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: The community has been looking at compositional generalisation more recently, and while Fodor and Pyshylynn is an oft cited work, there is a lack of a good definition of compositionality that researchers can agree on.   This paper suggests that a noisy channel with an encoder decoder setup is crucial for the emergence of compositionality. The authors propose a simple definition of compositionality in a non-hierarchical case, and discuss how 1) if no assumptions or prior information about the data is incorporated into the training process, the resulting methods will be uncompositional, 2) if this inductive bias is injected through the use of a noisy channel, there are losses (namely J_1, J_2) that can be used to encourage the rise of a compositional encoding.   The basic setup involves communication through a noisy channel. They then discuss how, if the encoding is compositional, there are particular losses (J_1, and J_2) that will be optimal. More importantly, when J_2 is optimal, the encoding is compositional. In their experiments, they use J_1 primarily, and demonstrate compositional emergence (according to some metrics) under some circumstances.