Compositionality with Variation Reliably Emerges in Neural Networks
Authors: Henry Conklin
Kenny Smith
Venue: ICLR 2023 poster (2023)
Keywords: compositionality
emergence
generalization
regularity

Abstract: Human languages enable robust generalization, letting us leverage our prior experience to communicate about novel meanings. This is partly due to language being compositional, where the meaning of a whole expression is a function of its parts. Natural languages also exhibit extensive variation, encoding meaning predictably enough to enable generalization without limiting speakers to one and only one way of expressing something. Previous work looking at the languages that emerge between neural networks in a communicative task has shown languages that enable robust communication and generalization reliably emerge. Despite this those languages score poorly on existing measures of compositionality leading to claims that a language's degree of compositionality has little bearing on how well it can generalise. We argue that the languages that emerge between networks are in fact straightforwardly compositional, but with a degree of natural language-like variation that can obscure their compositionality from existing measures. We introduce 4 measures of linguistic variation and show that early in training measures of variation correlate with generalization performance, but that this effect goes away over time as the languages that emerge become regular enough to generalize robustly. Like natural languages, emergent languages appear able to support a high degree of variation while retaining the generalizability we expect from compositionality. In an effort to decrease the variability of emergent languages we show how reducing a model's capacity results in greater regularity, in line with claims about factors shaping the emergence of regularity in human language.

Published as a conference paper at ICLR 2023
COMPOSITIONALITY WITH VARIATION RELIABLY EMERGES BETWEEN NEURAL NETWORKS
Henry Conklin Kenny Smith
o Institute of Language Cognition and Computation, School of Informatics
"Centre for Language Evolution, School of Philosophy Psychology and Language Sciences
The University of Edinburgh [henry. conklin, kenny. smit th www.thmeedaac......m..o.
ABSTRACT
Human languages enable robust generalization, letting us leverage our prior ex- perience communicate about novel meanings. This is partly due language being compositional, where the meaning of a whole expression is a function its parts. Natural languages also exhibit extensive variation, encoding meaning predictably enough to enable generalization without limiting speakers to one and only one way of expressing something. Previous work looking the languages that emerge between neural networks in communicative task has shown languages that enable robust communication and generalization reliably emerge. Despite this those languages score poorly on existing measures of compositionality leading to claims that language's 's degree of compositionality has little bearing on how well it can generalise. We argue that the languages that emerge between networks are in fact straightforwardly compositional, but with a degree of natural language-like variation that can obscure their compositionality from existing measures. We intro- duce 4 measures of linguistic variation and show that early in training measures of variation correlate with generalization performance, but that this effect goes away over time as the languages that emerge become regular enough to generalize robustly. Like natural languages, emergent languages appear able support high degree of variation while retaining the generalizability we expect from composi- tionality. In an effort decrease the variability of emergent languages we show how reducing model's capacity results in greater regularity, in line with claims about factors shaping the emergence of regularity in human language."
INTRODUCTION
Compositionality is a defining feature of natural language; the meaning a phrase is composed from the meaning of its parts and the way they're combined (Cann, 1993). This underpins the powerful generalization abilities of the average speaker allowing us to readily interpret novel sentences and express novel concepts.
Robust generalization like this a core goal of machine-learming: central to how we evaluate our models is seeing how well they generalize examples that were withheld during training (Bishop, 2006). Deep neural networks show remarkable aptitude for generalization in-distribution (Dong & Lapata, 2016; Vaswani et al., 2017), but growing body of work questions whether or not these networks are generalizing compositionally (Kim & Linzen, 2020; Lake & Baroni, 2018), highlighting contexts where models consistently fail to generalize (e.g. in cases of distributional shift; Keysers et al., 2020).
Recent work has looked whether compositional representations emerge between neural networks placed in conditions analogous to those that gave rise to human language (e.g. Kottur et al., 2017; Choi et al., 2018). these simulations, multiple separate networks need to learn to communicate with one another about concepts, environmental information, instructions, or goals via discrete signals like sequences of letters but are given no prior information about how to do so. A common setup is
"oode and Data be found tith www.hcooe.//aa../ccooo//oooo//ae able composi tional ioalityy

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Synonymy (Ella posiiin
C
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1
1
E
F
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Sonuy
F
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Poutica Signal
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A depiction of the probability tensor built with equation 1 where Object. Green indicates high probability and red low. (Left:) A perfectly regular language, Elsa is always encoded by 'AA' in the final two positions, Kirsty by 'BB' etc. (Right:) The same cube is shown (object labels removed) for a language with basic synonymy (Elsa can be encoded by 'A' or 'B') and homonymy (Jenny and Simon are both encoded by 'E'). We quantify the degree of synonymy by taking the entropy of each column (equation 2) and the degree of homonymy by taking the entropy of each row (cquation 3)
Figure 1:
a 'reconstruction game' modelled after a Lewisian signalling game (Lewis, 1970), where a sender network describes meaning using a signal, and receiver network needs reconstruct that meaning given the signal alone. The resulting set of mappings from meanings to signals can be thought of as language.
Previous work has shown that in this setup models reliably develop a language that succeeds not only in describing the examples seen during training but also successfully generalizes to held-out test set, allowing accurate communication about novel meanings. Despite this capacity to generalize, which a product of compositionality in natural languages, existing analyses of those emergent languages provide little evidence of reliable compositional structure (see Lazaridou & Baroni, 2020, for a review), leading some to suggest that compositionality not required order to generalise robustly (Andreas, 2019; Chaabouni et al., 2020; Kharitonov & Baroni, 2020).
If not compositional, then what? This interpretation leaves with major puzzle: if the languages that emerge in these models are non-compositional, how do they allow successful communication about thousands of unseen examples (e.g. Lazaridou et al., 2018; Havrylov & Titov, 2017)? If the meaning of a form is arbitrary rather than being in some way composed from its parts there should be reliable way to use such mapping generalize novel examples (Brighton, 2002). Here provide an answer to this question showing that emergent languages are characterised by variation, which masks their compositionality from many of the measures used in the existing literature. Existing measures take regularity as the defining feature of a compositional system, assuming that in order to be compositional separate semantic roles need to be represented separately in the signal (Chaabouni et al., 2020), or that symbols in the signal must have the same meaning regardless of the context they occur (Kottur et al., 2017: Resnick et al., 2020). Alternately they expect that each part of meaning will be encoded in only one way, or that the resulting languages will have a strict canonical word order (Brighton & Kirby (2006) used in Lazaridou al. (2018)). However, natural languages exhibit rich patterns of variation (Weinreich et al., 1968; Goldberg, 2006), frequently violating these four properties: forms often encode multiple elements of meaning (e.g. fusional inflection of person and number gender and case), language is rife with homonymy (where the meaning of form depends on context) and synonymy (where there are many ways of encoding a meaning in form), and many natural languages exhibit relatively free word order.
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object
wejectt
verb
Random
Ideal
Signel Postfors
Figure 2: Plots showing the max from the distribution over characters for each atom in each position, with a plot for each separate role (object, subject, verb). axis: positions, axis: id for each alom; Ar- Shown to the left are these plots for the synthetic ideally regular compositional language (with SVO order), and the maximally variable random mapping. The large plot shows data from the run of the small model with the highest variation This run's variation scores: freedom = 0.57, entanglement = 0.61, homonymy 0.61, symonymy 0.51, topsim 0.28, posdis 0.26
This offers us a different explanation of previous results: compositional systems may emerge, just with variation. show us that systems can have considerable variation while retaining the generalizability that makes compositionality so desirable. We focus on explicitly assessing variation independent of composition- ality and illustrate how emergent languages can generalize robustly with substantial variation. Our core contributions are as follows:
that doesn't necessarily undermine a their compositionality, natural languages
We introduce measures natural language-like variation
We show that the languages which emerge tend to exhibit high degree of variation which explains why previous metrics would classify them as non-compositional.
We find that language's 's degree of regularity correlates strongly with generalization early in training, but as the emergent language becomes regular enough to generalize reliably this correlation goes away.
We reduce the capacity of our models by reducing the size of the hidden layers, and show that lower capacity models develop more regular languages, predicted by accounts linking cognitive capacity and regularity in natural language
VARIATION, REGULARITY, COMPOSITIONALITY
Variation and compositionality in language are related but distinct. We look at them separately, taking language's generalization performance as indication of whether not is compositional (in line with Brighton, 2002; Kottur et al., 2017). Linguistic regularity the absence of variation has been studied broad array of contexts (see Ferdinand al., 2019, for discussion). describes how predictable a mapping from meaning to form is: if there's 's only one way of encoding meaning that mapping highly-regular (Smith Wonnacott, 2010). Conversely there's a variety of different ways of encoding meaning that mapping likely has high variation (low regularity). In our context - mapping meanings to discrete signals regularity is maximized by language of one-to-one mappings. For example where each position in the signal encodes one part of the meaning position 1 1 Subject and each character in that position refers to only one possible subject - A in position + Subject: Ollic and is the only character ever used refer to that subject. A maximally regular language encodes the same (part of) meaning with the same (part of) form every time, rather than affording speaker variety of ways to encode meaning.
high-level
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Model
iid, ace
undd acc
synunymy
entanglement
freedom
homonumy
variotion
tegsim
posdis
adeul
0.000
0.00
0.00
0.12
0.03
0.02
1.00
rondow
0.90
0.99
smoul
17.64
10.00
73.80
17.07
0.30
-042
0.54
-048
0.39
10.4
0.53
10.00
0.50
-0.0
0.21
-0.1
0.24
-0.03
and
-0.20
un
-0.42
2034
-0.19
-0.15
-0.25
0.12
0.22
20:55
medimm
07.73
10.00
82:13
+3.02
0.52
-9.0
0.00
-0.0
0.54
10.0
0.58
-0.0
0.50
-0.00
0.19
-0.2
0.19
-0.00
A mod.
-0.18
00.5
-0.45
-0.12
-0:15
-0.20
0.30
0.17
Targe
07.53
81.33
0.45
0.80
20.0
0.46
2000
0.89
20.00
0.80
20.00
0.14
2001
0.05
20.00
A and.
-0.01
-0.15
-0.01
20:35
-0.05
20.00
-0.05
0.05
40000
0.05
20.90
Table 1: Mean accuracy and variation with 95% confidence interval across 20 runs, taken from the epoch with the best o.o.d. generalization performance, along with the change in measures Abest between the least regular language that occurs between epochs and 10 and the best generalizing one. Also included are the variation measures applied a perfectly regular and maximally variable language one as well as an average across all 4 variation measures. Two measures of regularity from previous work (topsim and posdis) are included in the grey cells.
This kind of maximally regular system is intuitively compostional, given the meaning of a signal would be composed from the parts of meaning its characters map to and the position they re in (in line with Cann, 1993) but it's by no means the only kind of compositional system. To better characterise the space of possible languages in section 2.1 we introduce four kinds of variation drawn from kinds of variation attested in natural language and ways of quantifying each of them individually. Then in section 2.2 we look at some of the most relevant existing measures of 'compositionality and discuss how they could be interpreted in terms of regularity. Results from a standard emergent communication model in section 4 show that every run results in geeea-ggnnr (and therefore compositional) language but with varying degrees of variation. To better understand the relationship between variation and generalization we look over the time-course of training and find regularity is strong predictor of how well a language generalizes early on but this effect goes away as the models approach ceiling i.i.d. generalization. We take this as an indication that while language needs be more regular than a random mapping in order to generalize, it doesn' 't need to minimize variation in order to do so point made clear by natural languages. At the end of training when the emergent languages have become sufficiently regular for the task at hand, whether one is more regular than another doesn't ' necessarily correspond to better generalization.
In a final set of experiments we look at how to decrease the amount of variation in an emergent language. Limitations on humans' memory and cognitive capacity are thought to be a driving force in the emergence of compositional structure and regularity in natural language (Kirby, 2001; Hudson Kam & Chang, 2009; Smith & Wonnacott, 2010). Learners with less memory are believed to regularize their input because they more constrained in their ability to store low-frequency forms (Newport, 1990; Ferdinand et al., 2019). We reduce the capacity of our models by reducing the size of the hidden layers, and show that lower capacity models develop more regular languages, as predicted by accounts linking learner capacity and regularity in natural language and in line with previous work in this area (Resnick et al., 2020).
2.1 QUANTIFYING VARIATION
We introduce four kinds of linguistic variation Synonymy, Entanglement, Word-Order Freedom, & Homonymy and define measures of each. This is not intended to be an exhaustive list, but offers a starting point for thinking about linguistic variation in this context. Each of these measures is bounded between 0 and 1, where 0 indicates a perfectly regular language with no variation, and represents a maximally variable language. For comparison we generate a maximally regular compositional language which scores near O across our measures, and maximally irregular non-compositional language (where each meaning maps to a unique shown in table 1. Our task (described fully in section 3) asks models to map meanings to signals. With meanings comprised of roles - e.g. Subject, Verb, and Object - and semantic atoms which can occur in each role (e.g. Subject: Ollie, Isla ... Verb: loves, hates, ...). Prior work in this area sometimes refers to these as attribute- value pairs (see Lazaridou & Baroni. 2020, for a review including some mention of attribute-value pairs. P. 11). Similarly signals are comprised of positions (indices), and the character that occurs in each. We can frame linguistic concepts of variation in terms of how semantics (roles & atoms) map signals (positions & characters).
signal) which scores near 1, as
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All four measures start with tensor that describes the mapping between meanings and signals probabilistically. in terms of a probability distribution over characters in each signal position given a semantic atom in role. This encodes, for example, how likely character 'A' is in signal position 1 given that 'Ollie" is in the subject role of the signal's meaning. We can quantify this as a straight- forward conditional probability using maximum likelihood estimation, shown in equation 1. We estimate this repeatedly for every atom (Vatom,, E A,) in every role (Vr E R), looking at every character (Vcharp.5 E C) in every position of every signal (Vp P).
count count(charpp p.j. atom,,s) count
P(char pa palaaom,..)
The resulting tensor deseribes how often each letter occurs in position, given certain atom in role in the meaning (like Subject: Ollie)?. This tensor has dimensions semantic roles x semantic atoms max signal length x characters", where the last axis is probability distribution over all possible characters in a given position - here denoted by P(char, (alom...))..
Synonymy & Homonymy: Synonymy is minimised when each atom in a meaning maps a single character in a position. Homonymy is minimised when each character in a position maps to a single atom (Hurford, 2003). While a perfectly regular compositional language minimises these, natural language is rife with both synonymy and homonymy (e.g. 'loves", 'adores', 'fancies' all map to approximately the same concept; the homonymous 'bank' maps to a financial institution, the act of turning plane, and the land at the side of river). One-to-many mappings (synonymy) aren't a problem for compositionality, as each different synonym can still be composed with the rest of signal. Similarly many-to- mappings (homonymy) can be used compositionally, with meaning disambiguated by context. our setting synonymy is how many different characters refer atom in role. For example when r Subject and atom,,; Ollie how many characters have non-zero probability in each signal position? A perfectly regular language where 'Ollie' is always encoded by 'A' in position I would have probability of 1.0 on 'A' in position 1. A maximally variable language would have uniform distribution over all characters. We can take the entropy over characters a position H(P(charpl) (atharlaaom,..)) as measure of synonymy in that position (illustrated in figure 1). We take the position with the lowest entropy as a lower-bound estimate synonymy for that alomy,.. order to bound the value we divide it by the entropy of a same-sized uniform distribution H., (P(char, platom..;)) )). The synonymy of an entire language (C) is obtained by averaging across all atoms in role, then across all roles. language with no synonymy where each atom encoded by single character in position achieving close to O, and maximal synonymy where any character can refer to each atom achieving close to I (shown empirically in table 1).
[dd min H (P(char,latom,,)) vp PP
1
Synongny(C))
Ha PP(charplatom,,
We can assess homonymy in a similar way, looking at how many semantic atoms a character in a position can refer to. As depicted in figure I this akin applying the synonymy measure different axis of the probability tensor P. We estimate P(atom, (charps) to get a distribution over atoms given characters in a position". To get a lower-bound estimate of language level homonymy take the position with the lowest entropy over atoms and divide by the entropy of same-sized uniform distribution to bound between 0 and 1, then average across all characters and roles. When the resulting value close each character maps every atom. Approaching 0 each character uniquely refers to single atom.
'Here we use semantic roles given the meanings are sentences, this can be generalised to any analogous attributes dataset exhibits.
3 For all experiments reported here these values are x x x
For simplicity we re-normalize P to create probability distribution over atoms in a role which is equivalent directly computing TP (atom, charp.;) see appendix for further discussion.
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R
[C| min H
E
Homonomyy(C)
R
Hu (F(atom,lcharp..
Word Order Freedom Word order freedom is minimized when each role in the meaning is always encoded the same position(s) in the signal, resulting in a single canonical word order. Looking language like Basque we that compositional language
support number of different grammatical word orders (Laka Mugarza, 1996), with at least two equivalently valid translations of "Ollie saw Ernest:" Ollie Ernest ikusi zuen, Ollie ikusi zuen Ernest. Even in English which has relatively strict word order we see processes like topicalization that result in alternate orders that are equally acceptable Let's go down the lake for some fun; For some fun, let's ss go down to the lake, or even more commonly dative alternations (Chomsky, 1957) like Ollie gave Orson book; Ollie gave a book to Orson. While many languages have some constraints on word-order, even when there is maximal word order freedom the resulting language can still be clearly compositional, with characters encoding the meaning and their order conveying little information. language with free word order is equally likely encode any role E R in any position, while maximally regular language always encodes atoms from the same role in the same position(s). given atom,, is not encoded in position the entropy for each position (IP (cchar,, aatom,;)) : VP E P) (also computed as part of equation 2), and average across all atoms in that role Vi E A,. If all the atoms in role encoded in the same position the distribution resulting from the mean will be non-uniform, with some positions having lower mean entropy than others (the appendix includes an illustration of this in figure 4 and some discussion of why we opt not to directly estimate IP [positionn joosr,, atom,,))).
expect its distribution over characters be roughly uniform. So
take
14,1
F(role,)
Σ A
1
H (P(charrplatomm))) Vp E EP)
(4a)
To get a lower-bound estimate of the language-level word-order freedom we take the minimum from the mean distribution F(role,) and divide it by the entropy of a uniform distribution over characters to bound between 0 and 1, then average across all roles:
[R|
min ((rolee))
1
Freedom(C)
(4b)
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Entanglement is minimised when each role is encoded in different positions in the signal. While dis-entangled language is likely compositional, consider the English past tense form of 'go." 'Went' is irregular, encoding action and tense together, in contrast to the hypothetical regular form 'goed' where action and tense are encoded in separate parts of form (Anderson, 1992, 55). Despite this can go on to the entangled form 'went' compositionally in sentence: Ollie went down to the shore (for discussion O' Donnell, 2015, p. 105). While maximal entanglement where every role encoded in every position would be compositiooall. the existence of even high degree of entanglement does not preclude compositionality. given the entangled forms can be trraght-forwardde recomposed with others. We can quantify this by seeing two roles are consistently encoded in the same (or different) positions. We compare the means (role) ) from equation 4a for each possible pair of roles Tú, E "C2 by taking the magnitude of their difference, two roles are encoded in the same position the result will be close to zero. If the roles are maximally disentangled then the result will be close to the max (Foole)) (rooee)) )) for that position. To get a lower bound estimate (.oole),F(rroeee))
of two roles' entanglement max. When the resulting value approaches 0 all roles are mapped to different parts of the signal, as approaches all roles are encoded in the same positions (illustrated in appendix figure 5).
take the maximum of the difference and divide by the pre-difference

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Co mar (((roles) [F(role)))
E)tanglement(()) =
(5)
|RC2|
mar (((roles),
2.2 EXISTING MEASURES
Topographic Similarity (Topsim) (Brighton & Kirby, 2006) has been used as measure of compositionality wide array of contexts (e.g. Smith et al., 2003; Kirby et al., 2008; Lazaridou al., 2018). It assumes that in compositional system where a whole signal is composed from reusable parts, similar meanings will map to similar signals. This can be assessed by measuring the correlation between pairwise meaning-distancee and edit distances between their associated signals: perfectly regular compositional language without variation achieves a correlation score close to 1, while a non-compositional (random) mapping between meanings and signals achieves a correlation close to O. While languages that score highly are likely to be compositional synonymy and word order freedom can reduce the score for this measure, as they can result in similar meanings having dissimilar signals. Synonymy can two meanings with the same subject encode it with different characters. Freedom can mean signals for similar meanings with different word orders have high edit-distance despite containing many of the same letters.
Posdis& & Residual Entropy (Chaabouni et al., 2020) & (Resnick et al., 2020) provide entropy- based measures of 'compositionallty. Posdis captures the extent to which each position of the signal univocally refers to role in the meaning (e.g. subject, object, verb) and looks for each signal position to refer to only one role. This is similar to what our entanglement measure assess (though computed differently). Similarly, residual entropy assesses the degree to which sub-string of the signal encodes a single atom in a role (e.g. Ollie in the Subject) and is minimized when a sub-string refers to only one atom in a role. This requires there be minimal homonymy and entanglement in subset of the signal (across or more positions), with each unique sub-string in those positions referring to only one atom a role. As discussed above natural language shows us that even a high degree of homonymy and entanglement in language doesn't 't preclude its compositionality, We show empirically in table that a maximally regular language maximizes topsim and posdis while minimizing residual entropy (for brevity residual entropy results are deferred to appendix A.7). Like topsim, languages that score highly on these measures are very likely to be compositional the issue is that they take some kinds of variation and evidence of non-compositionaliyy.
METHODS
Models We implement a reconstruction game with a sender network and receiver network. The overall architecture used is intentionally similar to Chaabouni et al. (2020); Resnick et al. (2020) and Guo et al. (2021) to allow comparison of results. The sender network is comprised of an embedding layer, linear layer, and GRU (Cho et al., 2014) the receiver architecture is the inverse. A linear layer is used as the input of fixed length, so can be presented at once as a one-hot encoding while GRU spells out the variable-length signal a character at a time. The maximum signal length used here is 6, with 26 characters available to the model in each position. The sender is optimized using REINFORCE (Williams, 1992) due to the discrete channel, while the receiver is optimised using ADAM (Kingma& & Ba, 2014). Models are implemented using pytorch (Paszke et al., 2019), and make of portions of code from the EGG repository (Kharitonov et al., 2019). Full hyperparameters for the experiments presented here can be found in appendix 10
The sender is shown examples drawn from a meaning space of two place predicates (e.g. Ollie loves Osgood) generated using context free grammar, with three roles: subject, verb, and object and 25 atoms per role, resulting in a total of 15625 examples. This is equivalent to the attribute, value setup used in previous work (Resnick al., 2020; Chaabouni et al., 2020). Data is divided into 4 splits for training: 60%, validation 10%, i.i.d. testing 10%, and o.o.d. testing 20%.
Data
O.O.D. Evaluation Previous emergent communication work typically evaluates generalization on an in-distribution held out test-set. In order better align our findings with the broader literature on
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Small Model Regrassion: Regularity Variability vs, O.O.D, Accuracy
2.0
regrssion cod (b volee wih wiooodd Acorocy
varlbble
eebongloved
hamonory
syronymy
logole
-05
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30 100 150 200
250
300
epoct (regression window size 100 spochs)
Figure A model fit to sliding window data from 100 epochs at a time across 20 initializations between o.o.d. accuracy and each measure of variation. Shown are the regression coefficients (b values) our four measures of variation, and two previous measures of regularity (topsim and posdis) with o.o.d. generalization accuracy for the small model for each window.
compostional generalization in neural networks (e.g. Lake & Baroni, 2018; Kim & Linzen, 2020) we implement& a version the maximum compound divergence (MCD) algorithm from Keysers et al. (2020), and report results for both in-distribution generalization, and out-of-distributio generalization to an MCD split. Additionally we use an O.O.D. split because models often converge to ceiling i.i.d. performance, which potentially makes it difficult to look for correlations between generalization performance and attributes of the language, like regularity. For our small model i.id. performance 95% confidence intervals are ++049% while o.o.d. performance is +7.07%, allowing broader range of values with which to look for correlations (we include the same analyses on i.i.d. performance in appendix A.8 and in practice i.i.d. and o.o.d. results are very similar).
Capacity We look to see if models with less capacity arrive at more regular languages than their larger counterparts predicted by work in natural language (e.g. Hudson Kam & Chang, 2009). We vary model capacity by varying the size of the hidden layers used by the model reporting and comparing results of three different model sizes small, medium, and large with hidden layer sizes 250, 500, and 800 respectively.
RESULTS AND DISCUSSION
Our results for all model sizes are summarised table 1. As stated in section 1 language must be compositional in order generalize, in line with previous work in this area (Kottur et al., 2017) and linguistics (Brighton Kirby, 2006). All versions of our model get near ceiling i.i.d generalization and robust o.o.d. generalization indicating compositional system. Compositionality and variation are related, but distinct; while a system needs to be more regular than a completely random mapping in order to generalize compositionally it does not need to be perfectly regular. Natural languages show us that a system can support high-degree of variation while remaining compositional. line with this in all conditions of our model the language that emerges is substantially more regular than a random mapping, but more variable than a perfectly regular language consisting of one-to-one mappings.
The relationship between regularity and generalization We use linear mixed effect models to evaluate the relationship between our four measures of variation and o.o.d. performance, fitting model on rolling windows covering the time course of training (implementation details in appendix A.3). The resulting regression coefficient (b value) for window indicates how strong predictor measures are generalization performance over that period training. As shown in figure 3 early on language's regularity is a strong predictor of how well generalizes, but later in training this
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effect goes away. This is consistent with the idea that some regularity is needed for generalization, but maximal regularity is not required. Later in training, as a language emerges that is regular enough to succeed at the task (achieving ceiling i.id. generalization performance), the relationship between regularity and generalization trends toward non-significance. Supporting this we see languages become more regular over time with negative relationship between training step and variation (6 = -0.038, p < le - 10) in table 1 we also see that in every condition the model decreases the variation in its language between early training and the best generalizing epoch indicated by negative value for A best o.o.d. An important limitation of these results is that the language for every run is still vighal-variable (with the lowest mean variation score of any run being 0.43), possibly because the task here is quite simple in comparison to compositional generalization datasets in other domains g Kim & Linzen, 2020). As languages approach maximal regularity, regularity may again be a strong predictor of generalization performance but given none of our models approach minimal variation this remains an open question (further discussion of these results in appendix A.5).
How can a variable language still be compositional? Figure 2 helps us to understand what these highly variable but robustly generalizing languages look like. visualizes the word order for the run of our small model with the highest word order freedom meaning all other runs of that model exhibit even stricter word order. It shows that while the language is still much more variable than a perfectly regular one (this language has freedom 0.57, a compositional language with fixed word order has freedom = 0), it nonetheless exhibits a high degree of word order regularity, with verbs most likely encoded at the start of the signal, subjects in the middle, and objects at the end, but with each individual atom sometimes being encoded slightly differently. Given compositionality requires the meaning of a whole be function of its parts the pattern seen here where each role is encoded in part of the signal appears to meet that threshold despite its high variation.
Capacity effects regularity with increase in the number of trainable parameters resulting in an increase in variation across all measures with large arriving at significantly more variable languages than small or medium (p 0.05). Spearman correlations show model size does not correlate significantly with o.o.d. accuracy (p 0.24) but correlates with synonymy (r = 0.67), word order freedom (r = 0.69), entanglement (r 0.68), and homonymy (r = 0.68) indicating larger models develop more variable languages (all of which are significant p < 0.00001). This result is in line with work that points to constraints on human cognition as a key driver of regularization in natural language, suggesting that similar factors shape the regularity of emergent communication in neural networks. Previous work studying the effect of network capacity on emergent languages (Resnick al., 2020) found that while most model sizes could generalize well, larger models could do using a non-coomosiiionnal code' indicated by a higher residual entropy measure (which has similarities to our measures of homonymy and entanglement). This is consistent with our results, although believe this indicates that larger models develop language characterised by greater variation rather than non-compositionallty (residual entropy scores for our model can be found in appendix A.7).
Framing prior results in terms of regularity Existing measures (topsim and posdis) correlate negatively with model size (r -0.63, -0.71) strongly suggesting that rather than tracking compositionalliy these measures implicitly track the degree of regularity in a language, especially given that the magnitude of their correlation coefficient is similar that of our measures that explicitly assess variation. This helps us to interpret results suggesting compositionality doesn't correlate with generalization: if these measures assess regularity instead we know wide array of languages can be regular enough to generalize well without needing to maximize regularity to do so.
5 CONCLUSION
Neural networks reliably arrive at compositional languages when natural language-like variation is taken into account. Previously these languages' compositionality has been assessed on the basis of their regularity, but natural languages show us system can be rich with variation while retaining the generalizability that makes compositionality so desirable. Similar to natural language the capacity of learners is key driver of the degree of regularity that emerges. By accounting for variation we can see striking similarities between the structure of the languages that emerge and structures in natural language.

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ACKNOWLEDGMENTS
We'd like to thank Ivan Titov and Rob Truswell for discussions of an earlier version of this project. This work supported in part by the UKRI Centre for Doctoral Training Natural Language Processing. funded by the UKRI (grant EP/S022481/I 1/1) and the University of Edinburgh, School of Informatics and School of Philosophy. Psychology Language Sciences. This work was also funded by the European Research Council (ERC) under the European Union's iitoon's Horizon 2020 research and innovation programme (Grant agreement 681942 1942, held by KS)
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A APPENDIX
A.1 WORD ORDER FREEDOM GRAPHIC
7 7
Mic Chrite Liiiiersnnyy
7-1
Micel Cholor Enutiorrdyy
Figure 4: The figure shows an illustration of the Freedom measure applied a regular and variable language. At the top is reproduction of the perfectly regular language cube from figure where role Object where every semantic atom in the object position is encoded by two letters at the end of the signal. Red indicates low probability, and green high. Directly below it is the entropy of each column, which reveals the word order freedom (conversley for the entropy plots green corresponds to low entropy, red to high) this is the operation completed in equation 4a. As the language is perfectly regular the entropy is low in the last two positions across all semantic atoms the object role. As result when is consistently lower in the two final positions. To get a measure between and we divide the lowest value in the mean distribution by the entropy of uniform distribution of the same size this is done in equation 4b. The bottom graphic shows the entropy illustration for an alternate, irregular language, where different atoms the object position are most likely be encoded signal positions. As a result the mean distribution is nearly uniform, when we take the minimum it will closer to the entropy uniform distribution resulting in score close 1.
take the
of the entropies
get non-uniform distribution: entropy
variety of
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A.2 ENTANGLEMENT GRAPHIC
Photitic Syriol
74
7
11 1220
Porthor Syred
Figure 5: The figure shows the entanglement measure applied perfectly regular language. We start with the column entropies shown the uniformity graphic, and which are calculated using equation 4a. Shown are the column entropies for two different roles, object and verb. The mean of both are taken and then compared in the lower part of the graphic. We take the absolute value of the difference the two averaged entropies. two roles are encoded in the same part of the signal then the result will be close to zero: they both have consistently similar in the same parts of the signal. In the illustration this would look like the final difference bar being entirely red, here it's green in positions indicating disentanglement there. The maximum of the difference is then divided by the maximum the mean entropy for the respective roles before they were subtracted this bounds measure between and and makes the measure kind of percentage of the overlap between roles (this operation shown in equation 5). If the roles are disentangled we end up subtracting a high entropy value from low entropy value in each position, meaning the magnitude of the difference will be substantially greater than zero. We do this for each possible paring roles, getting entanglement scores for each pairing, then mean them to get language level entanglement.
A.3 ROLLING MIXED EFFECTS MODEL IMPLEMENTATION
We implement rolling mixed effects model using the python statsmodels package. We fit separate model for each of our 6 independent variables: synonymy, entanglement, freedom, homonymy, topsim, posids. The dependent variable across all of them is o.o.d. generalization performance. For each model we include two random effects, random intercepts based on the seed used to initialize that run of the model, and random slopes for the epochs of training. This allows the model account for variation between different models, given that some initializations outperform others.
The model is fit to window of 100 epochs of training data time, at each step it fits regression to 100 epochs data for 20 initializations of the model. It then moves forward one epoch at a time (e.g. the first fit of the model is epochs () 100, the second on 1-101, the third 2- 2-10 etc.). We plot the resulting regression coefficient (b value) obtained from each mixed effects model fit to each IV, at each window of data.
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For reference the corresponding command to run this model with the LMER package in R (a standard method for fitting these kinds of models) is: Imer(ood_acc ~ IV + (1 + Epoch Seed)) where is one of the variation measures.
A.4 O.O.D. ACCURACY Vs. VARIATION SLICES
In addition to the regression analysis presented in the results section we show relational plots for two different epochs in training: near convergence. In line with the regression analysis a more linear relationship between o.o.d. performance and variation is visible earlier in training before the language becomes regular enough for the task. Entanglement in particular shows steep negative relationship in the 100 epoch plot but totally scattered by epoch 500. Were variation at the end of training we would could easily conclude in line with previous work that they were not meaningfully related.
from mid way through and one from late in training
only assess the relationship between generalization and
It's worth noting that the pattern here may not appear as salient as it appears in the rolling mixed effects model presented earlier, there are two major reasons for this: first the rolling model considers 100 epochs at time, rather than single slice with only 20 data points, providing with 100 times data visualized here by which to assess the relationship between variation and generalization. Secondly the rolling model has random intercept based the seed used in each run of the model. This is important because in line with other work on o.o.d. generalization we see a substantial effect of initialization
generalization performance, by including it as random effect the rolling model can look at each seed separately to see if each seed's generalization performance over the run is related to its language's variation. So while in the visualizations below we may see some seeds which appear like outliers, the rolling model accounts for this, fitting a separate intercept for each run.
Epoch 100: O.O.D. Acc vs. Variation
0.54
0.70
0.64
0.52
0.65
0.62
0.50
0.60
0.48
0.60
0.46
0.55
0..44
0.42
0.50
0.40
0.50
0.38
0.68
0.300
0.56
0.54
0.200
0.44
0.125
0.22
Accenscy
Ascuracy
Acaurcy
Figure 6: Plots show each of the variation measures plotted against o.o.d. accuracy at the 100th epoch of training.
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Epoch 500: O.O.D. Acc vs. Variation
0.65
0.300
0.60
0.53
0.400
0.375
0.40
0.55
0.550
0.425
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0.24
0.20
0.20
0.15
0.18
0.7
B.A
0.3
0.6
0.0.0 Aucenny
0.O.D Auswvey
O.C.0
Awcriay
Figure 7: Plots show each of the variation measures plotted against o.o.d. accuracy the 500th epoch of training.
A.5 O.O.D. ACCURACY Vs. VARIATION DISCUSSION
As noted in section 4 we see a strong relationship between regularity and o.o.d. performance early in training but this effect goes away as the model converges. We attribute this to each run of the model decreasing the degree variation in its language over time, resulting in a language sufficiently regular to succeed at the task. Where because all languages are sufficiently regular, whether one is slightly more regular than another doesn't 't necessarily result better generalization performance. This dovetails with the overarching argument here that as seen in natural language even high-degree of variation doesn't t necessarily undermine a language's ability to generalize.
However it is worth noting that the relationship between regularity and generalization early on could be driven in part by more regular languages being casier for the listener to learn. Chaabouni et al. (2020) observes that higher topsim languages casier to acquire. By taking emergent languages from the end of training, and separately training a model to map between signals and meanings using supervised-leande
they show higher topsim languages require less training to converge. Here could be the case that early in training more regular languages are easier for the listener to learn, improving generalization performance early and explaining in part the early correlation between regularity and generalisation. However, this is an emergent model and languages are not static throughout training meaning what the listener tries learn is a 'moving-targer' changing at each step. For this reason framing emergent results in terms of results that look at the learnability of static languages would potentially seem draw a false equivalency. It's unclear if the learnability of language at timestep matters at n + 1 when the language has changed. Given this, and the fact that we see all conditions decrease variation in the emergent language over time, we believe the best interpretation of our results is that regularity matters for generalization until the language becomes sufficiently regular for the task. Once sufficient regularity is reached greater regularity correlation. Although it is
doesn't ' necessarily improve generalization performance possible learnability has some effect further study of the role learnability plays in an emergent context, where what is learned changes, needed understand the full picture.
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A.6 USE OF EQUATION 1 FOR ALL 4 MEASURES OF VARIATION
We use equation 1 (copied below in simplified notation) to calculate the conditional probabilities used all measures of variation:
count(char, position, atom, role) P(charlpositions alom,
(6)
count[posilion,, alom, role)
This gives us a distribution over characters for each position, for each atom, in each role. This distribution is intuitively useful for estimating synonymy which can be seen as the entropy over characters a position.
A.6.1 FREEDOM AND ENTANGLEMENT
However it's natural to wonder why we use this distribution again when calculating measures of word order freedom and entanglement. Both of these measures refer to how likely it is that a given role is encoded in position in the signal. Freedom looks how consistently the atoms in position, while entanglement looks at how consistently any two roles are encoded in the same position, Intuitively we might want to calculate distribution over positions given roles instead, like:
role are encoded
P(position, char, alom//ole) count(position, char, atom, role)
count(role)
then marginalize over characters and atoms so that we could directly estimate the probability of position given role P(position|role The problem with this is that every signal has char- acter in every position, and every meaning has more than one role (i.e. subject, verb, and object, rather than just having subject) meaning that the distribution If we were to only marginalize over atoms, to get a distribution over characters and positions P(position, charlrole) this is also nearly uniform, because different atoms are encoded using dif- ferent characters. So marginalizing over atoms combines distinct distributions for each atom into cear-uniform one. Similarly if we only marginalize over characters get distribution positions and atoms P(position, atoms/role) because every signal has a character in every position the resulting distribution is also uniform.
positions is always uniform.
Fundamentally the only relevant probability distribution which is consistently non-uniform is the one described in equation 1: P(char(pap P(Ccharlooiiionn, atom, role). Even though every signal has a charac- ter in every position every character is not equally likely given a specific position, atom, role combination. As a result this is the distribution we use to calculate measures of word order freedom and entanglement. In order to do so we first observe that in signal positions where an atom, role combination not encoded [Pcharr positiin, [(charlposition, atom, role) uniform as the distribution is not conditioned by the selected atom and role. Accordingly we take lower conditional entropy ((((char (position, alom, role)) (used in equation 2) as an indication that an alom, role combi- be encoded in position. By taking mean of this conditional entropy
((Pccharlposition
nation is more likely across all atoms in a given role (described in equation 4a) we can see if is consistently low in the same position(s) of the signal for all atoms in that role indicating adherence Equation 4b then aggregates this across all roles.
single word order.
Entanglement looks as we take low conditional entropy as an indication that an atom, role combination is encoded in a given position we compare the mean from equation 4a with means from other roles see if they consistently low in the same parts of the signal.
if there is consistent encoding of multiple roles in single position. Seeing
A.6.2 HOMONYMY
Given that homonymy assesses the probability that a letter in a position encodes each atom in role, is possible to look at this by estimating the distribution Pattoo char, position, role) directly. The same distribution can be calculated by instead taking the P(char P(charlposition, atom, role) distribution and re-normalizing it along the atom axis:
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P(cchapp
(alom,,;) papuurrpllaomm....
Vi E A,
Hi(charp,.
(8)
Σ Arl =1 P(charp.slatone
We find empirically that this equivalent to computing [atom chaar, position, role)) (see results in table 2) with the only differences between the two resulting from small rounding errors. In table we report results for both approaches to computing homonomy across model sizes to show their equivalency. Note these results are the means of 6 seeds so differ slightly from figures in the core results. When introducing the measures in section 2.3 of these two approaches we opt for the re-normalization of (Phharr position, atom, role) rather than computing new probability distribution because we believe this makes the formulation of the homonymy measure more intuitively related to the others, and makes the visualizations in figure direct reflection of how the measures are computed while producing equivalent results.
epoch
ideal
random
small
medium
large
homonymy
0.12
0.99
0.56 + 0.14
0.62 + 0.15
0.72 0.05
direct homonymy
0.12
0.99
0.56 + 0.14 0.62 0.15
0.72 0.05
Table 2: Homonymy refers to the method of computing homonymy used in the core results and described in equation while direct homonymy instead directly estimates the distribution P(atom/char position, role). Results are the mean of 6 initializations at the best generalizing epoch, so values differ slightly from those the main results which the mean of 20.
A.7 RESIDUAL ENTROPY
In addition to topsim and posdis reported the main results we also report results from one other measure from previous work, residual entropy (Resnick et al., 2020). The results here follow the same pattern as the other measures of variation with larger models arriving and more irregular languages. Additionally all conditions increase the regularity of the emergent language over the course of training. Also shown is the correlation analysis between Residual entropy and O.O.D. performance, showing like other measures of variation residual entropy is strong predictor early in training but that this effect goes away later on.
epoch
idcal
random
small
medium
large
best
0.0610
0.6250
0.2990++0.1 16
0.3780++0.1 12
0.4650-t:008
o.o.d.
0.5230+0.05
0.4460-0.08
0.2370=20.20
Table 3: Residual entropy scores at the best generalizing epoch and the diffcrence between the best generalizing epoch and one drawn from early in training. Results are the mean of 6 initializations.
A.8 I.I.D. CORRELATION RESULTS
We also include the correlation results between the measures of variation and in-distribution gen- eralization. The results follow similar pattern with degree of regularity being strong predictor of generalization performance early in training but this effect goes away as the emergent language becomes regular enough generalize well. Interestingly in-distribution and out-o--distribution correlations align almost exactly. This is reassuring in that it shows degree of regularity is important for generalization in general whether it is in or out of distribution.
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Small Model Regression: Residual Entropy vs. O.O.D, Accurocy
00
rigresice cod (b-ekke od Accrncy
0.1
1poth (egresioon waddow spochs)
Figure 8: The rolling mixed effects model coefficients between Residual Entropy and o.o.d. general- ization accuracy for the small model for each window.
Small Model Regression: Regularity Variability vs. L.D.D Accuracy
2.0
1.0
enorgheen
regeatte our vdell whil.d Acraad
0.5
-0.
50 100 190 200
200 opechs (mngendos spudla)
300
Figure 9: The model is fit window of data from 100 epochs at time across 20 initializations. The window slides forward one epoch at a time (i.e. epochs 0-100, 1-101 ...) and fits different model between i..dd accuracy and each measure of variation for each window. Shown the regression coefficients (b values) of our four measures of variation, and two previous measures regularity (topsim and posdis) with o.o.d. generalization accuracy for the small model for each window.
A.9 SIGNIFICANCE TESTING FOR VARIATION DIFFERENCES
params
synonymy
entanglement
freedom
homonomy
topsim
posdis
250 500
0.0275
0.1049
0.0574
0.0629
0.2565
0.0993
250 800
0.0001
< 0.0001
0.0001
0.0001
0.0001
< 0.0001
500 vs 800
0.0001
< 0.0001
0.0002
0.0001
0.0005
0.0001
Table 4: P Values obtained from a t-test comparing variation measures from different sized ini- tialization. The difference between large and small and large and medium are significant. Of differences between small and medium only synonymy and posdis are significant
A.10 HYPERPARAMETERS
Recurrent Unit: GRU
19

---

Published as a conference paper at ICLR 2023
Hidden Size: 250, 500, 800
Entropy Regularization Coefficient: (sender 0.5, receiver 0.0)
Batch Size: 5000
Learning Rate: le-3
Signal Length: 6
Character Inventory: 26
Training Epochs: 800
Embedding Size: 52
Roles: 3
Atoms: 25
Optimizer: (Sender: Reinforce, Receiver: ADAM)
20


Reviews:
[{"review_id": "i6JwX6aYpL", "reviewer": "Reviewer_uoNs", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper proposes a variation-based framework that is able to capture the compositionality in emergent languages. Contrary to most previous work, the authors show that compositionality is in fact correlated with generalization. The difference being that the learned compositionality is obscure and posses a high degree of variability and cannot be captured with the given metrics.", "summary_of_the_review": "The paper is clearly written and it indeed investigates an important research question in emergent communication. The hypothesis indicates some contrasting results from previous work and provide a novel view to study compositionality in emergent languages. Still, I believe the contribution is not clear when compared to prior works as outlined above.", "strength_and_weaknesses": "The paper does an intensive study on the previous metrics used for compositionality in emergent languages. The paper proposed 4 different metrics for evaluating compositionality that are able to marginalize the factors of variation in the language.\n\nThe closest metric that seems to be relevant to the proposed metrics is residual entropy. But I don't see any comparative evaluation with that in the paper and in the Appendix. \n\nAlso, Kottur et al. 2017, Resnick et al. 2020 also investigates the relation between capacity, compositionlity and generalization but it hasn't been captured here. ", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "RyCEhGxaSX", "reviewer": "Reviewer_UTH9", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper argues that the languages that emerge between networks are straightforwardly compositional with variations.\n\nThe paper introduces a variation-based framework and new measures to analyze regularity in mappings and exhibit compositional structure, which is clearly shown in experiments.\n\nIt shows that an emergent language's regularity is strongly correlated with generalization in early training, but it goes away after convergence.\n\nThe experiments show that small model capacity improves regularity.", "summary_of_the_review": "This paper introduces a new framework with multiple definitions to measure compositionally.\n\nHowever, the reviewer thinks it is still not above the acceptance line, mainly because the definitions may need improvement, as mentioned in the \"weakness\" section.", "strength_and_weaknesses": "***Strength***\n\n- It defines multiple practical measures for compositionality.\nThe definitions link multiple observations to multiple variations of linguistic concepts.\nObservations include position, character, object, and role.\nThe variations include Synonymy, word order freedom, entanglement, and homonomy.\n\n- It has findings for whether and when compositional structures are learned. It also finds the relation to model capacity.\n\n***Weakness***\n\n**1. Why are the definitions good ones to measure language compositionality?**\n\n*1A. Do they measure compositionality?*\n\nFor example, some natural languages have the word order freedom, and others do not. However, in both cases, the languages can be compositional.\n\n*1B. Do they cover all compositional phenomena?*\n\n**2. Contents of definitions**\n\nSince the joint probability is available, a conditional probability can be directly computed.\n\nIt would be helpful to explain why the proposed definitions are more reasonable than the standard definitions of the conditional probability distribution, which match the verbal definitions.\n\n*2A. Definition in 3a*\n\nAs stated in the text, word order freedom indicates whether \"each semantic role is consistently encoded in a particular part of the signal.\"\nA straightforward definition that matches the statement is the conditional distribution of position given role: P(position | role) (or 1 - P), which differs from the definition in 3a.\n\n*2B. Definition in 5a*\n\nFor each character in each position, \"a probability distribution over atoms in a role\" can be straightforwardly defined and computed as a standard conditional probability distribution P(atom | role, character, position). It does not equal the definition in 5a.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "ILjzLApkq0", "reviewer": "Reviewer_uQjZ", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "- This paper attempts to address the contradiction that prior works have shown emergent languages to generalize compositionally but without the emergence of compositional languages.\n- The authors argue that emergent languages are characterized by variation and that an emergent language's compositionality is distinct from its regularity. This variation masks compositionality from previous compositionality metrics like topsim, residual entropy, and posdis.\n- The authors introduce variation measures for synonymy, word-order freedom, entanglement, and homonomy.\n- To demonstrate that these measures follow the semantics of compositionality as we would expect:\n    - The authors compare a perfectly regular and a non-compositional random mapping and show that the variation measures take on extreme values, with close to 0 for the compositional mapping and close to 1 for the non-compositional mapping.\n    - Experiments show that an emergent language's regularity and variation correlate positively and negatively with generalization, as one would expect, early in training. This correlation goes away with increasing epochs as we get to the regime where the authors suggest all models converge to a sufficiently regular language to generalize compositionally.\n    - The authors verify the previously-published connection that reducing model capacity results in greater regularity of emergent languages, using the variation metrics.", "summary_of_the_review": "This paper has the potential to be an important one for the community. However, it needs to explain better why there is no correlation between the metrics and OOD generalization at model convergence. How does this paper positively answer the question, \"is compositionality necessary for generalization?\"? I would be inclined to increase my score based on the resolution of these concerns.", "strength_and_weaknesses": "Strengths:\n- This paper presents an important perspective on the compositionality of emergent languages and new metrics to support it. The contributions can potentially address the debate of whether or not compositionality is important for generalization.\n\nWeaknesses:\n- There is no good explanation for why we only expect a correlation of the compositionality metrics with generalization earlier in training. The correlation of the compositionality metrics goes to zero as a model converges. Doesn't this indeed say that the degree of regularity or variation does not matter for OOD generalization?\n\nAnother question:\n- In addition to the presented variation measures, is it reasonable to average the variation measures into an additional \"average variation\" metric to compare with the previous compositionality measures?", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works.", "empirical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works."}, "extra_text": {}}, {"review_id": "B32upozFwDO", "reviewer": "Reviewer_hjdA", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The submission aims to explain the negative results in the compositionality of emergent languages of prior work, in particular, the seeming double dissociation between the generalization ability of agents and the compositionality of their emergent communication systems.\nThis is achieved by defining measures of variation (nonregularity) that are shown empirically to be analogous to previous compositionality measures, alongside the claim that out-of-distribution (OOD) generalization performance is a better measure of compositionality.", "summary_of_the_review": "The motivation to disentangle regularity and compositionality in emergent languages is interesting and novel, but the implementation and generalizability of the idea are not made sufficiently clear to judge significance.", "strength_and_weaknesses": "### Strengths\n\n1. **Interesting motivation**: The manuscript aims to explain negative results in the compositionality of emergent languages, in particular, the seeming double dissociation between the generalization ability of agents and the compositionality of their emergent communication systems.\nThis problem is of interest to communities at ICLR.\n\n2. **Interesting contribution**. The idea that \"language variability obscures compositionality as measured in prior works in emergent communication\" is nice. \nThe paper also follows up on this idea with concrete proposals for measuring the variability that might confound prior measures of compositionality.\n\n\n### Weaknesses\n\n1. **Difficult to understand definitions and their generality.**\nThe definitions of the measures in Section 2.3 lack an introduction to what is meant by many of the concepts they depend on; for example, what is meant by\n\"character,\" \"signal position,\" \"semantic atom,\" \"semantic role,\" \"meaning,\" and\nby \"characters referring to words.\"\nBecause these basic concepts were not defined, it isn't easy to interpret the definition of the measures themselves and how they might measure language variability that confounds measures of compositionality, which is one of the paper's main contributions.\nFurthermore, how do these concepts map onto aspects of the emergent languages studied in the relevant prior work, and of natural languages?\n\n2. **Motivation for using OOD generalization performance to measure compositionality needs to be clarified.**\nSince the paper centers on refuting measures of compositionality in prior work,\nThe paper should clearly state how OOD evaluation is sufficient to measure compositionality. \nHowever, there seem to be only brief discussions of this \nin the middle of Section 3 and at the beginning of Section 4 \n(in addition to the broader discussions in the introduction).\n\n3. **Unclear how insights from the experimental setup generalize.**\nSection 3 has only the following as a comparison of how the setup in the paper relates to prior work:\n> This setup, while simple, is in line with previous work in this area (e.g., Guo et al., 2021; Chaabouni et al., 2020).\n\n    However, the comparison with prior work is critical because of the claim that prior work does not disentangle compositionality from regularity. As it stands, it is not clear how the results from the experiments in this paper will generalize to experimental setups of other works that are explicitly named as motivations, including Choi et al. (2018), Kottur et al. (2017), and Chaabouni et al. (2020).\n\n4. **Insufficient references to prior work in the compositionality of natural language.**\n\n    The forms of regularity/variability in Section 2.4 allude to prior work in linguistics, lexical semantics, compositionality in natural language, etc. However, no references to any prior work in these domains are made in this section. It is not likely that this manuscript independently originated the notions of synonymy & homonymy, word order, and \"entanglement\" of syntax and semantics. Some further spots that lack references are below in \"Minor points.\"\n\n\n### Minor points\n\n1. > However, natural languages exhibit rich patterns of variation (Weinreich et al., 1968), frequently violating these three properties...\n\n    Please also cite negative work in compositionality itself of human languages:\n    - Barbara H. Partee. 1984. Compositionality. Varieties of Formal Semantics, 3:281–311.\n    - [Dankers et al. (2022)](https://arxiv.org/abs/2108.05885)\n\n2. > ... the question of an emergent language's compositionality is related to, but distinct from, questions about its regularity.\n\n    At this point, I'm still not sure about the precise meaning of \"regularity,\" which makes it difficult to understand the significance of the double dissociation experiments discussed in this paragraph.\n\n3. > While languages that score highly on topsim, residual entropy and posdis are necessarily compositional, not all compositional languages will score highly ...\n\n    This is not entirely self-evident from the preceding two paragraphs. Can you add additional justification or state that you will more precisely define these concepts later?\n\n4. > \"e.g. 'loves', 'adores', 'treasures', 'cherishes' all convey approximately the same concept, exemplifying a one-to-many meaning-word mapping\"\n\n    I don't think this is the best example: The latter two words are most often used in the context of inanimate objects or concepts.\n\n5. > Natural language shows us that a compositional system can exhibit high levels of synonymy and homonymy while retaining the productive generalisation afforded by compositionality.\n\n    This should include some references to the vast literature on lexical semantics and pragmatics that it alludes to.\n\n6. > The freedom of order by which meanings are expressed in form has little bearing on whether or not the resulting form can be composed or interpreted compositionally ...\n\n    This statement discards the role of syntax in languages that are unlike Basque. Syntax clearly matters for the interpretation of lexical compositions in many languages.\n\n8. > ... in terms of a probability distribution over characters in each signal position given a semantic atom in a semantic role.\n\n    It's unclear what a \"semantic atom\" or a \"semantic role\" is, \n    both as abstract definitions and in terms of the specific experimental setup.\n    Similarly, it's not clear what \"characters\" nor \"signal positions\" are.\n\n9. > In order to better align our findings with the broader literature on compostional generalization in neural networks we implement a version of the maximum compound divergence (MCD) algorithm from Keysers et al. (2020), and report results for both in-distribution generalization, and out-of-distribution generalization to an MCD split.\n\n    I don't understand the motivation for this at this point in the paper.\n    This component of prior work needs to be better explained in the context of this paper, especially as it seems to be an essential part of the evaluation.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}]

Author rebuttal:

Decision: Accept: poster