CtD: Composition through Decomposition in Emergent Communication
Authors: Boaz Carmeli
Ron Meir
Yonatan Belinkov
Venue: ICLR 2025 Poster (2025)
Keywords: Emergent communication
Compositionality
Codebook learning
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
TL;DR: This work demonstrates that discretizing the latent space and communication channel with a discrete codebook significantly enhances compositional generation in emergent communication.

Abstract: Compositionality is a cognitive mechanism that allows humans to systematically combine known concepts in novel ways.
This study demonstrates how artificial neural agents acquire and utilize compositional generalization to describe previously unseen images.
Our method, termed \`\`Composition through Decomposition'', involves two sequential training steps.
In the \'Decompose\' step, the agents learn to decompose an image into basic concepts using a codebook acquired during interaction in a multi-target coordination game.
Subsequently, in the \`Compose\' step, the agents employ this codebook to describe novel images by composing basic concepts into complex phrases.
Remarkably, we observe cases where generalization in the `Compose' step is achieved zero-shot, without the need for additional training.

Published as a conference paper at ICLR 2025
CTD: COMPOSITION THROUGH DECOMPOSITION IN EMERGENT COMMUNICATION
Boaz Carmeli
Ron Meir
Technion - Israel Institute of Technology
Technion Israel Institute of Technology
boaz. carmel i campuss. techni on ac i1,
rme rêes eéee. technion. ac. il
Yonatan Belinkoy
Technion - Israel Institute of Technology
belinnko@teehnionn.cer
ABSTRACT
Compositionality is cognitive mechanism that allows humans to systematically combine known concepts in novel ways. This study demonstrates how artificial neural agents acquire and utilize compositional generalization to describe previ- ously unseen images. Our method, termed "Composition through Decomposition", involves two sequential training steps. In the "Decompose" step, the agents learn to decompose an image into basic concepts using a codebook acquired during interaction in a multi-target coordination game. Subsequently, in the 'Compose' step, the agents employ this codebook to describe novel images by composing basic concepts into complex phrases. Remarkably, we observe cases where general- ization in the 'Compose" step is achieved zero-shot, without the need for additional training.
INTRODUCTION
A variety of communication methods can be found in nature (Munz 20055 Mculenbrock & Morncault 2022, [Szukii 2016 Hölldobler, 1999). There are, however, many aspects of human language that are unique. One such aspect involves natural language's 's capacity to manage and process concepts. Humans are able manipulate and compose concepts variety of ways. A chief ability among these is compositionality the principle whereby new meanings arise from systematically combining
simpler concepts novel manner (Frege 1892 & Bowling 2019, Hupkes et al., 2020). Through
compositional generalization, humans describe previously unseen objects and attribute meaning
to unfamiliar scenes. However, neural networks struggle to achieve compositional representations
(Lepori et al. 2023 Xu et al. 2022 Bouchacourt & Baroni 2018 Dankers al. 2022 Dankers & Titov] 2023). One reason for this disparity lies in neural networks' struggle to process and manipulate discrete entities. Several methods have been proposed and evaluated during recent years by the emergent communication (EC) research community to overcome this difficulty. Among them are reinforcement learning (RL) based optimization (Williams) 1992. Lazaridou al. 2017). Gumbel- softmax (GS) sampling (Jang et al., 2017 2017 Havrylov & Titov (017)) 7),, and vector quantization (QT)
(Carmeli et al. 2023). We describe these methods in more detail Section
In this study, and consistent with previous work (Kottur et al. 2017), we emphasize that relying solely on discretization bias is insufficient for achieving compositionality. Additionally, we assert that before effectively composing basic concepts into complex ones, agents should acquire the ability to decompose complex concepts into basic ones. To demonstrate these claims, we train the agents to acquire a discrete concept codebook (Van Den Oord et al. 2017) through engagement in multi-target games (Mu & Goodman 2021) (Figure Left). which we expand upon in Section let them play a standard referential (REF) game (Lazaridou & Baroni 2020 Lazaridou et al.) 2017)) where they utilize the learned codebook to describe images using novel combinations of known 'words' (Figure Right). We refer method as "Composition through
2] Subsequently,

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Decompose
Compose
CB
CB Msg
Target-1 Target-2
Word
Concept
Target-1
Target-2
Word
Concept
Target
Phrase
O
0.1
0.4
0.1
Blue
>
0.2
0.3
Blue
D
Triangle
0.2 0.5
0.3.0.5
Triangle
0:3
0.2
Red
T Redillaa
Square
0.2(0.5
0.300
Square
Red
0.4
0.5
Green
O
Circle
0.5.0.8
0.7
Green
Circle
Figure I: CtD training process: Concepts are learned and stored in the codebook during the DECOM- POSE step (Left), then composed describe objects during the COMPOSE step (Right).
Decomposion" (CtD) and demonstrate its superior performance compared to existing methods by substantial margins. Notably, our method achieves perfect accuracy and compositionality. on multiple datasets. Learning a complex task by first learning a simpler task is reminiscent of the 'scaffolding' approach in developmental psychology (Wood et al. 1976) and of recent curriculum basedd methods in machine learning (Soviany al. 2022).
Our contribution comprises three essential elements for achieving compositional generalization: two that have proven useful in other setups and one introduced by us. Multi-target: We highlight the importance of multi-target coordination games in enabling neural agents to decompose complex objects into basic concepts. Discrete codebook: we establish the efficacy of employing a discrete codebook for representing these basic concepts in latent space. CtD: we introduce a novel two-step "composition through decomposition" approach, which leverages codebook -based communication in multi-target coordination games, surpassing current emergent communication methods in composition tasks and delivering perfect results on specific datasets.
2 EMERGENT COMMUNICATION AND COORDINATION GAMES
Much recent work studies the aspects of emergent communication (EC) by letting agents play
coordination game (Lewis] 1969) to accomplish a task that requires communication (Batali 1998]
Choi et al. 2018 Cao al.) 2018: Jaques et al. 2019 Das al. 2019 Tian et al., 2020 Gratch
et al. 2015 Yu et al. [0222. In the basic EC setup (Clark & Wilkes- Gibbs 1986 Lazaridou et al.
2017
2018). illustrated in Figure there a world X, which common to two agents: sender S
and receiver R. The sender and receiver observe x and X respectively. The world may be fully observable by both agents (X = xS X or partially observable (XS, XR X).
Both agents have some representation of their observable world, U and U.R Given its current representation of the world, the sender sends a message m over some communication channel to the receiver R. The message is sequence of discrete elements over some vocabulary, which we call words. The receiver uses the message to identify the target(s) out of a set of candidate objects, for example identify red triangle out of set of objects with different shapes and colors.
Many game variants have been proposed in the EC literature (Lazaridou & Baroni 2020 Lazaridou
al. 2017 Mu & Goodman 2021: Dessi et al. 2021 Denamganai & Walker (222)) We provide
detailed description of the main ones in Appendix variants, outlined next.
In this study, we focus on multi-target game
2.1 MULTI-TARGET COORDINATION GAMES
In multi-target coordination game Mu Goodman 2021), the sender communicates about a set of target objects T { out of a larger set of candidate objects C. For instance, the target set may be all red triangles out a larger candidate set of colorful shapes of varying sizes. Formally, assume a world X, where each object is characterised by feature-valle pairs (FVPs), (f1 Vi.... fn : vn). with feature having k; possible values, vi E [1] f. fk[k;]]. For instance, the SHAPE world Kuhnle & Copestake (2017) has objects such (Shapetriangle..oooorre;;
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Ys
I(Pr,
yr
YT
X
u
C
m
ΦΦ
g(.)
u
X
U
z
Z
U
Sender Network
Receiver Network
Figure 2:
The emergent communicating architecture. Sender network is the left, Receiver network is at the right, m is the communication channel and CB, is the codebook.
Each "phrase" 1: x {0, 1} labels object as or 1. For instance, the phrase Red Tri oriangle labels all red triangles as positive and all other objects negative. We identify the phrase Red Triangle with the natural language (NL) phrase "red triangle", which comprises the basic concepts "red" and "triangle". At each turn of the game, phrase is drawn at random from set of labeling phrases L,, and of candidate objects X X is randomly selected, comprising both target objects, T, adhering to the phrase, and distractors, ID that do not: ((x) = 1 if x E T and (xx = 0 if x E D.
The sender encodes each of the targets t, into continuous vector u E Rd, and computes target representative U = Σ u. The receiver in multi-target games similar to that in single-target games. Refer to Appendix A. details.
In this work we demonstrate that employing a multi multti-trrget setup crucial for extracting concepts from images, calling into question the ability of compositionality to arise from traditional single- target games. Although multi-target games are seldom used emergent communication studies, our experiments show that this setup is crucial for effective concept decomposition. Refer to Section 5.2 for the experimental results.
2.2 COMMUNICATION MODES
A key assumption in EC setups is that discrete channel with restricted capacity serves as facilitating bias for the emergence of compositionality (Havrylov Titov| 2017] Lazaridou Baroni 2020)
Vanneste et al., (022). Thus, a large body of work has been concerned with enabling discrete communication in artificial multi-agent systems (Foerster et al. 2016 Lazaridou al. 2017 Havrylov & Titov] 2017). However, the discretization requirement poses significant challenge to multi-agent neural systems, which are typically trained with gradient-based optimization. Several approaches have been proposed for overcoming this challenge, e.g., relaxing the discrete communication with continuous approximations such as the Gumbel--sfftax (GS) Jang et al.) (2017); Havrylov Titov (2017) quantization (QT) Carmeli et al. (2023). More details these methods given in Appendix A.2
In related studies, Tucker al. (0022) suggest using codebook discretize the latent space, with focus on balancing communication complexity and informativeness. However, their research does explore compositional generalization, which is characterized by the ability to construct complex phrases from basic, meaningful concepts. Refer to Appendix H.4 for a detailed comparison.
In this work, we demonstrate how communication protocol based
latent discrete codebook (an Den Oord et al., 2017), referred to as CB, can be used to develop a compositional language.
2.3 EVALUATING COMPOSITIONALITTY
A large body of work has attempted to characterize EC in light of natural language traits, such as compositionality (Hupkes et al., 2020 Chaabouni et al. 2020), systematic generalization (Vani et vral,,2021 pragmatism (Andreas & Klein 2016 Zaslavsky al. (021). and more. In this work we are mainly interested is evaluating compositionality. defined by agents' ability to construct complex meanings from the structure and meaning of more basic parts (Li & Bowling 2019 Andreas

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2019). A variety of metrics has been proposed in recent years Peters et al. (2024) for evaluating compositionality in emergent communication.
In this study we five such evaluation metrics for compositionalit: Adjusted Mutual Infor- mation (AMI) (Vinh et al. 2009) measures the mutual information between a set of EC messages and corresponding set of NL phrases, adjusted for chance. Positional Disentanglement (POS) (Chaabouni et al., 2020) assesses how well words in specific positions within an EC message uniquely map to particular concepts in a NL phrase. Bag of Symbols Disentanglement (BOS) (Chaabouni et al. 2020) assesses the degree to which words in an EC language unambiguously correspond to NL concepts regardless of their position. Context Independence (CI) (Bogin al. 2018) measures
the alignment between EC words and NL concepts by examining their probabilistic associations across a set of EC messages and NI. phrases. Concept Best Matching (CBM) (Carmeli al. (024) quantifies the best match between set of EC messages and a corresponding set of NI. phrases. We provide more information on these metrics in Appendix A.T
3 COMPOSITION THROUGH DECOMPOSITION
In this section, we present the CtD approach. We begin by outlining the two-step training regimen of CtD, followed by its utilization of a codebook to decompose the latent space into a discrete set of vectors. Finally, we detail the multi-loss optimization process used to concurrently optimize the vector representations of the codebook and the task's 's success.
3.1 TWO-STEP TRAINING REGIME
The CtD approach based on the idea of "Breaking down to build up". To achieve that, CtD involves two sequential training steps. First, in the DECOMPOSE step, agents are trained to learn codebook with distinct sets of concepts using a multi-target SINGLE-CONCEPY dataset. (Refer to Section 2.T for more details multi-target games.) For example, to let the agent learn the concept ue, we create data sample with (at least) two targets: a Blue Circle and a Blue Square. See Figure D (Left). Second, in the COMPOSE step, train the sender to describe an image from COMPOSITE-PHRAS dataset by composing together a set of words from the learned codebook. For example, after learning the concepts Blue and Tr iangle during the DECOMPOSE step, the sender needs to compose a description Blue Triangle during the COMPOSE step. See Figure (Right).
The training steps differ in the data they (T,, Dig Ty, ITEE) composed from a set of the sender's targets and distractors and the receiver's targets and distractors, respectively. In the DECOMPOSE step, all targets share a phrase composed from exactly one concept (FVP). Unlike Mu & Goodman (202I). we do not use distractors in this step, demonstrating their redundancy for concept learning step, all targets share phrase composed from a set of concepts (FVPs) with predefined length, I. Importantly, the sender's ss targets, Tÿ. need not be the same as the receiver's 's TV but all targets must share the same phrase. The number of targets and distractors may vary and is part of the configuration of each game.
Formally, each data sample de E D is quadruple
multi-target setup. In the COMPOSE
Code-words are extracted from the codebook based on their similarity with the image representation U.S. During the DECOMPOSE step the top most similar vectors are extracted from the codebook, where I is a dataset-dependent parameter. The sender then concatenates these vectors to form bag-of-words message, Z'.
3.2 LEARNING WITH A DISCRETE CODEBOOK
CtD uses a discrete codebook (Van Den Oord et al. (2017); Zheng & Vedaldi (2023) to encourage the sender to transmit disentangled image features or concepts. The codebook consists of set of learnable vectors (code-words), each representing a discrete concept in latent space, which we term word. Discretization achieved by replacing an input representation vector with the closest word in the learned codebook. The words in the codebook are updated during training best represent the distribution of data. A key advantage of using a codebook over other discretization methods is its ability to leverage discrete latent space, learned during the DECOMPOSE step, for communicating
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Table Number of concepts and phrases in the experimental datasets for the two training phases.
SIGLE-CONCEPP
COMPOSITE-PHRAN
Unique Concepts
Image Objects
Train Phrases
Val Phrases
Test Phrases
Image Objects
Phrase Length
Uniquely Identified
Dataset
THING
50
25024
950
958
5 yes
SHAPE
17
203
33
34
no
MNIST
10
1-2
70
15
15
2
2
no
Coco
80
261
14
26
2-3
2
no
QRC
50
1
25024
950
958
5
yes
compositional phrases during the COMPOSE step. We provide formal definition of the codebook in Appendix
3.3 TRAINING WITH MULTIPLE-LOS, FUNCTION
We train the system end-to-end by minimizing the loss: game-specific and typically involves either cross coss-entropy (CE) for MREF games, binary cross-entropy (BCE) for DIFF games, or mean squared error (MSE) for RECON games. Minimizing leads high accuracy on the game. The codebook loss L. (Oord et al. 2018 is optimized by minimizing the MSE between the latent vectors z and the code-words w,
L. BICc. The task loss L, is
C. ||s][2] w + Bellz - sg[w]||
(1)
where sg(-) denotes the stop gradient function, needed to overcome the discreteness of the codebook and B2 is for more details.
that balances the two codebook loss components. Refer to Appendix G
The codebook loss encourages the sender's output representation, US (see Fig. to close to the nearest word in the codebook. This is accomplished by utilizing the stop gradient function, which effectively employs a "straight-through" estimator. This mechanism allows gradients to flow through the quantization step during back-pmt proppaaaaon (Van Den Oord et al.) (017). Minimizing the codebook loss often leads to high compositionality score as measured by the CBM and AMI metrics.
The losses capture distinct aspects of the system and, as shown in Section often compete with each other. We experimented with various values of 31 and B2, ranging from 0.1 to 1.0 and found no significant difference results. To ensure consistency across all game setups, we both 1.0 for all experiments. Refer to Appendix Gor details.
4 EXPERIMENTAL SETUP
Our experimental setup follows the two-step training regime outlined by the CtD method. Firstly, we train the agents to DECOMPOSE. For that construct share single concept. Subsequently, we train the agents to COMPOSE using COMPOSITE-PHNE -PRASE dataset where targets share set of concepts. We compare the CtD approach with C/D regime, in which agents are trained to COMPOSE without prior training them to DECOMPOSE. We also explore a variant in which only a single target is used during the COMPOSE step, akin to the classic REF game.
dataset where all target
We evaluate game performance based on the accuracy of the agents in identifying the target(s) and the level of compositionality observed in their communication, as measured by the compositionality metrics.
4.1 DATA SPECIFICATIONS
We use five datasets in our experiments summarized Table THING (Carmeli et al. 2024) is synthetic dataset of 100K objects encoded by concatenating five one-hot vectors. This dataset is best suited for evaluating compositionality in a highly controlled environment. SHAPE (Kuhnle & Copestake 2017 is visual reasoning dataset of colorful objects over black background
Datasets
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This dataset requires learning long phrases from images and is widely used by the EC community. MNIST (LeCun et al., 1998) is a dataset of handwritten digits, ranging from 0 to 9. For evaluating compositionality, created 2-digit version of the dataset by combining two images from the original dataset. Refer to Figure / for an example. Coco (Lin et al., 2014a) is a dataset of real-world multi-object images with categorical captions. QRC is synthetic image dataset introduced by us, employing two-dimensional QR codes to encode information akin to the THING dataset. We use this dataset evaluate results on non-compositional dataset. We provide more information on each of these datasets in Appendix
Rule construction Each data sample in the dataset comprises targets and distractors. These samples adhere to labeling phrase, dictating the shared concepts among the targets. We generate variants for every dataset, a COGGE--CONCET and a COMPOSITE- PEEEEE...EE..... In the SINGLE-CONCERS labeling phrase consists of single concept. The length of the labeling phrase in the COMPOSITE- PHRASE varies across datasets. Refer to Table details. Importantly, during training we set the message length match the length of the phrases the dataset. For example, we set the message length of the labeling phrase Red Triangle to 2. Constraining the message length to match the phrase length in the data restricts CtD's ability learn variable-length communication. This limitation is further discussed in Appendix F and in Appendix [ (Limitations).
the
Data splits In the SINGLE-CONCEPE variant we split the data randomly into training, validation, and test sets. This approach aligns with our belief that agents cannot generalize across concepts; for example, learning the concepts Red and Tri Triangle does not enable the agents to learn the concept Square. However, in the COMPOSITE-PIRRAA phrase labels in each split. Specifically, if a labeling phrase such as Red: Square appears in the test set, does not appear in the training set. This segregation allows us to evaluate the extent to which agents have learned to generalize by composing known concepts in novel ways. In all our experiments we use 30,000 samples for training, 1000 for validation and 1000 for test.
variant, we ensure that there is no overlap between
4.2 COMMUNICATION BASELINES
We compare results with two communication baselines, Gumbel-softmax (GS) Havvylov & Titov| 2017: Dang
Jang et al., 2017) and Quantized (QT) (Carmeli et al.] 2023). See Section for details. We configured the GS vocabulary match the number of concepts in each dataset. Additionally, for QT, we set the word length to enable the encoding of at least as many concepts as there are in the dataset. As expected, the two-step training regime did not yield any benefits for GS and QT, do not report those results.
4.3 TRAINING DETAILS
The EC setup encompasses numerous configuration and hyper-parameters that can adjusted during experiments. To ensure a fair comparison, we modify only the parameters being tested. Specifically, we maintain consistency the architecture of the agents (ug and uy. in Figure [ and network dimensions across all communication types. Furthermore, for the different communication types. Agent architectures, up and ug. vary slightly across games to optimize the encoding of images into latent vectors U and UT. Refer to Appendix G for more details on the configuration and training parameters and procedures.
select optimal vocabulary parameters
5 RESULTS
In this section, we present experimental findings. We begin by outlining primary results depicted in Figure For detailed numerical results, please refer to Table Appendix C In Section [.2] we provide supplementary analyses and results from ablation experiments. Results for additional configurations and experiments are provided in Appendices and We discuss the limitations of the CtD approach in Appendix

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Single Concept
Composite Phrase
1.0
Acc
Codebook
ms mt
Acc
Quantized
0.8
0.8
0.6
0.7
Gumbel
0.6
0.6
0.5
T
Thing
0.4
Shape
MNIST
M
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COCO
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CBM
Figure 3: Accuracy and CBM results for the four compositional datasets (excluding the non- compositional QRC) and the three communication modes (Gumbel-softmax in green, Quantized in red and Codebook in purple) for the dataset (Right).
dataset (Left) and the COMPOSITE PHREEEE
5.1 MAIN RESULTS
Decomposition (D) performance Analyzing agents' performance on the SINGLE- -OCCCEPT
dataset (Figure 3 Left) shows that codebook-based communication (indicated by purple letters in Figure and the 'D' rows in Table 4 in Appendix [) achieves perfect accuracy (ACC) and compositionality (AMI, POS, BOS, CI and CBM) across the THING, SHAPE, and MNIST games. However, poorer results were observed for the Coco and non-compositional QRC datasets (Table in Appendix C which we further investigate below. all setups, QT (represented by red letters in Figure 3 outperforms GS (green letters) in both accuracy and compositionality, as measured with CBM, while CB communication surpasses both.
Composition through decomposition (CtD) performance Evaluating agents' performance on the COOMPOSITE-PRAAAE dataset (shown the right side of Figure and the 'CtD' rows in Tables and reveals that on the THING dataset, the CB-CtD approach achieves perfect accuracy, AMI, CI and CBM scores, and near-perfect BOS score (0.98). On the SHAPE dataset CB-CtD B-D achieves near-perfect accuracy (0.99), along with perfect CBM and CL. The BOS score for CB-CtD (0.84) significantly outperforms those of GS-CtD (0.06) and QT-CtD (0.11) by wide margin. high CI (0.929) and CBM (0.95) scores are also achieved for the MNIST dataset, showcasing agents' ability utilize compositional communication. However, results are less conclusive for the Coco dataset (Table 4, which exhibits lower compositionality levels. Conversely, for the non-compositional QRC dataset, all compositionality metrics are notably low, and using an initialized codebook from the DECOMPOSE step degrades performance from 0.98 to 0.95 as shown in the bottom-right corner of Table 2 Notably, results for the GS and QT protocols, shown with green and red letters in Figure 3 are lower compared to CB (purple letters) across all compositional datasets illustrated in Figure along both axes of this two-dimension space. Refer to Table 4 for detailed GS and QT results.
Zero-shot (CtD-ZS) performance To underscore the agents' ability for compositional general- ization, we train them on the SINGLE-CONCEPT dataset and evaluate their performance on the COMPOSITE- PHRR-F dataset without further training. Comparing the 'CtD' and 'CtD-ZS' rows in reveeeS that zero-shot (ZS) performance is comparable to, and in some cases (e.g., MNIST) surpasses, the results achieved with additional training. We attribute a portion these striking results to the difficulty to further train the network on the COMPOSITE- PHIAASE dataset with multi-loss objective, as demonstrated dataset (0.48) is markedly lower compared to the CtD performance this dataset (0.95). This unsurprising discrepancy indicates that learning a codebook during a dedicated DECOMPOSE step does not confer advantages for non-compositional datasets.
Figure 6. Notably, the zero-shot accuracy performance on the QRC
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Table Accuracy results and compositionality metrics for codebook- bbase communication and the COMPOSE step (excluding Coco). Depicting COMPOSE without DECOMPOSE (C/D), COMPOSE through DECOMPOSE (CtD) and zero-shot COMPOSE results after training the agents DECOMPOSE (CID-ZS). The results are averaged across five runs with different seeds. The highest standard deviations are 0.117, 0.035 and 0.050 for C/D, CtD and CtD-ZS, respectively.
THING
SHAPE
ACC
AMI
POS
BOS
CI
CBM
ACC
AMI
POS
BOS
CI
CBM
CB-C/D
0.25
0.16
0.01
0.05
0.03
0.25
0.26
0.52
0.05
0.09
0.13
0.47
CB-CID-ZS
1.00
1.00
0.05
0.98
0.81
0.67
0.06
0.84
1.00
1.00
CB-CID
1.00
1.00
0.05
0.98
1.00
1.00
0.99
0.78
0.07
0.84
1.00
1.00
MNIST
QRC
ACC
AMI
POS
BOS
C1
CBM
ACC
AMI
POS
BOS
CBM
CB-C/D
0.41
0.86
0.08
0.29
0.38
0.58
0.98
0.94
0.00
0.01
0.01
0.17
CB-CID-ZS
0.89
0.95
0.25
0.26
0.97
0.96
0.48
0.96
0.02
0.37
0.27
0.52
CB-CID
0.81
0.92
0.09
0.26
0.93
0.95
0.95
0.96
0.00
0.01
0.17
Ace
0.6
0.4
0.2
BOS
Targets:
10
2
10
Figure Accuracy, AMI, CBM, BOS and CI (Y-axis) versus number of targets (X-axis). Illustrating DECOMPOSE step for GS (Left) QT (middle) and CB (right) communication the THING game.
Composition without decomposition (C/D) performance To further demonstrate the importance of the DECOMPOSE step for agents' ability communicate complex objects during the COMPOSE step, we compare CtD accuracy and compositionality ('CB-CtD" rows in Table 2 against results achieved by the agents with uninitialized codebook ('CB-C/D' rows in that table) across the COMPOSITE-PHIe PHRASS dataset. Notably, utilizing a codebook initialized during the DECOMPOSE step enables agents to achieve significantly improved results during the COMPOSE step. Specifically, with an appropriately initialized codebook agents achieve perfect accuracy. AMI, CI and CBM on the THING dataset, in contrast to accuracy, AMI, CI and CBM of 0.27, 0.172, 0.027 and 0.25, respectively, with an uninitialized codebook. Similar improvements were achieved for the SHAPE and MNIST datasets. Interestingly, on the non-coopositional QRC dataset, accuracy reaches a near-perfect result of 0.98 even without initialized codebook, and incorporating it did not improve the CBM score. In contrast, the GS and QT protocols did not show consistent performance improvements when using the two-step CtD approach compared to the single C/D step. Refer to Table 4 in Appendix C.2 for details.
5.2 AUXILIARY AND ABLATION RESULTS
In this subsection, we present results from several auxiliary and ablation experiments conducted further clarify the outcomes obtained with the CB-CtD approach. Additional details and more ablation results are presented in Appendices C and
Learning with multiple targets To assess the necessity of a multi-target setup we conducted an experiment where we varied the number of targets in the THING dataset during the DECOMPOSE step. As illustrated in Figure 4 reducing the number of targets enhances accuracy for the GS and QT protocols, and has a marginal negative impact when CB is used. However, there is a noticeable decline in all compositionality metrics, and transitioning from a two-target to single-targe setup for the CB protocol significantly reduces compositional performance, rendering it nearly random. Experiment results for the SHAPE and MNIST datasets presented in Appendix D.2
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1.00
500
Whgh
0.75
347
1.86
291
200
0.25
347
267
163
0.08
-0.25
100
200
12
317
36
14
-0.75
16
-1.00
Figure 5: Left: Codebook utilization for the 17 SHAPE concepts trained COMPOSITE- PHRASE dataset and evaluated with CBM on 1,000 test samples, achieving a perfect score. Right: Heatmap of code-word similarities from the same run.
Vocabulary size In this work, consistent with prior research (Mu Goodman 2021 Bogin et 2018), we set the vocabulary size, |v], to match the number of basic concepts, |c| present in the data. See Table for detailed information on each dataset. The results show that the GS communication tends to use subset of the vocabulary with an average ratio of 0.66. The QT communication uses more words than there are concepts, enjoying vocabulary to concept ratio of 1.21. Conversely, CB communication uses all words in the vocabulary, precisely matching the number of concepts in all but the Coco dataset. Appendix we show results for experiments involving an over-complete codebook that permits more words than concepts in the dataset. Future work may explore dynamic allocation algorithms to determine the optimal vocabulary size during training.
Codebook utilization and visualization Figure (Left) illustrates codebook utilization for the 17 SHAPE concepts trained COMPOSITE-PHRR ASE dataset and evaluated with CBM 1,000 test samples. Each phrase the test set is composed of 4 concepts, totaling 4, 000 concepts. As shown, each concept (top row) corresponds exactly one codebook index (left column), resulting in a CBM score of 1.00. Figure 5 (Right) presents heatmap of code-word similarities, showing that the codes are generally well- sepalatee,,,,, with the highest similarity score between any vector pairs being 0.35. For additional details and an analysis of over-complete codebook utilization, refer to Appendix
Multi-loss optimization Balancing between compositionality and task performance presents an optimization challenge. In Figure we illustrate the training and validation losses (left Y-axis), and accuracy (right Y-axis) metrics for the THING (Top) and SHAPE (Bottom) games, comparing codebook initialization from scratch (Left) to initialization from a DECOMPOSE step (Right). In the case the THING dataset (Top-left sub- sub-figures for training and validation). commitment loss fails to converge when training from scratch, resulting in reasonable accuracy but poor compositionality, Initializing the codebook from the DECOMPOSE step (Top-right sub-figures) leads perfect accuracy and minimal losses from the outset. The SHAPE experiment (Bottom-left sub-figures) demonstrates a different scenario. While both losses are minimized initially, overfitting occurs, indicated by the increasing task loss on the validation set (orange line, Bottom, second left sub-figure). However, initializing the system from a pre- trentrd codebook (Bottom-righh sub-figures) prevents this phenomenon, resulting in near-perfect accuracy and compositionality.
RELATED WORK
The necessity multiple targets: Most studies exploring emergent compositional communication through referential games use single-target setup. While many (Choi et al. 2018 Bogin et al. 2018 achieve high accuracy in extracting multi-word phrases from raw pixel datasets, none report a perfect compositionality score (see Appendix H.3 for more details). In this work. show for the first time that both perfect accuracy and compositionality can be achieved for a multi-word image dataset. We argue that multi-targel setup is crucial for decomposing image representations into human-relevant

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Thing-CrD Banng-CDD-Ton Train
Thing-CID- viD-Viiiatiion
Thing- Cang-Ctt-Taain
Thing-CiD ming-CiD-vvllieeii -validation
Shape CID
Shape CTD Validation
Shape CLD Train
Shape CtD Validation
20
20
20
10
/y
0.95
Total Logs
Lons
Comm Loss
Accuracy
Figure 6: Multi-objective optimization. Top. THING game; Bottom SHAPE game. Left, training from scratch (CB); Right, starting from an initialized codebook (CiD). X-axis: number epochs. We use different Y-axis values for optimal visualization.
concepts, though further research is needed to confirm this. Mu & Goodman (2021), the only known work using multiple targets, reports maximal AMI score of 0.66, suggesting that while multi-target setup is likely necessary, it is not sufficient for compositionality to emerge.
Codebook discrete communication channel Vector quantization (Van Den Oord al. 2017
and dictionary learning (Gregor & LeCum 2010) are common methods to discretize and disentangle latent spaces (Hafner et al. al.]|]]].00 2020). Xu et al. (2022) found that increasing disentanglement pressure in 3-VAE- models (Higgins et al. (017) degraded generalization for compositional tasks. Tucker et al. 2022) applied /3- VAE in EC, showing that the information bottleneck principle achieves human-like trade-off between communication complexity and task informativeness. However, they neither measured nor demonstrated compositionality. Refer to Appendix H.4 for a detailed comparison. In contrast, (Tamkin et al. 2023) proposed using VQ-VAE (Van Den Oord al. 2017) for enforcing a discrete latent space in transformers (Vaswani 2017). but did not explore its application in the context of EC. This technique revolves around online cluster learning (Zheng & Vedaldi (023). which, unlike 3-VAE, introduces an architectural bias that encourages compositional generalization. Following Tamkin al. (023), we VQ-VAE discretize the EC communication channel and achieve fully compositional language.
Iterated Learning Iterated learning (IL) framework rooted in the concept of cultural transmis- sion (Kirby) [001 Kirby et a 2008), modeling the transfer of knowledge across generations through a teacher-learner dynamic. multi-agent neural IL, one agent generates data that another agent learns from, creating an iterative cycle where each learner becomes the teacher for the subsequent iteration. This thain-like structure mirrors the cultural evolution of language and knowledge, where compositionality is believed to play pivotal role. Li & Bowling (2019) and [enn et al. (2020) were among the first to apply IL in emergent communication settings, using reinitialization of agent weights between iterations to simulate the iterative learning process.
CONCLUSIONS
In this work we demonstrate how neural networks achieve compositionality similar to natural language, using a dual-phase training approach referred to as CtD. Through an initial DECOMPOSE phase, focused concept learning, the network learns meaningfully represent concepts in its latent space. Consequently, leveraging these learned concepts, it can accurately describe unseen complex objects even without further training. Our method assumes that there exists foundational set of concepts upon which data is structured during the decomposition phase. An essential follow-up up task to demonstrate that such data can be self-represented by the sender without supervision. This capability raises an intriguing inquiry into identifying the most fundamental concepts that agents must grasp to facilitate the composition novel meanings.
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REPRODUCIBILITY
All datasets used in this work are either publicly available or can be easily generated using Python. A detailed description of each dataset provided Appendix B Appendix [A.3 Afferffers a comprehensive explanation of the evaluation metrics, with Python implementations available online. Please refer to the respective papers for additional details. Appendix [ details the codebook configuration and its hyperparameters. General training procedures and hyperparameter settings are outlined in Appendix All experiments were conducted on single A100 GPU with 40 GB of RAM, and each experiment was completed in less than day. The code for data preprocessing and all experiments will be made publicly available after the paper accepted.
ACKNOWLEDGMENTS
This research was supported by grant no. 2022330 from the United States Israel Binational Science Foundation (BSF). Jerusalem, Israel. BC and YB were supported by the Israel Science Foundation (grant no. 448/20), an Azrieli Foundation Early Career Faculty Fellowship, and AI Aligmment grant from Open Philanthropy. RM was partially supported by ISF grant 1693/22 and by the Skillman chair in biomedical sciences.

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Appendices
A
COORDINATION GAME SETUPS
In this section we describe coordination game variants, communication protocols, and evaluation metrics in more detail.
A.1 GAME VARIANTS
Many coordination game setups have been proposed and explored in recent years (Tin al. 2020
Lazaridou et al. 2017 Leibo et al., [al.]221) 2017 Lazaridou et al.] 20200] Lowe et al.) 2020 Choi et al. 2018
Qiu et al. 2022 Denamganai & Walker 2020). In this section, elaborate four game variants,
summarized in 3 The referential (REF) game and the reconstruction (RECON) game represent
the most common setups. DIFF is a multi-target game initially proposed by (Mu & Goodman 2021 and MREF is our variant, which combines elements from both the REF and DIFF games.
REF game This is the classical 'referential' game (Lazaridou et al. 2017). At each turn of the game, candidate objects C {ei)=_ C X. are drawn uniformly random from X. One of them is randomly chosen to be the target t, while the rest, = C t, serve as distractors. The sender S encodes the target object t via its encoder network ug. such that u² ut(() E Rd the encoded representation of t. then uses its channel network 2g to generate a message 20²) 2n( (t)). The channel and message have certain characteristies that influence both the emergent communication and the agents' performance in the game. The main communication modes described in Appendix A.2
At each turn, the receiver R encodes each candidate object c; 1,2....... n) via its encoder network Ug. obtain us (c;). We write U" E R refer the set of encoded candidate representations, each of dimension d. The receiver then decodes the message via its decoder channel network zg. obtaining z" z (m) E Rd. During training the entire system is optimized end-to-end with the cross-entropy loss based on similarity between the candidates C and the message m such that:
exp(==(m) us(x))) Exec exp(=e (m) us()))
c - log
where x; is the predicted target. Note that gradients from optimizing the contrastive loss CCE allow the receiver improve its latent world representation Uy independently of the sender. At test time, the receiver computes a score matching each of the encoded candidates to the decoded message softmax(2" (-" U,), where 'softmax' is applied component-wisg to U =uu((1)).... (g(xx))) The receiver's predicted target object is the with the highest score, namely f argmax, (f,,..., }.).
RECON game This is the well known Reconstruction game. In this variant, the receiver needs to reconstruct the target sent by the sender. At each turn the sender draws target random from X, encodes it via its encoder network such that u" ut(t) E Rd and uses its channel network 2n generate message m 2p (u") 2p (t)). The receiver R decodes the message m via its decoder channel network 2g, obtaining t" = = R2d During training the system is optimized
Table 3: Targets, distractors and loss function for game variants. 'Multiple' implies at least two.
Sender targets
Sender distractors
Receiver targets
Receiver distractors
Game
Loss
REF
Single
No
Single
Yes
CE
RECON
Single
No
Single
No
MSE
DIFF
Multiple
Yes
Multiple
Yes
BCE
MREF
Multiple
No
Single
Yes
CE
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end-to-end with the mean square error (MSE) loss between t and t" such that
CASE 1 71
Σ
12
|t:
(3)
{d)} C (8\(). are drawn from X and a candidate set C is constructed by C = {c) = DD Ut. I. The receiver computes a score matching each of the candidates O, to the decoded target t" using some distance metric d(z;,,,) such as negative cosine similarity. Accuracy is then computed as in the REF game. This variant does not use distractors. It is based on the assumption that compositionality will emerge simply by posing a bottleneck on the communication channel. Prior work (Kottur et al. 2017: Bouchacourt & Baroni 2018) show the limitation of this assumption.
At test time, n - distractor objects ==
DIFF game DIFF is a multi-target game variant suggested by Mu & Goodman (2021) In this game variant the sender needs to communicate about a set of target objects T = [44 out of a larger set of candidate objects C. For instance, the target may be all red triangles out of a larger candidate set of colorful shapes. Formally, the DIFF game assumes a world X, where each object is characterised by feature-value pairs (FVPs), (fi Vi....... fn Un), with feature i having k; possible values, E [ ]. For instance, the Shape world (Kuhnle & Copestake 2017) has objects like (shape:triangle, colorredd). (olaeorerangll.coooorre)) Refer to Figure 8 for an example. Labeling phrases are boolean expressions over these FVPs. In this work we only use conjunctive expressions.
Each phrase ( X + {0, 13 labels each object as 0 or For instance, the phrase Red Triangle labels all red triangles as positive and all other objects as negative. We identify the phrase Red Triangle le with the NL. "red triangle", which comprises the concepts "red" and "triangle". At each turn of the game, phrase is drawn at random from set of labeling phrases IL, and a set of candidate objects X C X is randomly selected, comprising both target objects, T, adhering to the phrase, and distractors, D, which do not: ((x) = 1 if x T and ((x) 0f x D.
The sender encodes each of the targets E T into a vector representation ut E Rd, and compute a target representative = _ >i 44. Similarly, a distractor representative d is computed by averaging over the distractors. The sender then concatenates i and d and uses its channel network zg to generate message 2 (u') z (u,((E, d))), where (---) is the vector concatenation operator.
The receiver encodes each candidate object c E X" into a vector representation u. = (c) E Rdd
decodes the message m into representation z" = = (m) E Rdd and computes a matching score between each encoded candidate and the message representation, g(2", (()) During training the system is optimized end-to-end with a binary cross entropy on correctly identifying each target:
[
BCE
1
Σ
[y log(o((;)) + (1 yi) -log(1 o
where is the label of candidate c,, d. = ==="='"00__00000="0>>"" vx,)) and ( 14e v. A candidate is predicted as target if its score o > 0.5. Notably, as receiver observes multiple targets cross-entropy loss cannot be applied. The DIFF setup is more conducive to emergence of compositional communication, since the sender needs to form generalization, rather than merely transmit the identity of a single object. Importantly, this variant requires the sender to communicate information about both the targets and distractors, allowing the receiver to discern whether candidate aligns more closely with the target or distractor set.
MREF game This is multi-target variant suggested by us to minimize the required supervision and to align the DIFF game more closely with the classical REF game. In contrast to the DIFF variant, the sender in the MREF game does not use distractors. At each turn of the game, a phrase / is drawn at random from a set of labeling phrases L,, and a set of target objects x E T c X where 1(x:) = is drawn from X. The sender calculates a target representative as in the DIFF game and communicates it to the receiver.
The MREF receiver is similar to the REF receiver. It observes a single target and a set of distractors D and uses cross-entropy loss distinguishes between them. The MREF game differs from the REF game solely in its use of multiple targets by the sender. We contend that employing multiple targets during the DECOMPOSE step is crucial for compositional communication to emerge.
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A.2 COMMUNICATION MODES
In this section we describe several communication modes used in emergent communication setups. Each communication mode is characterized by its message encoding method and the channel capacity it permits.
Continuous communication (CN) represents messages as floating point vectors. Though con- tinuous, one may think of each vector element as if it represents a concept, and the vector itself represents a phrase. CN is expected to lead to good performance, provided that the channel has sufficient capacity. With CN, the system easily be trained end-to-end with sack-propagation. CN precludes the emergence of a discrete language, let alone compositional one. Thus, one may use it to assess accuracy upper-bound without expecting a high compositionality score.
Reinforcement learning (RL) addresses discreteness by employing RL algorithms (Williams) 1992] Lazaridou et al., 2017). RL-based communication protocols have demonstrated inferior performance in referential games compared to other methods (Havrylov & Titov 2017) and are therefore not claborated on further in this study.
Gumbel-softtmx (GS) is a continuous approximation for categorical distribution. In the commu- nication context, discrete message is approximated via sampling procedure. Details are given in Havrylov Titov (2017); Jang et al. (2017). The GS end result multi-word message. where each word has the size of the alphabet and holds one (approximate) concept. GS allows for end-to end-to-end optimization with gradient methods, and for discrete communication inference time. However, the channel capacity is limited, and large alphabet size is both inefficient (due to the need to sample from a large number of categories) and does not perform well in practice.
(QT) is discrete approximation continuous message (Carmeli et al. 2023). It uses differentiable rounding approach to generate discrete vectors. In all our experiments we the scaling factor 1.0, thus, effectively generate binary vectors. contrast to GS, QT allows significant channel capacity even at limited word lengths.
Quantized-commmnicttoo
A.3 EVALUATION METRICS
In this subsection we provide more details on the five evaluation metrics used in this work.
Adjusted Mutual Information (A.I)) measures the mutual information between a of EC messages and a corresponding set of NL phrases, adjusted for chance (Mu & Goodman (021)) Given test set D, let MI denote the set of messages generated by the sender and L the set of NL phrases (e.g., Red Tri Triangle, Blue Square) that appear as labels in the data. Formally, AMI (Vinh
al. 2009) is calculated by
I(M,L)
LM, max(H(M)), (L)) (MI L))
(5)
where [(M, L) is the mutual information between M and L,, H(-) is the entropy, and E[[(M, L)) is computed with respect to a hypergeometric model of randomness. See (Vinh et al. 2009) for motivation for this distribution.
Positional disentanglement (posdis) measures whether words in specific positions within EC messages consistently refer to particular NL concept (Chaabouni et al.) 2020).
Denoting by wj the j-th word of an EC message m E M and of E L the NL concept that has the highest mutual information, T(::), with wy: of arg max [ww,, c). In turn, cá is the second most informative attribute: dg arg max [w,,, c). Denoting H (w;) as the entropy of the j-th position, used for normalization, positional disentanglement (posdis) is defined as:
mien I(w,, ct) Ilw,, o²) H(w,)
posdis(M, Mite
Σ
(6)
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Where mien represents the length of the EC messages, which are all uniform in our case, and positions with zero entropy are excluded.
Bag-of-symbols disentanglement (bosdis) evaluates the extent which words the EC language unambiguously correspond to NL concepts, irrespective of their position within an EC message (Chaabouni al. 2020
Denoting by now a counter of the word w in a message m E M, and ci E L the NL concept that has the highest mutual information, I(--), with Rw: of arg max, I (n c). In turn, c² is the second most informative attribute: co arg max [no,, c). Denoting H (mhw) as the entropy of new used for normalization, bag-of-symbols disentanglement (bosdis) defined as:
I(n G) [Tiww (2)
Nosdis(M,L) = W
(
WEW
Context independence (CT) seeks to quantify the alignment between words E M and concepts C L by examining their probabilistic associations (Bogin et al. 2018). Specifically, P P(wle) represents the probability that word w is used when concept is present, while P(clw) denotes the probability that a concept e appears when a word w used. For each concept c, the word we most frequently associated with it is identified by maximizing P(clw): we arg max P(clw) The CI metric is then computed as the average product of these probabilities across all concepts:
1 Σ CEL
CI(M,
c(welc)- P(clwe)
(8)
The CI metric ranges from 0 to 1, with indicating perfect alignment, meaning that each word retains its meaning consistently across different contexts and is thus used coherently.
Concept Best Matching (CBM) quantifies the best match between set of EC messages and corresponding set of NL phrases. Recently introduced by Carmeli et al. (0024) this metric aims to establish an explicit one-to-one mapping between EC words and NL concepts. Consequently. well-suited for evaluating the compositionality
datasets comprising images paired with compositional NL captions. CBM constructs bipartite graph of EC words and NL concept and employs the Hungarian algorithm (Kuhn 1955 Hopcroft & Karp 1973) to find the best matching pairs between them.
B DATASETS
In this section we provide more details on the five datasets used in this work.
THING (Carmeli et al. 2024) A synthetic dataset of 100, 000 objects which we design for con- trolled experiments. Each object the dataset is composed of five attributes, each with possible values. Overall, the THING datasets contains 50 concepts. Refer to Figure 7 (a) for the complete concept list. Each object in the dataset is uniquely identified by five FVPs. In contrast to the other datasets, objects in the THING game encoded by concatenating five one-hot vectors, one per FVP. There are 50 unique values and 4 communication words (SOS, EOS, PAD, UNK) in the vocabulary. Thus, the vector dimension representing an object is identifies an object in the dataset.
54 270. Each such vector uniquely
SHAPE (Kuhnle & Copestake 2017) visual reasoning dataset of objects over black background. Refer to Figure X for few examples. Following Carmeli et al.) (2024), we use version of the dataset that contain four attributes: the shape attribute with five values; the color attribute with six values; horizontal position with three values; and vertical position with three values. Overall, the SHIPP dataset contains 17 concepts, and a maximal labeling phrase of 4 FVPs which sum to 270 unique 4-concept labels. The dataset includes various images sharing the same label. For instance, the two images on the left side of Figure g depict a yellow square positioned at the left-center side of each image.
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Shape
Color
Size
Age
Material
circle
red
petite
new
wood
ellipse blue
tiny
vintage
metal
square green
small
antique
plastic
rectangle
yellow medium
modern
glass
triangle
white
large
classic
fabric
oval gray
huge
retro
ceramic
pentagon
orange
miniature
contemporary
paper
hexagon
purple
gigantic
historic
leather
star heart brown
pink
massive
preowned
stone
enormous
timeless
rubber
Figure 7: (a) The words used by the THING game and QRC games. Each object is composed from five words, one from each category. (b) QRC objects, each composed from 5 words. The top two QRCs in this illustrated example are the targets. They share the concept triangle. The bottom two QRCs serve as distractors, thus not contain the t triangle concept.
+
Figure 8: Two SHAPE examples from the SINGLE-CONCHR dataset. (Left) Yellow concept. (Right) Ellipse concept.
MNIST (LeCun al. 1998) A widely-used dataset consisting of collection of handwritten digits, ranging from to 9, each captured as gray-scale image with 28 x 28 pixels. For evaluating compositionality, we created 2-digit version of the dataset by combining two images from the original dataset. See for example Figure Right. To maintain similar image dimensions across the DECOMPOSE and COMPOSE steps, one the images in each pair used for DECOMPOSE step is blank image with its location (right/leftt randomly chosen. See Figure | (Left). Overall, the MNIST dataset contains 10 digits, and a maximal labeling phrase of FVPs which sum 100 unique 2-digit labels. The dataset contains many different images with identical labels.
Coco (Lin et al., 2014b) Common Objects in Context is a widely-used benchmark dataset designed capture real-world images containing multiple objects in various contexts. Each image is accompanied by description of the objects within it. Overall the data contains 80 distinct object categories, namely concepts. Each image contains or more identified objects. We filter the dataset to retain images with at most 3 objects. For the DECOMPOSE step we chose images that contain exactly one object. For the COMPOSE step we chose images with two or three distinct objects where we set the target images in each data sample to hold exactly two objects annotated with the same concepts. Refer to Figure 10 for few examples.
QRC A synthetic dataset, introduced by us, which employs QR codes to encode information similar to the THING dataset. Each QRC in the dataset encodes five concepts, one from each category. Informationally, this dataset resembles the THING dataset. We experiment with it to evaluate whether
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/
I
4
5
5
3
4
2
H
1 2
1
Figure 9: Training for decomposition using MNIST images. Concepts can be learned from images with single digit (Left) or from images with two digits (Right). Illustration of two targets (Top) and two distractors (Bottom) for each data format. The target for the two-digit setting (Right) is '4'. Data from the two-digit setting more similar to the data seen by the agents during the COMPOSE step. In the COMPOSE step, all targets in data sample have the same two digits.
Figure 10: Coco dataset examples. (Left) SINGLE-CONCEPT. (Top-left) fire hydrant, (Bottom-left) Giraffe. (Right) COMPOSITE-PHRASEE (Top-right) Cat and Banana, (Bottom- right) Cup and Laptop.
encoding compositional information non-compositional manner, as is the case for QR codes, impedes the development of compositional language by the agents. An example from the QRC dataset is depicted in Figure 7
C DETAILED RESULTS
In this section we provide detailed results for experiments described in the main body of the paper as well as for additional experiments we conducted to shade more light various aspects of the CtD method compared to other approaches suggested in the literature.
C.I MREF GAME RESULTS
In Table we provide detailed numerical results for the experiments shown in Figure 3 We analyse the results for the main experiments in Section 5 Below we describe complimentary results and additional insights.
We use the MRFF setup for these experiments. In this setup the sender observes 20 targets and no distractors and the receiver observes one target and 20 distractors. Targets in each sample of the SINGLE-CONCEPT dataset share single concept while targets at the COMPOSITE- PHRSSE dataset share a composite phrase.
Rows in the table report results for experiments with five datasets (TIING, SHAPE, MNIST, Coco, and QRC) and three communication protocols (GS, QT and CB) along three training regimes. For each pair: The first row shows results for the DECOMPOSE phase ([comm]-D). The second row shows results for the COMPOSE phase, without initial decomposition training ([comm)-C/D) The third row shows results for the 'CtD' method ([comm)-CtD)) where agents trained the
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Table 4: Results for the MREF game. The sender observes 20 targets and no distractors, while the receiver observes one target and 20 distractors. Bold numbers indicates best results on the COMPOSITE-PHRASE dataset for each game.
Dutasct
comm
#C
#p
#w
#m
ACC
AMI
POS
BOS
CBM
#w/#ic
THING
GS-D
50
50
50
1
15
15
0.349
0.752
0.994
0.963
0.474
0.336
0.30
GS-C/D
50
50
958
5
47
801
0.993
0.313
0.003
0.021
0.037
0.226
0.94
GS-CiD
50
50
958
5
19
832
0.741
0.371
0.010
0.036
0.080
0.250
0.38
QT-D
64
50
50
58
58
0.822
0.834
0.918
0.822
0.779
0.828
1.16
QT-C/D
64
50
958
5
64
963
0.932
0.449
0.021
0.030
0.030
0.225
1.28
QT-CiD
64
50
958
5
64
967
0.653
0.420
0.040
0.034
0.035
0.260
1.28
CB-D
50
50
50
50
1.000
1.000
1,000
1.000
1.000
1.000
1.00
CB-C/D
50
50
958
50
644
0.273
0.172
0.025
0.046
0.027
0.258
1.00
CB-CtD
50
958
50
958
1.000
1.000
0.033
0.975
1.000
1.000
1.00
SHAPE
GS-D
17
17
17
14
0.569
0.612
0.678
0.576
0.551
0.570
0.82
GS-C/D
17
17
34
187
0.230
0.579
0.028
0.053
0.135
0.548
0.94
GS-CID
17
17
34
4
17
104
0.135
0.717
0.011
0.066
0.240
0.609
1.00
QT-D
17
17
23
23
0,813
0.881
0.881
0.692
0.762
0.770
1.35
QT-C/D
32
17
34
31
322
0,413
0.568
0.063
0.063
0.125
0.560
1.82
QT-CID
17
34
27
123
0.100
0.757
0.227
0.110
0.205
0.714
CB-D
17
17
17
1
17
17
1.000
1.000
1,000
1.000
1.000
1.000
1.00
CB-C/D
17
17
34
4
17
396
0.213
0.532
0.041
0.103
0.139
0.47
1.00
CB-CID
17
17
34
4
17
192
0.988
0.745
0.045
0.841
0.999
1.00
1.00
MNIST
GS-D
10
10
10
1
9
9
0.886
0.966
1.000
1.000
0.947
0.898
0.90
GS-C/D
10
10
15
2
10
26
0.360
0.773
0.242
0.288
0.433
0,806
1.00
GS-CID
10
10
15
2
10
23
0.799
0,904
0.086
0.280
0.779
0.862
1.00
QT-D
16
10
10
1
11
11
0.999
0.999
0.998
0.933
0.998
0.999
1.10
QT-C/D
16
10
15
2
15
45
0.294
0.719
0.159
0.136
0.324
0.638
1.50
QT-CID
16
10
15
2
12
23
0.391
0.736
0.173
0.211
0.344
0.768
1.20
CB-D
10
10
10
10
0.999
1.000
1.000
1.000
1.000
1.000
1.00
CB-C/D
10
10
15
2
36
0.422
0.837
0.047
0.287
0.377
0.539
1.00
CB-CD
10
10
15
32
0.811
0.919
0.086
0.260
0.929
0.950
1.00
Coco
GS-D
80
80
80
56
56
0.501
0.551
0.78
0.64
0.32
0.318
0.70
GS-C/D
80
80
26
54
87
0.442
0.719
0.299
0.286
0.223
0.535
0.68
GS-CID
80
80
26
2
49
95
0.509
0.746
0.294
0.285
0.277
0.592
0.61
QT-D
128
80
80
82
0.789
0.682
0.892
0.791
0.611
0.663
1.03
QT-C/D
128
80
26
110
0.571
0.585
0.304
0,231
0.328
0.638
QT-CiD
128
80
26
51
92
0.628
0.773
0.310
0.262
0.245
0.750
0.64
CB-D
80
80
80
1
77
77
0.827
0,902
0.956
0.919
0.831
0.857
0.96
CB-C/D
80
80
26
2
62
143
0.634
0.736
0.272
0.274
0.280
0.582
0.78
CB-CtD
80
80
26
2
56
97
0.654
0.805
0.283
0.295
0.342
0.638
0.70
QRC
GS-D
50
50
50
1
1
0.069
0.000
0.000
0.000
0.028
0.028
0.02
GS-C/D
50
50
958
31
214
0.766
0.041
0.007
0.011
0.026
0.173
0.62
GS-CiD
50
50
958
5
0,203
0.000
0.000
0.000
0.005
0.116
0.00
QT-D
64
50
50
1
50
50
0.528
0.685
0.828
0.727
0.572
0.594
1.00
QT-C/D
64
50
958
5
64
968
0.973
0.514
0.002
0.010
0.013
0.170
1.28
QT-CID
64
50
958
5
62
555
0,814
0.077
0.002
0.010
0.014
0.222
1.24
CB-D
50
50
50
1
50
50
0.485
0.756
0.839
0.723
0.479
0.643
1.00
CB-C/D
50
50
958
5
50
954
0.985
0.955
0.003
0.007
0.011
0.168
1.00
CB-CtD
50
50
958
5
50
958
0.956
1.000
0.001
0.006
0.013
0.172
1.00
COMPOSITE-PHRASE dataset using parameters initialized from the DECOMPOSE experiments in the first row.
The *#v' column reports the vocabulary size. For QT. vocabulary size must be to the power of 2. '#e' and '#p' indicate the number of unique NL concepts and phrases in the test set, respectively. The 'I' column reports phrase length. For the SINGLE-CONCERS COMPOSITE- PHRASE dataset, this parameter indicates the number of concepts used to describe a composite object in the dataset. "#w" and #mm' report the number of unique ECC words and messages
dataset = 1. In the case of the
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generated by the sender, respectively. The 'ACC', 'AMI', 'POS', 'BOS', 'CI' and 'CBM', report the accuracy, jijuutte-muttull inttualiiffrrmatinn, positional disentanglement, bag-of-symbols disentanglement, context independence and conceet-best-mateee between number of generated words (#h) to the number of concepts (#c) in the dataset. This ratio reveals interesting differences between communication protocols. Refer to Section 5.2 for details.
respectively. The #w/#cc column reports the ratio
C.2 GS AND QT CTD RESULTS
To further evaluate the importance of codebook- communication in the CtD approach, we assess performance using the GS and QT protocols. Specifically, we compare the performance of GS and QT when trained on the HOMPOSITE-PHRASS dataset without prior initialization from the SINGLE-CONCEPT datasets (C/D) to their performance when the CtD method is applied.
For the THING dataset, the CtD accuracy for both GS (0.741) and QT (0.653) is lower than that of C/D (0.993 and 0.932, respectively), while the compositionality metrics remain roughly the same. Similar trends are observed for the SHAPE dataset. Results for the MNIST dataset are somewhat different. The CtD accuracy for both GS (0.799) and QT (0.391) is higher than that of C/D (0.36 and 0.294, respectively). We observed no substantial differences in compositionality metries across the two protocols and three datasets.
We conclude that the CtD approach offers advantage over C/D for the GS and QT protocols across any of the evaluated datasets.
C.3 EVALUATING THE COMPOSITIONALITY METRICS
There clear differences among the five metries used to evaluate compositionality, despite all being designed to measure the same phenomenon.
The CBM metric the only one not based on information theory; instead, it aims maximize the matches between EC words and NL concepts. This makes it the most interpretable metric, with results that are easier align with our expectations of the language that should emerge.
The CI metric shows high correlation with CBM (0.89). The main distinction between the two that CI a statistical learning metric based on IBM Model (Brown et al.) (993), utilizing the expectation matiiiinamaamiiiiiioonn algorithm (Dempster et al. 1977). Consequently, this metric requires training and is less interpretable, particularly when compositionality is low.
The AMI metric, used by Mu & Goodman 1 to assess their multi-target study, also shows high correlation with CBM (0.76) and CI (0.70). This metric relies on cluster labeling. The exceptionally high AMI scores for C/D (0.95) and CtD (1.0) on the non-compositional QRC dataset highlight limitation of this metric that warrants further investigation.
The BOS metric, initially proposed by Chaaboumi et al. (2020), relies mutual information. It shows a stronger correlation with CI (0.86) compared to CBM (0.69). The metric assesses the difference between the most and second most informative concepts, which can potentially skew results, as evidenced by the CB-CtD results on the THING and SHAPE datasets.
The POS metric, which is used to assess positional disentanglement, yields low scores across all COMPOSITE-PHRASE datasets, with maximum score of 0.342 observed for the Coco QT-CtD setup. Since we do not assume positional meaning in the messages, we find this metric less relevant to our experiments.
C.4 DIFF GAME RESULTS
In T we report results for a series of experiments using the DIFF game setup, which similar to the setup proposed by Mu & Goodman (202T). In contrast to the MREF game, agents in the DIFF game observe 20 targets and 20 distractors in each turn, and optimization done with BCE loss. For further details, refer to Section A.I The structure of Table 5 along with the description of its columns and rows, mirrors that of Table absent in the main table, denotes the dimension of the codebook's words and is independent of the dataset. Despite experimenting with various sizes, we did not observe significant differences among them.
4 and is detailed Section C.I The 'd' column, which is
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Table Results for the DIFF' game with 20 targets and 20 distractors observed by the agents during both phases. The 'd' column indicates word dimension for each dataset.
Dataset
comm
#c
#p
#w
ACC
AMI
POS
BOS
CI
CBM
#w/#fc
THING
CB-D
100
50
50
1
50
50
0.998
0.994
0.998
0.991
0.975
0.982
1.00
CB-C/D
100
50
958
5
50
765
0.697
0.149
0.009
0.067
0.033
0.260
1.00
CB-CtD
100
50
958
5
50
981
0.995
0.619
0.010
0.939
0.963
0.970
1.00
SHAPE
CB-D
200
17
17
1
17
17
1.000
1.000
1.000
1.000
1.000
1,000
1.00
CB-C/D
200
17
34
4
17
591
0,670
0,339
0.021
0.067
0.107
0,445
1,00
CB-CID
200
17
34
4
17
297
0.890
0.633
0.061
0.649
0.761
0.909
1,00
MNIST
CB-D
100
10
10
0.996
1.000
1.000
1.000
1.000
1.000
1.00
CB-C/D
100
15
58
0.771
0.677
0.159
0.217
0.250
0.555
1.00
CB-CtD
100
10
15
2
10
23
0.964
0.920
0.251
0.282
0.925
0.947
1.00
Coco
CB-D
100
80
80
78
78
0.887
0.906
0.958
0.916
0.847
0.858
0.98
CB-C/D
100
80
26
2
66
185
0,792
0.650
0.243
0.227
0.250
0.548
0.83
CB-CtD
100
80
26
2
67
141
0.836
0.734
0.308
0.309
0.341
0.610
0.84
QRC
CB-D
400
50
50
1
50
50
0.929
0,954
0.975
0.940
0.894
0.894
1.00
CB-C/D
400
50
958
5
50
986
0.916
0.272
0.001
0.007
0.011
0.166
1.00
CB-CiD
400
50
958
5
49
936
0.899
0,194
0.004
0.012
0.016
0.167
0.98
While some differences in results exist between the two setups, qualitative observations remain similar. Specifically, with CtD, agents improve both accuracy and compositionality results across all datasets (except QRC) compared to CB setup that does not utilize learned codebook (C/D). CtD outperforms the GS and QT protocols in the THING, SHAPE, and MNIST datasets and achieves results comparable QT on the Coco dataset. As observed previously, the non-compositional QRC dataset does not benefit from the CtD approach.
C.5 DATA MISMATCH BETWEEN DECOMPOSE AND COMPOSE STEPS
The CtD training approach presents an optimization challenge due to potential data mismatch between the DECOMPOSE and COMPOSE steps. Figure 9 depicts two data options for the MNIST SINGLE- CONCEPT dataset. While training on a single digit (Figure / Left) may seem more intuitive, training with two digits in each image, where only one is the target (Figure 9 Right), is more similar the data seen during the COMPOSE step. Indeed, training the DECOMPOSE step with the two-digit version resulted in better accuracy (0.810 vs. 0.710) and CBM (0.961 vs. 0.902) compared to the one-digit version, respectively. The mismatch between the SINGLE- SINGLE-CONCEP" and the COMPOSITE-PHER datasets one of the reasons for the lower performance on the Coco dataset. Images for this game vary significantly between the two datasets.
C.6 QRC: A NON-COMPOSITIONAL DATASET
The QRC dataset comprises synthetic QRC images encoding information akin to that of the THING dataset. Refer Figure for the complete list of THING concepts and few QRC image examples. As such, this dataset presents an intriguing setting wherein images encode compositional information in conposopoiiii way.
We utilize the QRC dataset to elucidate various aspects of the CtD approach. One such aspect, as reported in [ouchacourt & Baroni (2018), demonstrates that agents can achieve high accuracy in REF games by conveying low-level details about the target. A comparison of the CtD outcomes for the THING and QRC datasets in Table 4 further underscores this observation. Interestingly, these datasets encode the same information in contrasting manners. While representations of the THING data is entirely compositional, that of the QRC data not. Consequently, although accuracy is high for both datascts, 1.0 and 0.956 respectively, the CBM for the THING dataset is perfect (1.00), whereas for the QRC dataset, it tends toward randomness (0. 172).
Moreover, the perfect AMI score for the QRC game highlights its inadequacy in evaluating composi- tionality in such datasets. Table 6 describes a concrete example for this phenomenon, extracted from the experiment reported in Table As seen, the sender in the game generates two entirely distinct messages, comprising mutually exclusive words, for two phrases that vary in only a single concept (ceramic c Vs. leather).
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Table 6: Non-compositional messages for the QRC game. Changing single concept in phrase results in changes to all words in message.
Phrase
Gold concepts
Generated words
circle.red, www.le.ed.mmssivve...o www.ssiiee.lasiicccrraiiiceee www..red..aasive.lasssic..ommmee
1.11.29.35.44 46 1.11.29.35.48
37.1.32.43.38 13.27.25.34.36
D LEARNING WITH MULTIPLE TARGETS
In this work, we argue that multiple-targets setting is essential for compositionality to emerge. We report results for the varied-targets experiment in Section 5.2 To further support the importance of the multi-target setting for the emergence of compositionality, we include results from experiments on additional datasets, well as multi-target experiments conducted for the COMPOSE training phase.
D.1 MULTIPLE TARGETS DURING DECOMPOSE
Figure presents additional results from the varied-targets experiments on the SHAPE and MNIST datasets, as discussed Section 5.2 As shown, reducing the number of targets led significant decrease in all compositionality metrics across all six configurations.
Interestingly, decreasing the number of targets on the SHAPE dataset increases accuracy (orange line) when GS and QT communication are in used. We attribute this phenomenon to the model's s tendency to describe the target using low-level features when a smaller number of targets is used. This phenomenon is less pronounced in the MNIST dataset, probably due to the shorter phrases used (2 concepts) compared to the 4-concept phrases used in the SHAPE dataset. With CB communication, the model is trained to optimize both task and commitment losses (See Section 3 for details). Consequently, an inherent dependency exists between accuracy and compositionality. making it more challenging analyze the results of one independently from the other.
Shape GS
Shape
Shape
0.8
0.4
0.0
MNIST- GS
MNIST QT
MNIST CB
0.8
0.6
Targets
Ape
CBM
BOS
A0c
CBM
B08
CBM 808
01
Figure 11: Learning concepts requires multiple targets. Illustrating results of the DECOMPOSE step on the SHAPE (Top) and the MNIST (Bottom) datasets.
D.2 MULTIPLE TARGETS DURING COMPOSE
While multiple targets are indispensable for the DECOMPOSE step, the classical REF game relies on single target. The use of single target requires less supervision, making it more appealing for studying emergent communication. Table presents a comparison of results between communicating with 20 targets versus single target during the COMPOSE step. In the SHAPP and MNIST games, there is a moderate decline in performance, which we attribute to differences in representing a single image versus collection of images sharing the same concepts. Refer to Appendix C.5 and Figure for more details on the image differences in the MNIST dataset. Conversely, in the THING and QRC datasets, objects uniquely identified, so single and multiple images have the same representation,
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Table 7: Comparing performance of single vs multiple targets during the COMPOSE step of the MREF game.
Dataset
Target(s)
#p
fm
#w
ACC
AMI
POS
BOS
CI
CBM
Thing
20
958
958
50
1.000
1.000
0.033
0.975
1.000
1.000
1
958
958
50
1.000
1.000
0.032
0.975
1.000
1.000
Shape
20
34
192
17
0.988
0.745
0.045
0,841
0.999
1,000
1
4
34
489
17
0.696
0.696
0.036
0.606
0.709
0.883
MNIST
20
2
15
32
10
0.710
0.895
0.210
0.279
0.828
0,902
1
15
72
10
0.662
0.628
0.083
0.163
0.552
0.782
COCO
20
26
97
56
0.654
0.805
0.283
0.295
0.342
0.638
1
26
322
79
0.922
0,426
0.195
0.173
0.117
0.357
QRC
20
955
958
50
0.956
1.000
0.001
0.006
0.013
0.172
1
958
958
50
0.984
1.000
0.001
0.008
0.012
0.167
and thus no differences in performance are observed. In the Coco dataset, images differ vastly from each other even when sharing the same concepts (see Figure Thus, the representation of single image significantly differs from creating representation by averaging multiple images. While accuracy for a single image game variant (0.922) is notably higher than accuracy for the 20-targets variant (0.654), AMI, CI and CBM (0.805, 0.342 and 0.638, respectively) for the 20-target variant are much higher than those for the single target (0.426, 0.117 and 0.357, respectively).
E CODEBOOK AS A DISCRETE COMMUNICATION CHANNEL
In this section, we offer additional details on the two codebook variants employed in our experiments. We begin with a formal definition of the codebook used, followed by comparison of the results from these two codebook configurations on the MNIST dataset.
Formally, we define a discrete latent codebook CB E IR Wx where W |w| is the number of words the codebook and the dimension of each word wy The discrete latent variables w are then calculated by a nearest neighbour lookup over the codebook: w g(=) wy where = argmin, || wy 12 and = ze [ug (x)) is the latent vector generated by the sender's 's network for given data sample We refer to this plain codebook setup as P-CB.
We follow a recent work (Zheng Vedaldi 2023) that suggests a re-initialization method to encourage the usage of all words in the codebook. We refer to codebook with re- re-initializattio as C-CB. Defining (y(!) be the average usage of code vectors in each training mini-batch, it updated as
(1) n
N N((11)
7
(1 (1-7),
B
where n is the number of encoded samples that will be quantized to the closest codebook entry Wk. the number of samples batch and y is decay syper-parameter which we set to 0.99.
Code words are then reinitialized based on their usage. We follow the probabilistic random selection suggested by Zheng & Vedaldi (202)) for sampling an anchor set from batch. Specifically, we exp ()
consider probability p ΣE, exp(- D where D is the distance between z and wk- Our goal reinitialize less-used code words while refraining from modifying used ones. For that we define a decay factor Og calculated for each of the code words,
(10) where is small constant to ensure the entries are assigned with the average values of words along
exp
different batches, 5 is constant which we set to 10 as in (Zheng Vedaldi 2023). and K is the number of words in the codebook. The update is then done by
(1) wk w (t-1) (1 ( + 2(0) 0
(1)
(11)
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Table A comparison of the performance between a standard codebook (P-CB) and re-initialized codebook aimed at reducing dead codes (C-CB) on the MNIST dataset.
Codebook
Size
Acc
AMI
POS
BOS
CI
CBM
Umbig
Para
P-CB
10
0.999
1.000
1.000
1,000
1,000
1.000
0
0
P-CB
15
0.339
0.664
0,987
0.980
0.627
0.399
0.601
0
P-CB
20
0.999
1.000
1.000
1.000
1.000
1.000
0
0
C-CB
10
0.999
1.000
1.000
1.000
1.000
1.000
0
0
C-CB
15
1.000
0.936
0.882
0.762
0.840
0.840
0
0.160
C-CB
20
0.999
0.885
0.801
0.675
0.665
0.665
0
0.335
where ={ Kx is the sampled anchor. We set hyper-parameters and constants according the recommendations in Zheng & Vedaldi (023)..
E.1 CEERCCOMPLETE CODEBOOK
Table Bale@Joompnn compares the performance plain codebook (P-CB) with that codebook employing the re-initialization method (C-CB) proposed by Zheng & Vedaldi 2023). The results evaluated for both complete and over-complete codebooks.
As observed, increasing the C-CB codebook size does not reduce task performance but does decrease the CBM by introducing more paraphrases, with scores 0.16 and 0.335 for the 15 and 20 code- book words, respectively. This effect is primarily due to the C-CB algorithm, which continuously re-initializes dead codes. To further evaluate this, we conducted experiments using the same configu- ration with the original CB code (P-CB). As seen, the codebook initialization for the 15-word size was unsuccessful, leading to low accuracy (0.339) and the usage of only 4 codes, with high ambiguity rate (0.601). In contrast, for codebook size of 20, the initialization was successful, resulting in perfect accuracy (1.000) and optimal scores across all compositionality metrics.
F.2 CODEBOOK UTILIZATIOO
Table presents the utilization of the two codebooks (P-CB and C-CB), initialized with 15 and 20 random words. The results, evaluated using CBM test set of 1,000 samples, reflect only successful matches, with the remaining cases classified as ambiguous or paraphrased, as detailed in Table & Notably, P-CB with 20 code words demonstrates 100% utilization for the presented words, indicating that the remaining 10 words are"dead code" that were never used.
F VARIED MESSAGE LENGTH ANALYSIS
In this section, we provide a detailed analysis of the impact of message length on accuracy and compositionality metrics, for both CB-based and RNN-based communication protocols. We highlight the limitations of RNN-based protocols in handling variable-length messages and propose several potential improvements for CB-based communication. The implementation of these improvements is left for future research.
F.1 THE IMPACT OF MESSAGE LENGTH ON ACCURACY AND COMPOSITIONALITY
In Figure 12 we compare accuracy and compositionality metrics across the four compositional datasets for the three communication protocols. For CB-based communication, both accuracy and compositionality increase significantly as message length grows, reaching an optimal point that matches the phrase length. Beyond this point, both metrics decline. contrast, for RNN-based communication, accuracy continues improve with increasing message length (except for GS on THIng), while compositionality metrics either decline or stay unchanged. The variations in accuracy behavior underscore the limitations of the RNN mechanism in identifying an optimal message length. As further seen in Table IO both GS and QT typically make use of the maximum allowed message length. This aligns with observation that high-capacity channel enables better accuracy by
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Table Assessing codebook utilization using the CBM metric on 000 samples from the MNIST
test set. The results pertain to the DECOMPOSE phase for codebooks containing 15 and 20 code words.
Zero
One
Two
Three
Four
Five
Six
Seven
Eight
Nine
Ground Truth
96
90
100
109
112
103
103
102
91
P-CB with 15 code words
Index
n/a
n/a
n/a
2
n/a
n/a
n/a
Util (#)
0
0
90
0
94
112
0
103
0
Util (%)
0
100
100
0
P-CB with 20 code words
Index
8
1
3
5
7
4
0
9
Util (#)
96
90
100
109
94
112
103
103
102
91
Util (%)
100
100
100
100
100
100
100
100
100
100
C-CB with 15 code words
Index
11
1
8
5
7
4
0
12
Util (#)
96
90
63
91
94
64
103
103
61
Util (%)
100
100
63
83
100
57
100
100
74
67
C-CB with 20 code words
Index
14
1
9
5
8
4
7
15
Util (#)
90
55
95
71
65
66
54
50
Util (%)
56
100
55
87
76
58
64
52
64
55
Thing-GS-40
1.0
0.6
0.4
QT-C/D
-T-C-Q
MNIST- CT-CI
COCO CO-D-QT-C/D
1.0
0.8
0.4
0.2
0.0
Thing-CB-CID CB-CID
Shape Shape-CB-CO CB-CID
MNIST-CB-CID CB-CID
COCO-CB-C0
0.6
0.4
0.2
0.0
CSPP
Figure 12: An evaluation of accuracy and compositionality metrics (Y-axis) across varied message lengths (X-axis) for the three communication protocols (GS, QT, CB) the four compositional datasets (THING, SHAPE, MNIST, and Coco).
conveying low-level details. This unintended phenomenon indicates that additional regularization is necessary for the RNN to foster compositionality. In this work, to enable fair comparison, we set the maximum message length match the length of the phrases in the dataset for all communication protocols. Figure presennss CtD results for CB, but C/T results for GS and QT, as the latter generally performs better than CtD for these communication protocols.
F.2 CB-BASED VARIED-LENGTH CONTROL
Several alternatives can be considered for the oracle-based length configuration currently utilized by the CB protocol. First, message length could treated as an additional hyperparameter, with its optimal value determined validation set. This method should perform well, as suggested
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Table 10: comparison between the potential and actual average message length for the two RNN- based communication protocols (GS and QT). Bold font highlights results where the message length matches the phrase length of the datasets.
THING
SHAPE
MNIST
Coco
Msg len
GS
QT
GS
QT
GS
QT
GS
QT
1.000
1.000
1.000
0.998
1.000
0.979
1.000
1.000
2.000
1.996
1.996
2.000
1.515
1.882
1.938
2.000
3,000
2.818
3.000
2.979
1.992
2.885
3,000
3,000
4.000
3.965
3.905
3,961
3,998
3.526
4.000
4.000
5.000
4.919
4.952
4.618
4.860
4.612
5,000
5.000
6.000
5,870
5.902
5.988
7.000
6.938
6.939
6.964
8.000
7.771
by the CB results in Figure 12 provided the lengths of the phrases are uniform. However, a more sophisticated mechanism is required when the dataset contains serieh-length phrases. One possible approach is to train a similarity threshold that learns to dynamically extract varying numbers of words from the codebook. We leave the exploration of this and other varied-length control mechanisms for future research.
G CONFIGURATION AND TRAINING DETAILS
modified version of the Egg framework (Kharitonov et 2019 In version the communication modules, 2g and 2g, used by the sender and the receiver, respectively, are totally separated from their perceptual modules, which we term 'agents'. See schematic illustration in Figure 2 This separation allow us to use the exact same communication modules for different games. The Gumbel-Soffmax (GS), Quantized (QT), and coodbook-based (CB) protocols are implemented at the communication layer. For GS we use an implementation provided by the Egg framework, where we do allow temperature be learned, and set the straight-through estimator False. For QT protocol we followed parameter recommendations from Carmeli et al. (2023) and use binary quantization all experiments. For CB we adapted the implementation code provided by [Zheng Vedaldi 2023) and a code from Oord al. (2018) Both GS and QT uses recurrent neural network (RNN) for generating multiple words within a message. Refer to Table [1 for details on specific The CB-based protocol takes the message length parameter, which we set to for the DECOMPOSE step and to the maximum phrase length, as determined by the dataset, for the COMPOSE step. Refer to column I' in Table 4 for the exact message- length value for each dataset.
We run all experiments
RNN and other cupee-pprameterr
Table 11: Agents' hyper-parameters used for obtaining the results in Table
Batch Size
Sender Targets
Sender Distr
Receiver Targets
Receiver
Cell Type
Sender
Sender Embed
Receiver Hidden
Receiver
Ir
Distr
Hidden
Embed
10
0.0005
20
20
20
LSTM
100
500
100
500
The communication protocols further differ in their vocabulary-size settings. We aim to set this size, v, to match the number of basic concepts in the data, which is dataset dependent. For GS v is equal to word length, which set d such that 2 c. For CB, vocabulary size, is equal to the number of vectors in the codebook. which we to match c, the number of concepts in the dataset. See columns 'd' and "#e" in Table 4 for the actual values of these parameters.
match the number of concepts, in the dataset. For QT v 2d We
Agent architectures, ug and ug. vary slightly across games to best encode the input X into latent vectors U and U Specificallly, for the THING game we employed two fully connected
Availlabl at htt http:h////gttthh..ooo/aaa///////
Available httplhhiw.iiae.....oo..ooaoa/aaa
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layers with input dimension of d 270. Objects in that game encoded by concatenating five one-hot vectors, one per attribute. For the SHAPE, MNIST and QRC games we used four-layers convolutional neural network, similar Mu & Goodman (202T). For the Coco game adopted the Resnet50 (He et al. 2016) pretrained architecture to emhed images into the feature space, followed by two fully connected
layers.
Codebook initialization Proper codebook initialization is crucial for optimal performance in both the DECOMPOSE and COMPOSE phases. Initializing the codebook with too similar vectors leads to difficulties in associating different concepts with distinct words, while initializing with vectors that are too dissimilar results codebook underutilization. We observed that adopting the online clustering approach proposed by /Zeng & Vedaldi (2023) significantly enhances codebook performance. Moreover, the quality of codebook initialization the sole distinction between the C/D and CtD results, obtained during the COMPOSE step. As demonstrated in Table 2 this discrepancy profoundly influences agents' performance.
Codebook training the original VQ-VAE work (Oord et al. 2018), the authors discuss two types of loss: commitment loss [[|sg[z] wll and dictionary loss (l sg[w][B). In an appendix to the paper, they propose using an exponential moving average (EMA) instead of dictionary loss. After experimenting with both approaches, found that EMA outperforms dictionary loss in all our setups.
In subsequent study online clustering (Zheng & Vedaldi 2023), the authors utilize EMA to re- initialize inactive code vectors, a process conducted independently of the commitment and dictionary loss formulas. Our experiments revealed that with re-initialization, using both the dictionary and commitment losses is more effective than substituting dictionary loss with its EMA counterpart. Therefore, we adopt the loss and re-initialization methods proposed by Zheng & Vedaldi (2023) across all experiments.
We tested various values of 82, which balances the commitment and dictionary losses, ranging from 0.1 to 1.0. After finding no significant impact on results with different values, we set it to 1.0 for all experiments.
Early stopping We conduct experiments over multiple epochs and choose the checkpoint exhibiting the lowest validation loss. Importantly, the CtD optimizes a trade-off between the task loss and the codebook loss. We use 31 hyper-parameter balance this trade-off. After testing values ranging from 0.25 to 1.0 and observing no significant differences, we set 31 to 1.0 for all experiments. Refer Section 3.3 for more details. We note instances where these losses are conflict. Refer to Figure for examples. Although we consistently select the checkpoint with the lowest combined loss across all experiments, choosing the checkpoint that minimizes the task loss yields improved accuracy, while selecting the checkpoint that minimizes the commitment loss enhances compositionality.
We run all experiments on single A100 GPU with 40 GB of RAM. Model size is less than 10MB. We use the 'Adam' optimizer with learning rate as specified in Table [1] We usually trained the model for 200 epochs which took about 10 hours to complete. Our code available at https: / thub. com/ bca rme i/egg_gtt.. Please contact the authors via email for access.
H COMPARISON WITH EARLIER WORKS
This section describes additional related works and offers more detailed comparison with two specific lines of research.
H.1 LEARNING WITH MULTIPLE LOSSES
Several works identify the inherent sccuracy-compositionalll trade-off. Tucker et al. (002)) identify this as trade-off between complexity and expressiveness. Guo et al. (2021) study the trade- off between contextual complexity and unpredictability. Rita et al. (2022) observe that the loss can be decomposed into an information term and co-adaptation term, which stems from the listener's difficulty to cooperate with the sender. Two-term losses are inherent to codebook-baut architectures and naturally map the the two complementary tasks. While achieving high
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accuracy requires minimizing the task loss, achieving high compositionality requires minimizing the codebook commitment loss.
H.2 TWO-STEP TRAINING
Recent work compositionality in neural networks highlights meta-learning (Finn al. 2017) as key to out-of-distribution generalization. Russin et al. (2024) proposes that compositional generalization can be achieved using two training loops: the inne-llop generalizes o.o.d. due to the inductive biases from the outer-loop. Lake & Baroni (2023) show that transformers can achieve compositional generalization through in-context learning (ICL) in the inner-lopp. after training the outer-loop on next-word prediction. While technically different from CtD, these insights support our results. In CtD, the inner-loop learns concepts, and the outer-loop composes complex phrases using them.
H.3 COMPARISON WITH OBVERTER
A study by BBoii et al. 2018) introduces Context-Consse
Obverter architecture, demonstrating the emergence of discrete communication from images. They report both accuracy and composition- ality, measured using CI, and compare their results with earlier Obverter findings from Choi al. (2018). Both studies use a dataset similar to our SHAPE dataset. Their version consists of 8 shapes and 5 colors, with the shapes 3D.
Their dataset contains 8 x 5 = 40 unique NL phrases, each consisting of a shape and a color. In contrast, our dataset has x 5 x 270 unique NL phrases, with each phrase being 4 concepts long. Refer to Appendix B for details. Achieving high compositionality scores in our setup is, therefore, more challenging.
Additionally, in Bogin et al. (2018) and Choi et al. (2018) setups, the receiver observes a single distractor, while our setup, the receiver deals with 20 distractors, making the random baseline in their setup (0.5) significantly higher than ours (0.05). Furthermore, their data split allows the same phrase to appear both the training and test sets, making it easier for agents to perform well on the test set.
Despite these differences, which simplify the task these studies, Bogin et al. reported a CI score of 0.4, Chole et al.) only demonstrated the potential segmentation of emergent communication (EC) messages into natural language (NL) concepts. In contrast, by using the CtD method, we achieved perfect accuracy and compositionality scores, on the more complex task, which includes 20 distractors and a more challenging train/test split.
H.4 COMPARISON WITH VQ-VIB
study by Tucker et al. (002) is the only one we know of that suggest to use discrete codebook in emergent communication. Their usage of codebook is significantly different than ours. In their work, Tucker et al. explore the trade-off between complexity, measured by the number of bits allocated for communication, and informativeness, which corresponds to accuracy in solving a referential task. They demonstrate that a balance between complexity and informativeness can be achieved using a discrete codebook, referred to as VQ-VIB.
Notably, Tucker et al., do not address the compositionality of the emergent communication, nor do they provide any compositionality measurements, which is central focus of our work. Additionally, the dataset they used consists of single-color phrases that do not require compositionality to be solved.
Moreover, Tucker et al. employ variational auto-encoder (VAE) to learn distribution over input images, whereas our approach uses a deterministic auto-encoder to structure the codebook. While they suggest method for extracting multiple vectors from the codebook by segmenting the input vector U and finding the nearest vector for each segment, our approach instead identifies the / code-vectors most similar to U
In summary, despite both CtD and Tucker et al. (2022) using VQ- -Q-V-bbbaeed codebooks, they do so in fundamentally different ways and for distinct purposes.
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I A WIDER VIEW OF THE ACCURACY COMPOSITIONALITT TRADE-OFF
In this section, we refer to few works related to the accuncy-compsttionalyy trade-off aspects highlighted in the main body of the paper. Additionally, we reference recent studies that address similar aspects in more conventional setups and suggest promising future directions.
Channel capacity and information Bottleneck Broadly speaking, wide channel aids agents in achieving high accuracy. For instance, with continuous communication (see Section A.2). which practically offer unlimited capacity, agents are able to achieve perfect accuracy REF games (Carmeli) et al. 2023). Conversely, the information bottleneck (Slonim 2002, Kharitonov et al. (020) serves as the primary inductive bias assumed by the EC community for the emergence of natural language traits. Hence, an inherent trade-off exists between accuracy and compositionality objectives.
Discrete channel As a somewhat orthogonal line of thought, the EC community assumes that discrete communication is an essential bias for the emergence of natural language traits (Lazaridou et al. 2017; Choi et al. 2018 Havrylov & Titov] 2017). This assumed bias, which goes beyond simply adding an information bottleneck (Koh et al. 2020p, makes the most sense as the most notable differences between natural language and neural networks relate to this aspect.
Measuring compositionality Adding to these challenges, until recently (Carmeli et al. 2024), a
straightforward and intuitive metric for assessing compositionality was lacking (Hupkes et al. 2020 Dankers Titov 2023 Andreas 2019). Consequently, evaluating the impact of channel capacity and discreteness accuracy and compositionality posed significant challenges.
Common communication and optimization methods Previous studies have proposed various
strategies for managing the trade-off' between accuracy and compositionality within the discrete communication constraint (Lazaridou et al. 2017: Havrylov & Titov, 2017: Carmeli et al. (023). The most common approaches (GS and RL) typically operate under the assumption of oowccppci discrete channel. Alternatively, methods like quantized communication (Carmeli et al.) (2023) aim to address the discreteness constraint through quantization, thereby enabling a wide yet discrete channel. While these methods often achieve respectable levels of accuracy compositionality, they struggle to improve both simultaneously.
Variational auto-encoders (VAE) Another approach involves the use of auto-encoder architectures (Vincent et al. 2008), typically within the RECON game framework (see Section I.. to establish the necessary information bottleneck. By leveraging the Beta-VAE (Higgins et al. 2017) and similar architectures (Tucker et al.] 2022), compositionality is believed to be attained through the disentanglement of the latent space. These methods, often referred to as catturee--a-ddrettioon operate under the assumption that the representation of concepts can be aligned with dimensions in the latent space. In contrast, the VQ-VAE. architecture (Van Den Oord et al. (017)) employ a discrete codebook, aiming to represent concepts directly as points in latent space in a so-called features-as-points embedding.
Superposition and ceatuue-as-dirrettioss Recent advancements in mechanistic interpretability (Olah) 2023 Elhage et al. 2022) have shed light on the challenge of disentangling the latent space, revealing that superposition is inherent phenomenon in neural networks (Bricken al.) (023). To address this issue, some researchers propose the use of sparse auto-encoder (SAE) architectures (Geadah et al.) 2018)) to learn a dictionary of meaningful features. However, these efforts have achieved only limited success thus far. Notably, SAE architectures compromise the information bottleneck assumption by assuming a wide but sparse information channel. We are not aware of any work that studies such architecture under the EC setup.
Codebook and ceature-as-points A notable recent study by (Tamkin et al., 2023) incorporates a discrete codebook into the transformer architecture. They demonstrate that with such discrete bottle- neck, interpretable features can be represented by combining a number of code words. Moreover, they offer an analysis comparing the distinctions between featuresaa -pontts and features-ad as-directions, favoring the former. We find this comparison particularly relevant to our work and to emergent communication architectures in general.
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Published as a conference paper at ICLR 2025
Conclusion In conclusion, argue that learning communicate while utilizing codebook, as done in the CtD approach, enjoys the advantages of features-a as as-points explained by (Tamkin et al.) 2023), while VAE-based architectures, which seek for a features-as-dee asdirrection representation, suffer from the less-compositional feature-as-directionn representation.
J CTD LIMITATIONS AND FUTURE WORK
Several aspects of the CtD approach warrant further investigation.
Self-supervision While the original REF and RECON games require no supervision, the DIFF and
MREF multi-target games necessitate Oracle supervision to identify targets sharing similar concepts. This supervision directs the network in extracting concepts interest to the Oracle. Hence, exploring methods for enabling the sender to identify similar images without Oracle supervision is an important improvement that require additional research.
Dynamic word allocation Although initially aligned the size of the codebook with the number of concepts in the vocabulary (see Appendies [ Fnddd for specifics), there is potential for a dynamic word allocation strategy. In this approach, the codebook itself would autonomously determine whether to initiate a new code or utilize an existing one to describe potentially novel concept. Exploring algorithms such as those proposed by Ghahramani & Griffiths (2005), which facilitate the dynamic allocation of new vectors for emerging concepts, presents a promising avenue for future research.
Varied-length control Unlike the GS and QT protocols, which support communication of varied- length messages, the CB protocol requires the message length as an input. Specifically, this input determines the number of vectors to be extracted from the codebook. In Appendix F we discuss this limitation in details. Investigating more flexible configuration for vector extraction based on similarity thresholds would be valuable.
Repeated words CB-based communication generates bag-of-words messages, where identical concepts cannot be repeated within the same message. This limitation is not an issue when describing single object in datasets like THING or SHAPE, repetition (e.g., mentioning the concept 'Blue' twice) is unnecessary. However, in cases such as an MNIST image depicting the number 11, the need arises to repeat the concept twice to accurately describe the two identical digits. Although this might appear to be limitation of the CB-based protocol, repetition is, in fact, necessary for describing multiple instances of an object, as required by datasets like MNIST and Coco. RNN- based approaches also lack built-in mechanism for "sequential sampling without repetition." " which can lead to unnecessary repetition of concepts when describing a single object. To the best of our knowledge, this issue has not been addressed in previous research, and we propose it as topic for future investigation.
Index-based Communication In the proposed CB communication approach, the sender transmits the full latent vector of concept to the receiver. In contrast, words in natural language function as indices pointing to the latent space. is feasible to send the index of a word from the codebook instead of the entire vector, provided the receiver can map these indices back to their corresponding meanings. This index-bases communication would require the receiver to have access the codebook. Addressing this potential enhancement is left for future research.
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Reviews:
[{"review_id": "zT1Lo2YWQt", "reviewer": "Reviewer_dKHK", "summary": "The paper introduces \"Composition through Decomposition\" (CtD), an approach enabling artificial neural agents to achieve compositional generalization by breaking down and recomposing concepts. CtD consists of two phases: in the \"Decompose\" step, agents learn to identify basic concepts in images through a codebook-based communication setup; in the \"Compose\" step, they use these learned concepts to describe novel images. This structured approach allows for zero-shot generalization to unseen compositions. Experimental results on multiple datasets show CtD can outperform standard methods, achieving high accuracy and compositionality.", "questions": "I didn't fully get why zero-shot is better than further training in MNIST. The authors say this is because of the difficulties of further training, but why?\n\nThe initialization of the code book is a very interesting observation. So how would one set this appropriately in practice to make sure it's successful? Should it always match the number of basic concepts?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "The approach of \"Composition through Decomposition\" (CtD) method stands out as a two-step approach where agents first learn to decompose complex objects into simpler concepts before recomposing them. It is an interesting way to get agents to perform compositional inference.\n\nUsing a discrete codebook to handle basic concept representations is well-grounded, showing the potential for generalization without additional training. This idea, inspired by linguistic encoding methods, enables efficient compositional representation and surpasses traditional methods in performance on multiple metrics.\n\nThe paper evaluates the CtD approach across diverse datasets (e.g., THING, SHAPE, MNIST), demonstrating high accuracy and compositionality scores. The performance evaluation using zero-shot and multi-target settings strengthens the claim that CtD enables compositional generalization.\n\nThe authors us multiple metrics (e.g., AMI, CBM, BOS) to give a clear picture of the model's strengths and weaknesses.\n\nI generally thought this paper was well-written and the presentation was good.", "weaknesses": "\"Several methods have been proposed and evaluated during recent years by the\nemergent communication (EC) research community...\" -> isn't meta-learning another one to mention here?\n\n\"Notably, our method achieves extremely high performance, characterized by perfect accuracy and\ncompositionality, on multiple datasets.\" -> just say it achieves perfect accuracy, no need to say extremely high\n\n\"we assert that before effectively composing basic concepts into complex ones, agents must acquire the ability\nto decompose complex concepts into basic ones\" -> must sounds quite strong here. Do you really show that there is no other way to do this? Or is your method one way to accomplish compositionality?\n\nYou're using \"employed\" a lot when really you could just say \"use\"\n\nI didn't get how the beta of the loss function (game and codebook-tradeoff) was set at first but later it said that the authors \"experimented with various values of β1 and β2, ranging from 0.1 to 1.0 and found no significant difference in results.\" What do you make of this? Why does it not make a big difference? Is this because the loss is dominated by one part in any case?\n\nThere is a lot of things going on in Figure 3. Why are there arrows in there? This seems to mostly just show exactly what is in the text already.\n\nI like the ablation studies although it could be a bit better explained why multi-target makes a difference and how the differences between the data sets in this ablation can be explained.\n\nThe paper discusses a multi-loss optimization, but the complexity and potential sensitivity of the CtD approach to hyperparameter settings (e.g., β1 and β2 values) could make it less accessible for broader use. \n\nFor some datasets, such as COCO, the author found limited compositional performance but this wasn't really discussed any further.", "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": "", "extra_scores": {}}, {"review_id": "XwJAvSKbCO", "reviewer": "Reviewer_Ktng", "summary": "This study presents \"Composition through Decomposition\" (CtD), a method that enables artificial neural agents to achieve compositional generalization, allowing them to describe new images by systematically combining learned basic concepts. CtD involves two stages: first, a “Decompose” step where agents learn to break down complex images into discrete basic concepts using a codebook developed through multi-target coordination games. Then, in the “Compose” step, agents use this codebook to describe novel images by recombining basic concepts, achieving zero-shot generalization in some cases.", "questions": "My questions are based on the weaknesses listed above:\n\nCould the authors discuss potential methods for automatically discovering or learning relevant concepts during the decomposition phase? How might this approach be modified for real-world applications where predefined concepts are not available?\n\nCould the authors add a paragraph in Section 3 or in the introduction that clearly outlines the key innovations of their approach? This would help readers better understand which components are novel and which build upon previous work", "limitations": "", "rating": 8, "confidence": 2, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "Originality: Fairly original, builds upon previous work but with somewhat novel contributions\n\nQuality: Very pertinent experiments on a wide range of tasks with a wide range of metrics\n\nClarity: Sections 1, 2, 4, 5, 6, and 7 are very clear and well written\n\nSignificance: Significant contribution to understanding how compositionality can emerge in a learning system, which is an important concept to understand faster and more effective learning", "weaknesses": "1. It seems to me that in order to properly do the CtD approach, you need to already know the concepts you want to compose ahead of time in order to setup the 2 phases of training. I don't know how realistic this is in real-world settings.\n\n2. I think the paper should make it clear what the novel part of the work is (from what I understand it is only the 2 phases of training), because now it seems like all 3 parts of section 3 are novel\n\nPotential additional citation:\n- https://arxiv.org/pdf/2002.01365", "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": "", "extra_scores": {}}, {"review_id": "ag3gB61Jkz", "reviewer": "Reviewer_LvJV", "summary": "The paper studies how to improve the model’s compositional generalization ability. Specifically, the authors propose a two-stage training pipeline, in which the model first learns to decompose an image into basic concepts using a codebook and then recombines the learned features to describe novel concepts. The experiments on different image datasets showcase that the proposed method indeed improves the model’s ability compared with other baselines. However, the proposed method needs a carefully selected training set, which limits its applicability to more practical scenarios. Also, the paper hasn’t discussed an important line of work related to this problem, i.e., iterated learning, which is a multi-generation-based training pipeline that can amplify the inherent bias towards compositional mappings automatically. I guess combining the method proposed in this paper and multi-generation training can further improve the model’s ability on compositional generalization. In summary, I think the paper has the potential, but due to the reasons above, I would like to give a negative score for the current version.", "questions": "Please refer to the weakness part.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The presentation is good, and the paper is easy to follow.\n- The experiments are well conducted, covering both toy data and real images.\n- The conclusions drawn from the experiments are inspiring. (E.g., I like the results in Figure 3.)\n- The zero-shot results are interesting.", "weaknesses": "- The paper doesn't mention the multi-generation-based approach for the compositional generalization problem. Actually, the two-stage training proposed here can also be analyzed using similar theoretical tools provided in related works, e.g., [3]. Furthermore, [1] also studies the compositional generalization problem in the context of emergent communication, which is identical to the one studied in this paper. Such an iterated training fashion has proven to be effective in many other fields, e.g., molecular graph prediction [3], visual VQA [2], large VLM like CLIP [4], etc. It might be helpful to discuss (or even compare) with methods in this line of work. So, providing more discussions about the potential synergies or tradeoffs between the decomposition-composition approach and multi-generational training would make the paper stronger.\n- The discussions and analysis throughout the paper are high-level. A more in-depth discussion of the dataset selection design in different phases would make the paper stronger. For example, the authors mentioned in line 190 that “In the DECOMPOSE step all targets share a phrase composed from exactly one FVP”, what will happen if this assumption is violated? How will it influence the final results? Will the network be robust enough when this assumption is mildly violated? Since this assumption is too strong to be true in many practical scenarios, relying too much on this assumption might harm the contribution of the paper. I believe conducting ablation studies where the single-FVP assumption is systematically relaxed to varying degrees would make the paper stronger.\n\n[1] Ren, Yi, et al. \"Compositional languages emerge in a neural iterated learning model.\" ICLR 2020\n\n[2] Vani, Ankit, et al. \"Iterated learning for emergent systematicity in VQA.\" ICLR 2021\n\n[3] Ren, Yi, et al. \"Improving compositional generalization using iterated learning and simplicial embeddings.\" NeurIPS 2023\n\n[4] Zheng, Chenhao, et al. \"Iterated learning improves compositionality in large vision-language models.\" CVPR 2024", "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": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)