ( 1957 ) Fodor and Pylyshyn ( 1988 ) ) . It is often measured using dedicated metrics such as topographic similarity ( Brighton and Kirby ( 2006 ) ; Lazaridou et al . ( 2018 ) ; Kriegeskorte ( 2008 ) ; Bouchacourt and Baroni ( 2018 ) ) , context independence Bogin et al . ( 2018 ) , conflict count Kuciński et al . ( 2020 ) , or positional disentanglement ( Chaabouni et al . ( 2020 ) ) . In signaling games it bears a strong resemblance to the concept of disentangled representations , see ( Higgins et al . ( 2017 ) , Kim and Mnih ( 2018 ) , Locatello et al . ( 2019 ) ) . In machine learning context , ∗Corresponding author . †Now at Google . 35th Conference on Neural Information Processing Systems ( NeurIPS 2021 ) . compositionality is perceived as a generalization mechanism ( Lake et al . ( 2016 ) ) and has been used e.g . for goal composition ( Jiang et al . ( 2019 ) ) or knowledge transfer ( Li and Bowling ( 2019 ) ) . In this paper , we theoretically show that inductive biases on both the training framework and the data are needed for compositionality to emerge . A similar observation has been made by Kottur et al . ( 2017 ) ; however , our result is more fundamental and points out a common misconception that compositionality can be learned in a purely unsupervised way . Such a result can be perceived as a discrete analog of Locatello et al . ( 2019 ) , applicable in the communication context . We then prove that adding an inductive bias in the loss function coupled with communication over a noisy channel leads to the spontaneous emergence of compositionality . This shows the catalytic role of noise in this process . Intuitively , this can be attributed to the ( partial ) robustness of compositional language with respect to message corruption caused by a noisy channel . We experimentally verify that a certain range of noise levels , dependent on the model and the data , promotes compositionality . We provide a wide range of experiments that illustrate the influence of different priors . For the inductive biases in the training framework , we look into the impact of the network architecture as well as implementation and temporal variation in noise . On the data side , we study the effect of scrambling visual input or its description . We also study the generalization properties of the proposed training framework . 2 Related work . The topic of communication is actively studied in multi-agent RL , see Hernandez-Leal et al . ( 2020 , Table 2 ) for a recent survey . Compositionality is often investigated in the context of signaling games ( Fudenberg et al . ( 1991 ) , Lewis ( 1969 ) , Skyrms ( 2010 ) , Lazaridou et al . ( 2018 ) ) . Recent research has shown that strong inductive biases or grounding of communication protocols are necessary for the protocol to be compositional ( see e.g . Kottur et al . ( 2017 ) , Słowik et al . ( 2020b ) ) . The inductive bias can be imposed into the architecture of the agents or the training procedure . For instance , Das et al . ( 2017 ) place pressure on agents , to use symbols consistently across varying contexts , by a frequent reset of the agent ’ s memory . A model-based approach was proposed by Choi et al . ( 2018 ) and Bogin et al . ( 2018 ) , who build upon the obverter algorithm ( Oliphant and Batali ( 1997 ) , Batali ( 1998 ) ) . Słowik et al . ( 2020a ) explore games with hierarchical inputs and shows how agents implemented as graph convolutional networks obtain good generalization . Korbak et al . ( 2019 ) implemented the idea of template transfer ( Barrett and Skyrms , 2017 ) by pre-training the agents on simpler subtasks before the target task . Kirby ( 2001 ) studied the iterative learning paradigm , where each generation of agents learns the language spoken by the previous generation before starting to communicate . In the machine learning literature , this idea was explored by Li and Bowling ( 2019 ) , Cogswell et al . ( 2019 ) and Ren et al . ( 2020 ) with the generation transfer typically implemented as reinitializing the weights of agents ’ neural networks . Such an approach inevitably introduces noise into the learning process . This naturally leads to a question of whether the noise itself may be a sufficient mechanism of compositionality , which we will try to address in this paper . Guo et al . ( 2020 ) have shown that the choice of a game has a large impact on the properties of a communication protocol emerging in that game , foreshadowing what we call grounding . Kim and Oh ( 2021 ) study emergent language in the group setting with varying population sizes and connectivity . Liu et al . ( 2021 ) cast constructing structured neural architectures as a communication problem . The noisy channel model of communication was famously introduced by Shannon ( 1948 ) . The idea of noise as a driving force in the emergence of communication was first proposed by Nowak and Krakauer ( 1999 ) , who showed that word-level compositionality is the optimal solution to the problem of communication in a noisy environment under a particular fitness function . Tucker et al . ( 2021 ) consider a noisy channel communication , where the agents learn to communicate via discrete tokens . Noise is also used in deep learning , e.g . as a regularizer ( see e.g . dropout ( Srivastava et al. , 2014 ) ) or a mechanism allowing backpropagation through a discrete latent ( see e.g . Salakhutdinov and Hinton ( 2009 ) , Kaiser and Bengio ( 2018 ) ) . Noise in the latter context was used in Foerster et al . ( 2016 ) in order to learn to communicate . The authors observed that it is essential for successful training . 3 Noisy channel method . We discuss the language and compositionality in Section 3.1 . The impossibility result and the need for biases in emergent compositionality is the content of Section 3.2 . The communication task considered in this paper as well as the catalytic role of noise is described in Section 3.3 . Theoretical results from this section hold in a somewhat idealized situation , but experiments in Section 5 are performed in a more realistic setup . The difference is described in Section 4.1 . 3.1 Language and compositionality . Consider a set of objects described by some features , and let a set F contain a combination of these features ’ values . For example , the features could represent shape , say squares and circles , and color , say red and green , in which case F = { red square , red circle , green square , green circle } . The features could be identified with partitions of F . More formally , each feature can be defined via equivalence relation , with features values corresponding to equivalence classes of this relation . In our example , the color corresponds to the partition { red square , red circle } ( ’ red ’ ) and { green square , green circle } ( ’ green ’ ) , while for the shape corresponds to the partition { red square , green square } ( ’ square ’ ) and { red circle , green circle } ( ’ circle ’ ) . We assume that objects with feature space F can be defined in a space X and are generated by a two-stage process : first , the feature values are sampled from f ∈ F , then an element of X is sampled according to a distribution conditioned on f . In general , a language is defined as a mapping from objects to strings over some finite alphabet A ( sometimes called messages ) , ` : X → A∗ . In this paper , we will study a subset of languages ` , where the range of the language has a fixed length , equal to the number of features . We say that ` is compositional with respect to a given feature if a change in i-th feature only impacts a corresponding j-th index of the message . Continuing the previous example , let A = { a , b } and consider a language ` mapping red squares , red circles , green squares , and green circles to aa , ba , ab , and bb , respectively . Then ` is compositional with respect to color and shape features since the change of color only impacts the first index in the message ( and analogously for the shape ) , see Figure 1 ( a ) . Consider a permutation π : F → F . In our running example , suppose that π is an identity , except that it swaps red circle with green circle , i.e . π ( red circle ) = green circle and π ( green circle ) = red circle . The resulting language ` π would then map red squares , red circles , green squares , and green circles to aa , bb , ab , and ba , respectively . This language is not compositional with respect to color and shape features , since if we change a shape value in red circle , both symbols in the message will change ( from bb to aa ) , see Figure 1 ( b ) . However , ` π is compositional with respect to a different set of features ( shape and ’ different color-shape ’ ) , see Figure 1 ( c ) . Consequently , compositionality should be defined together with features , with respect to which it holds . In the next section , we show that this observation has significant implications for learning . 3.2 Inductive biases and compositionality . This section investigates whether compositionality can spontaneously emerge in an unsupervised way . The answer to this question is negative since the underlying features can not be inferred from the data . Theorem 1 . For a uniform distribution , µ on F and a permutation π : F → F , the distribution µ ◦ π−1 is also uniform . While this result is elementary to prove ( see Appendix F ) it has deep implications for the emergence of compositionality in the learning process . Suppose that data represent a balanced set of all features ( i.e . features are sampled from µ ) and recall the two-stage generation process described in Section 3.1 . If f ∼ µ ◦ π−1 has the same distribution as f ∼ µ , then the distribution of the observed data does not depend on π. Consequently , any emergent compositional language ` with respect to some features is not compositional with respect to other ( permuted ) features . We arrive at the following conclusion : Any learning process which hopes to achieve compositionality must involve some priors related to the data and learning framework . Theorem 1 can be viewed as a discrete version of Locatello et al . ( 2019 , Theorem 1 ) . There are multiple ways of grounding the learning process , including imposing inductive biases on the agents and designing loss functions to disentangle features . We study these , together with a new mechanism : injecting noise into the communication channel . In the next section , we show that this mechanism provably achieves compositionality .

Summary: This paper adds results to the literature on learning compositional emergent communication protocols. Two results are theoretical: that inductive biases are required in order for compositional communication to emerge, and that adding a noisy channel with a specific loss function leads to compositional language emergence. The third result is a small-scale empirical corroboration of the latter theoretical result in a speaker-listener game.