Compositional Generalization in Unsupervised Compositional Representation Learning: A Study on Disentanglement and Emergent Language
Authors: Zhenlin Xu
Marc Niethammer
Colin Raffel
Venue: NeurIPS 2022 Accept (2022)
Keywords: compositional generalization
generalization
compositionality
disentanglement
emergent Language
unsupervised representation learning
discrete representations

Abstract: Deep learning models struggle with compositional generalization, i.e. the ability to recognize or generate novel combinations of observed elementary concepts. In hopes of enabling compositional generalization, various unsupervised learning algorithms have been proposed with inductive biases that aim to induce compositional structure in learned representations (e.g. disentangled representation and emergent language learning). In this work, we evaluate these unsupervised learning algorithms in terms of how well they enable \textit{compositional generalization}. Specifically, our evaluation protocol focuses on whether or not it is easy to train a simple model on top of the learned representation that generalizes to new combinations of compositional factors. We systematically study three unsupervised representation learning algorithms - $\beta$-VAE, $\beta$-TCVAE, and emergent language (EL) autoencoders - on two datasets that allow directly testing compositional generalization. We find that directly using the bottleneck representation with simple models and few labels may lead to worse generalization than using representations from layers before or after the learned representation itself. In addition, we find that the previously proposed metrics for evaluating the levels of compositionality are not correlated with actual compositional generalization in our framework. Surprisingly, we find that increasing pressure to produce a disentangled representation (e.g. increasing $\beta$ in the $\beta$-VAE) produces representations with worse generalization, while representations from EL models show strong compositional generalization. Motivated by this observation, we further investigate the advantages of using EL to induce compositional structure in unsupervised representation learning, finding that it shows consistently stronger generalization than disentanglement models, especially when using less unlabeled data for unsupervised learning and fewer labels for downstream tasks. Taken together, our results shed new light onto the compositional generalization behavior of different unsupervised learning algorithms with a new setting to rigorously test this behavior, and suggest the potential benefits of developing EL learning algorithms for more generalizable representations. Our code is publicly available at https://github.com/wildphoton/Compositional-Generalization .

Compositional Generalization in Unsupervised Compositional Representation Learning: A Study on Disentanglement and Emergent Language
Zhenlin Xu Mare Niethammer Colin Raffel Department of Computer Science University of North Carolina at Chapel Hill (zhenlinx, mn, craffel) unc. edu
Abstract
Deep learning models struggle with compositional generalization, i.c. the ability to recognize or generate novel combinations of observed elementary concepts. In hopes enabling compositional generalization, various unsupervised learning algo- rithms have been proposed with inductive biases that aim to induce compositional structure in learned representations (e.g. disentangled representation and emergent language learning). In this work, we evaluate these unsupervised learning algo- rithms in terms how well they enable compositional generalization. Specifically, our evaluation protocol focuses on whether or not it is easy to train a simple model on top of the learned representation that generalizes to new combinations of compo- sitional factors. We systematically study three unsupervised representation learning algorithms 3- VAE, 3-TCVAE, and emergent language (EL) autoencoders - on two datasets that allow directly testing compositional generalization. We find that directly using the bottleneck representation with simple models and few labels may lead worse generalization than using representations from layers before after the learned representation itself. addition, we find that the previously proposed metrics for evaluating the levels of compositionality are not correlated with the actual compositional generalization our framework. Surprisingly. we find that increasing pressure produce disentangled representation (e.g. increasing / in the (-VAF) produces representations with worse generalization, while repre- sentations from EL models show strong compositional generalization. Motivated by this observation, we further investigate the advantages of using EL to induce compositional structure unsupervised representation learning, finding that it shows consistently stronger generalization than disentanglement models, especially when using less unlabeled data for unsupervised learning and fewer labels for downstream tasks. Taken together, our results shed new light onto the composi- tional generalization behavior of different unsupervised learning algorithms with a new setting to rigorously test this behavior, and suggest the potential benefits of developing EL learning algorithms for more generalizable representations.
1 Introduction
human's ' ability to recognize or generate novel combinations of seen elementary concepts, also known compositional generalization, is desirable for building general artificial ingelligence (AT) systems [22] 16 3. The Lioognition-B--Comooe
theory by Biederman 3 influenced the carly development of computer vision models that are inherently compositional, e.g., hierarchical
features [I3 [4] and part-based models [37 38). However, modern deep learning systems still struggle with this key capability of human intelligence 33 few works studied specific spatial and
36th Conference on Neural Information Processing Systems (NcurIPS 2022).

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object-wise compositionality 42 30 or more general compositionality in the space of pre-defined
attributes [4 39 or the semantics of human language descriptions 49
Humans often express complex meaning in a compositional manner: we combine elementary rep- resentations describe observations. For example, an object with simple geometry is described by separate and independent properties such as color (red, blue, position (left, right, close, far away...), and shape (circle, triangle, ...) Therefore, compositional representations are thought as helpful or even essential to achieve compositional generalization [22 15
However, consider- ing that there are exponentially many possible combinations of given set elementary concepts, we need to deal with this combinatorial explosion for real- weoldw visual observations. It is unrealistic to an- notate enough data to learn the fine-grann ane-grained compositionallty. Therefore, unsupervised compositional representation learning is appealing because it does not require comprehensive labeling. However, unsupervised representation learning heavily relies on the design of an effective inductive bias (e.g. on the representation formulation) to induce the emergence of compositional representations.
3 28
A widely explored representation formulation with explicit compositionality disentanglement. The most common formulation of disentanglement is that the generative factors of observations should be encoded into different factors of low-dimensional representations, and a change of single factor in an observation leads to a change in a single factor of the representation. State- of- unsupervised disentanglement models 20 24
are largely built on top of variational generative models [25]. To measure the level of disentanglement, various quantitative metrics have been proposed that are defined based on the statistical relations between the learned representations and ground truth factors with an emphasis on the separation of factors. A summary of disentanglement metrics and methods provided in 31 Another representation learning approach with an inductive bias towards compositionality is emergent language learning. Natural language allows us to describe novel composite concepts by combining expressions of their elementary concepts according to grammar. Therefore, linguists have been interested in studying the compositionality of discrete codes evolving during multi-agent communication when agents learn to complete a task cooperatively 19, 29 19 40]. Compositionality metrics with language structure assumptions, e.g. topographic similarity [4] were used to evaluate the learned language. However, for the above two types of methods, relatively few studies (36] 41 6 I have directly evaluated how well the learned representations generalize to novel combinations on downstream tasks, which is the main motivation for compositional representation learning in the first place.
In this work, we study the compositional generalization performance of representations learned from unsupervised learning algorithms with two types of inductive biases for compositionality; disentanglement and emergent languages (EL). Instead of measuring the compositionality and disentanglement metrics defined based on various assumptions, we directly measure the generalization performance on novel input combinations with a two-stage protocol. Specifically, with a dataset divided into train and test sets ensuring that the test set contains novel combinations of concepts that never appear in the train set, we first learn an unsupervised representation model from unlabeled images in the train set. With very few labeled samples from the train set and the frozen unsupervised representation model, we train simple (e.g. linear) models on top of learned representations to predict the ground truth value for each generative factor of the dataset and evaluate these simple models on the test set. These choices are aligned with common practices in recent deep representation learning works, for example, self-supervised representation learning [10] and semi-supervised learning with generative models (26). Different from previous studies (e.g. [6, (61) that measure unsupervised learning performance (e.g. image reconstruction), we evaluate the performance on downstream tasks. We also emphasize how easily we can obtain downstream task models with the learned representation, e.g. when using very few labels and simple linear models. These designs highlight the generalization performance of the unsupervised learning stage, different from a setup that uses many more or even all labeled samples of the train set in the downstream task learning stage 10 41 or performs unsupervised learning on the entire dataset [31]. More importantly, we study not only the compositional generalization of intermediate representations the model bottleneck, e.g. where the disentangled latent variables are formulated, but also the representations from layers before or after it.
With the above evaluation protocol for compositional generalization, we explore selected unsupervised learning algorithms by varying (1) the hyperparameters of each algorithm that may control the levels of compositionality; (2) image datasets and the amount of data for both unsupervised and supervised learning stages; and (3) design choices of EL learning. First, we find that, compared to the low-
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shared embedding layer
Latent
p((
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my M2.
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Figure 1: Architectures of disentanglement models (left) and emergent language models (right).
dimensional latent variables from the model bottleneck, representations from the layers before or after the model bottleneck enable better compositional generalization. Second, we find that attaining metrics does not always
higher scores on previously proposed sumpsiitonaliyydisstianggmmm correlate with better generalization performance. Finally, the representations learned from EL models show stronger generalization performance than disentanglement models. These findings reveal the divergence between the efforts to achieve better compositionality disentanglement metric scores and the initial motivation to obtain better generalization performance. To our best knowledge, this is the first study to compare representations in disentanglement models and emergent language learning through the lens of compositional generalization with unified evaluation setup. We also discuss the advantage of the emergent language representation format versus disentanglement and connect with recent related research in representation learning.
2 Unsupervised Learning with Compositional Representation Inductive Bias
In this section, we introduce more details on unsupervised learning algorithms with two different compositionality-seekiii inductive biases the representation formulation: disentangled representa- tions in Section 2.1 and emergent languages in Section 2.2
2.1 Learning Disentangled Representations
The concept of disentanglement assumes that high-dimensional observations of the real world can be represented by low-dimensional latent variables z, where each dimension z encodes independent factors of variations in x. For unsupervised disentanglement learning algorithms, select the popular 3-VAE and 3-TCVAE methods which both modify the evidence lower bound (ELBO) objective in the variational autoencoder (VAE).
3-VAE use a hyperparameter for the Kullback-Leibler (KL) regularization term of the vanilla VAE loss to control the bandwidth of the VAE bottleneck:
(eg (m/x) [log pe (x z)] (KL(go()>)]ll(()))
(1)
where p(z) is the assumed prior distribution of the latent variables and its conditional distribution 2s [z(2/x] x is parameterized by a neural network (encoder) whose parameters are & and the posterior corresponds to the VAE loss.
px(x)z) parameterized by a decoder whose parameters
3-TCVAE further decomposes the KL term in Eq. ① into mutual information, total correlation, and dimension-wise KL terms, and penalizes the total correlation with the hyperparameter 3:
E (x( Tog
Tog [o (x; z) (gg(() II go (o())) - Σ (KL((()))lxzz))) (2)
where (x(x: 2), KL(g (z)]l II, (=y)) and E, (L({(z)) are the mutual information term, total correlation term and the dimension-wir wise KL term respectively. The proposed 3-TCVAE uses 7 and tunes only.
2.2 Learning Emergent Language
An alternative compositional representation learning method emergent language (EL) learning, which aims to learn representation that mimics the properties of natural language. The emergent language consists of sequences discrete symbols from a vocabulary. Since the model combines discrete symbols in the vocabulary to represent complex semantics in observations, one expects that

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meaningful compositionality might naturally emerge in communication between multiple agents using the emergent language solve tasks. We consider the typical speaker-listener model (two- agent communication) for EL. learning, as shown in Fig. [ We apply EL. learning to the image reconstruction task to be consistent with the reconstruction objective used by variational auto-encoder- based models. Note that in our setting the terminology "speaker-listeerr" is equivalent to the more common "encoder-decoder" terminology. The task is as follows.
1. The speaker receives input x and encodes it as message m = {m², m ...... sequence discrete symbols from the vocabulary V [c1,02, Cny of size ny. The maximum length of m is 7msg.
2. The listener model receives the message m and the outputs x, aiming to accurately recon- struct the encoder input x.
In this work, we use a speaker and a listener that are both hybrids of a convolutional neural network and an LSTM recurrent neural network. The flattened convolutional embedding of the input image, EncConv (x), is used as the initial cell state of an LSTM encoding module (EncLSTMM, EncLSTM generates a discrete distribution q [z) over at each time step t autoregressively (with the embedding of the discrete token sampled in the previous step - 1 as input):
q(m") x) (
emb(m (mm emb(m'-
(3)
where emb(.) is the learnable layer that projects discrete token into high- high-dimensional embedding.
We use the Gumbel-Softtax [23 32 sample from the discrete distribution q(m' (xx) and the
"straight-throug"" (ST) gradient estimator (2) for quantization (from soft-distribution to one-hot
vector). This allow us to estimate the gradients from the discrete sampling process.
m (uumbeeelSSof [x)))
To allow the message to be of variable length, which better mimics natural language, we set one token in V to be the end-of-sequence (EOS) token that indicates the message end.
When the listener decodes the message m, it first maps each discrete symbol into an embedding based on a learnable embedding layer and uses a decoding LSTM layer (DecLSTM) to process the sequence of embeddings recurrently.
Emb' m)) DecLSTM(emb(n1) (mmb(mm))))m)))))))mm)m))mmm)))) emb(mm))........ emb(m' (1))
(m)
(5)
We use the output of DecLSTM at the ending step I' as the embedding of the message be the input of convolutional decoder for image reconstruction:
Emb(m) = Emb'' T m)) where T = min (Ameg: argmin(m' = EOS,i {1..N)).
(6)
Finally, the convolutional decoder (DecConv) reconstructs the input by:
DecCony(Emb(m)).
3 Experimental Design
3.1 Datasets
We are interested in whether representations can generalize to novel combinations of seen concepts. Therefore, we need datasets that provide ground-truth labels of elementary concepts for (1) creating train/test splits and (2) downstream task evaluation. We consider datasets with nggen independent generative factors F=
where the space of factor fü is S,. For example, if f1 color, then S₁ could be {yellow, red, bl.e..... The data space D is defined by the Cartesian product of the spaces of each factor, and therefore the cardinality of the dataset is | IT |S
In our study, we used two public image datasets studied in the disentanglement literature: dSprites 35
and MPI3D [17]. The dSprites dataset contains images of 2D shapes generated from 5 factors F (shape, scale, rotation, and y position]. of the square and ellipse shapes, we limit the range of orientations to be within [0, x 22)). Then the
avoid label ambiguity due to the rotational symmetry
cardinality of each factor's space (3, 6, 10, 32) respectively, which makes |D] 183, 320. MP13D is set of 3D datasets synthesized or recorded in a controlled environment with object held

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by a robotic arm. In our evaluation, the challenging real-worle version (MPI3D-Real) is used. It has 7 factors F = (object-color(6), object-shape(6), object-size(2), camera-height(3), background-eolor(5) horizontal-axis(4)) vertical-axis(40) with the corresponding cardinalities of the space in parentheses, leading to a total of 1006,800 images.
3.2 Compositional Generalization Evaluation Protocol
Our evaluation protocol emphasizes the compositional generalization that models can achieve on downstream tasks. Our objective is to measure how easily an unsupervised representation learning method can produce compositional generalization using a simple model on top of the learned representation. (1) Data splits. We first split a dataset into train/test sets randomly while ensuring that all samples in the test-set are novel combinations of elementary factors seen in the train-set. (2) Unsupervised representation learning. We learn unsupervised representations from the unlabeled images of the train-set of size Nirain with selected algorithm. (3) Learning for downstream tasks. Then, we freeze the learned representation model and use the Nlabe! labeled samples from the train set (Niabel << Ntrain). to train simple classifier regressor to predict the ground truth value for each factor fi of the dataset. (4) Testing generalization performance. Lastly, we test the performance of the downstream task models on novel combinations of seen values of elementary factors.
Readout model. We argue that it is important to use simple read-out models and a limited number of labeled training samples evaluate downstream tasks. Otherwise, the performance gain from the downstream task learning stage is mixed with that of the unsupervised learning stage. For example, if the unsupervised representation model is an identity mapping, we can still get great performance with a powerful read-out model and enough labeled samples. In our main article, we use linear models for downstream tasks. However, perfectly disentangled but linearly inseparable representations may still show poor performance with a linear readout model. Through sanity checking experiments (discussed Appendix ??), the linear readout model can still generalize well on nonlinear oracle representations possibly due to the limited value range of attributes in our datasets. In addition, extra results using non-linear readout model (Gradient Boosting Trees) are in Appendix ?? and the main observations to predict the values of the generative factors ridge
consistent. The linear models regression, using the R² score as the evaluation metric, and logistic regression, using classification accuracy the evaluation metric. Since the R² score can be negative while R 0 indicates random guessing, we clip all negative R²2 scores to zero
Representation Mode. In unsupervised disentanglement learning, low-dimensional latent variables with explicit disentanglement regularization are used as the representation for downstream tasks, e.g. the mean values of Gaussian distributions of the latent variables in the VAE. If the disentangled latent variables each represent single ground truth factor, only a simple mapping between factors and the corresponding variables must be learned to achieve good performance. However, it is questionable if the learned latent variables disentangle in the assumed structure and therefore improve generalization. On the other hand, the simple linear models in evaluation protocol may not be capable to process the latent variables (discrete messages) in emergent language (EL) learning because we would not expect discrete sequential latent variables to be easily linearly separable. Therefore, also evaluate the intermediate features the layers before or after the model bottleneck. Specifically, in addition to the latent variables (Ztaten)) also the features immediately after the convolutional encoder (Zpoa) or before the convolutional decoder (Zpre) as representations of images, shown in Fig. []] We evaluate the use of Zpoat and Zpee in both disentanglement and emergent language models.
3.3 Implementation details.
Data Splits For the main experiments, than what common machine learning setups and previous studies have used [36 AT]. However, considering the number of possible combinations increases exponentially for real data with an increased number of generative factors, using fewer training samples even at the unsupervised learning stage can help to obtain more meaningful conclusions for real-world scenarios.
a 1:9 train/test split. The train set size (10%) is smaller
Model architectures. Fig. shows the architectures for disentanglement and emergent language learning models. The encoder and decoder in disentanglement learning models are symmetric architectures with a convolutional network and a multi-layer perceptron (MLP) similar to the design in [5]. We scale up the size of the model by doubling the width of all layers, which improves the
5

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performance of all models. Since our emergent language learning model uses the same autoencoding task as disentanglement learning, it also uses a symmetric encoder-decoder architecture. Instead of MIPs, the EL model uses L.TTM modules to encode and decode latent variables. The sizes of the MLP module in the disentanglement models and the LSTTM module in the EL models are matched for a fair comparison. We use Bernoulli decoder for the autoencoding task, which uses pixel values normalized to [0, I] as probabilities.
tlyperparameters We follow previous studies 31 36 for disentanglement models to set our nyperparameters. We set the number of disentangled latent variables, Zlatent] and the maximum length of the emergent latent message, Remag. to 10, unless specifically mentioned. For the pre-trainn pre-training stage, we use batch size 64 and train the model for 500,000 steps for dSprites and 1,000,000 steps for MPI3D-Ress using the Adam optimizer with learning rate 0.0001. For each specific model, we collect results from three different runs with different random seeds.
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Figure 2: Generalization performance (accuracy for classification tasks and R2 score for regression tasks) of three representation models: 3-VAE, 3-TCVAF, and emergent language on dSprites.
4 Key Studies and Results
4.1 Compositional latent variables may not be the best representations for downstream tasks
We first study the generalization behaviors of different representation modes. For each unsupervised learning algorithm, we vary the hyperparameters that were designed to control the compositionality of representations. For 3- 3-V and 3-TCVAE, we simply vary 3. For emergent language models, we use the communication bandwidth, defined as the number of bits in the message and calculated by logz (m ), Rmma E {8, 10, 12} and ny E {128, 256, 512]. Fig. 2 shows the results for accuracy and R--score vs. 3 and the number of bits when Niabel = 500 for the dSprites dataset. We highlight the following observations:
Emergent language learning As expected, linear models do not work well on Ziaent for EL models. Zpos and Zpre are more suitable. Zpoa consistently outperforms Zure, which reveals that the emergent language bottleneck induces compositional latent structures useful for downstream tasks after being processed by the DecLSTM module.
Disentanglement learning Surprisingly, mismatched with the goal of disentanglement, Zaatent in 3-VAE and 8-TCVAF is not the optimal choice for downstream tasks. For 3 -VAE and 33 -TCVAE, increasing 3 to decrease the bandwidth of the bottleneck (which was thought of as the source of disentanglement (5)) reduces generalization performance. When 3 is larger, Zpre works best. For most cases, the representation of 3 = 0 is best. When 3 = 0, the regression task seems to favor Zpre while ZpusI performs better for classification tasks.
Implications. Both disentangled representation learning and emergent language learning try to induce compositionality through the inductive bias on the representation's 's compositional structure. The Ziatent representation itself does not perform well as its structure may be too complex to be processed by simple linear models. But if Ziatent can generalize well, its decoded version Zpost will perform well. In EL models, Zpost consistently performs better than Zpe. which demonstrates the improved generalization with the language-like bottleneck. However, disentanglement models may

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Mode
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Figure Compositionality metries vs generalization performance in the dSprites dataset. The disentanglement metrics (SAP, IRS, DCI, MIG) of the B- 3-VAE (dots) and 3-TCVAE (crosses) models are not postively correlated with generalization performance in all the three representation modes. The compositionality metric for emergent language (EL), topographical similarity (TopSim), shows no strong correlation with generalization performance.
learn useless disentangled representations since increasing the penalty either the KL-term of the ELBO or the total correlation consistently lead to worse generalization performance. To further confirm this conclusion, we also measure the disentanglement metries on the learned 3-VAE and 3-TCVAE models in the next section.
4.2
Compositionality Metrics May Not Represent Generalization Performance
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Figure 4: Generalization performance vs Niabel- Three representation modes of B- V-E with 8300, 3-TCVAE with 8=0,, and emergent language (EL) with 2y= are evaluated.
Figure 5: Generalization performance (with Niabel 500) of 3-VAE with 8=0, and Emer- gent language (EL) with ny=2556 on MPI3D- Real when using (5%) and (10%) unlabeled data.
We further evaluate existing compositionality metrics on learned representations. For 3-VAE, 8- TCVAE with various B. we measure four common disetanglement metrics: Separated Attribute Predictability (SAP) Score (27). Interventional Robustness Score (IRS) (43), Disentanglementt (DCI) M. and Mutual Information Gap (MIG) 7 based on the implementation in disentanglement-ln
31 The large-scale studies used by Locatello al. 2019 31 broadly measured these metrics on a few datasets. For emergent language learning models, we vary the number of bits in the discrete messages and measure topographical similarity, common compositionality metric for emergent languages that uses the (Spearman) correlation PSpearman between the pairwise distances of the inputs and the distances the corresponding representations. We compute the cosine distance for input attributes and the editing distance for messages. Since we have the train/test data split for the unsupervised lcarning stage, we evaluate these metrics on both splits. The metrics these two splits are similar, and only show the ones for the train split.
We find that both 3-VAE and 3-TCVAE show positive correlations between and the disentangiement metric scores, stronger in dSprites and weaker in MPI3D-Res where the highest scores usually occur for moderate values. However, neither of the two datasets show the same pattern as Fig. where generalization performance is negatively correlated with B. Therefore, for 3 3-VAE and TCTAE. models with higher disentanglement scores do not achieve a better generalization performance. Fig- confirms the noncorelation or even negative correlation between compositionality metrics and generalization performance on the dSprites dataset. The topographical similarity of emergent language models does not show strong correlation, e.g. PSpearman < 0.5 with compositional

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generalization for both dSprites and MPI3D-Real datasets. The observations are consistent with some previous studies on emergent language [6] and disentanglement [T.
Implications. Existing compssiionallyyihenaageeennnn metrics do not measure the generalization performance of learned representations. However, should be careful about interpreting the results as compositionality in representation learning does not necessarily help compositional generalization. As these metrics were defined more or less based on compositional annotations by humans, they can only measure particular types of compositionality. However, the compositionality exhibited in representation learning, especially with unsupervised algorithms, may not match with human definitions, e.g., language where editing distance is poor measure of similarity, and therefore cannot be captured by those metrics. Since designing generic compositionality is challenging or maybe even impossible, one should directly evaluate the compositional generalization if it is the ultimate goal.
4.3 Representations Learned by Emergent Language Models Generalize Better
In Fig we observed some clues that "post" representations of EL models generalize consistently well on both tasks. In this section, we take closer look at the generalization performance of representations learned by EL by comparing them with disentanglement models.
Varying the number of labeled samples for downstream learning. We evaluate the performance of downstream models trained with different numbers of labeled samples Niabet E {100, 500, 1000). We compare three models: B- B-VAF and 3-TCVAE with 3 = 0 (since B = O consistently performs best, as shown in Fig. 2 and the EL model with ny = 256. Fig. shows the results for dSprites. When Ntadel is low, c.g. Naaeel 100 and 500 for dSprites, 2post of EL consistently beats all other models in all representation modes for both classification (accuracy metric) and regression (R² score metric). More importantly, even when Naahel is large, VVE/O--CVVEEEE models do not have consistent representation mode that shows similar performance as Epost of the EL models: their Epost worse at regression and Epre. is worse at classification.
Using less unlabeled data for unsupervised learning. Furthermore, we reduced the train-spil ratio 5% test unsupervised learning algorithms with less unlabeled data. We compared the performance of the 0 D-VAE and EL models on MPI3D-Real in Fig. With 5% unlabeled training data, the post representation of EL models outperforms the pre/post O-VAE model both classfication or regression tasks and all Nusel with an even larger margin. In other words, the generalization performance of representations of 0- VAE models degrades faster with reduced unlabeled data.
Implications. Representations learned by emergent language models generalize well even with limited unlabeled data for unsupervised learning and labeled samples for downstream learning.
4.4 Ablations on Emergent Language Models
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Figure 6: (Left) Ablation study of Emergent Language (EL) with ny = 256 and Niabel = 500 in MP13D-Real using fixed-length messages (EL-fix) and greedy sampling (EL-fix-det). (Right) Generalization performance of EL models with zpost and Niabel = 500 the MPI3D-Real dataset, for different bandwidths by varying message sizes Umag E (8, 10, 12} and vocabulary sizes ny {128, 256, 512]. Three Nmag are plotted segments of different line styles with increasing ny/bits.
Since EL models showed superior compositional generalization performance over disentanglement models, we conduct ablation studies on important hyperparameters and design choices of EL models on the MP13D-real dataset. We first study the impact of bandwidth controlled by either length the messages or the size of dictionary. We can see that increasing the bandwidth generally improves compositional generalization. In some cases, for similar bandwidth, shorter sequences/a larger vocabulary is favored, e.g. 5128 vs. 12 Since the MPI3D-Real dataset only has 6 + 6 6 2 +3

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3 + 40 + 40 = 100 distinct values for all generative factors, simple choice of language can express the values of factors fixed order using Tomg and ny 100. Apparently this behavior is not learned by the current design of EL models, possibly because of optimization issues due to poor gradient estimation for discretization, regardless of the good generalization performance. However, EL. models can learn their own language with additional redundancies that require more bandwidth.
We also ablate the two characteristics of the EL models we have considered thus far: allowing variable-length messages and using stochastic sampling. We can turn an EL model into one with fixed-length messages by always generating Renag tokens (EL-fix) and additionally with deterministic messages by using greedy sampling (EL-fix-det). We can see that as we remove these two designs, the generalization performance is worse, especially after making the model deterministic. Notably, the EL model with fixed- messages and using deterministic sampling (EL-fix-det) is very close to the popular discrete representation learning model VQ-VAE [46] that uses a shared vocabulary over spatial locations of the feature map. Therefore, our study may indicate that the use of discrete latent variables of variable length and stochastic sampling can enable unsupervised learning models to learn better representations for downstream tasks. We also found that while the EL model allows variable-length codes, at convergence still almost always uses the maximum message length on both the training and testing set. This is not surprising given that the reconstruction task drives the discrete message to be longer so that more information can pass through the discrete bottleneck.
5 Limitations of Our Study
Our goal is provide comprehensive study of learning algorithms, including their hyperparameters. However, our study is limited on the variety of other design choices to restrict the experimental complexity. While we studied both synthetic and realistic image datasets, both these datasets relatively simple with the same small number of generative factors and each of the factor follows uniform distribution. For learning algorithms, we focus on studying the inductive bias on the representation format while fixing the model architecture design which can impact the results. Moreover, we did not study hyperparameters beyond those related to the latent representations. Specifically, we did not study how the type and configurations of the optimizer and the batch size would change the results; instead, we followed common setups in previous studies.
6 Related Work
Compositional generalization was shown in previous work on disentangled representation learning
21 to generate images of novel combinations of concepts. Zhao et al. (50) systematically
evaluated generative models in few compositional generalization tasks without exploring whether
disentanglement is correlated with generalization performance. Recently, Montero et al. (36) studied the compositional generalization along with the interpolation and extrapolation generalization of two VAE-based disentanglement models. Similar to [50]. the performance is evaluated on the unsupervised learning task, e.g. image reconstruccion/geeeraait the compositional generalization. Different from (36] that manually selects the train-test splits with various difficulty,
However, we directly evaluate
random splits which is earlier for studying different split ratios.
The comprehensive study on the unsupervised learning of disentangled representation by Locatello et al. [31 included an evaluation on downstream tasks. However, they train unsupervised models on the whole dataset and therefore are not able to evaluate the generalization as we do. [TO] evaluated the downstream out-o--distributton (OOD) generalization that includes the interpolation and extrapolation generalization of unsupervised and weakly supervised disentanglement models, while we focus compositional generalization. A very recent work [41] included compositional generalization behaviors of unsupervised and weakly supervised disentanglement models in their broad study on generalization. Unlike our evaluation that trains simple downstream models with small amount of labeled samples, they use all labels in the train set to learn MLP models. Furthermore, none of these works evaluated the representations beyond the latent variables at the bottleneck layer as we did.
In emerging language (EL) learning, Chaabouni et al. 6 found that regardless of the degree of compositionality measured by topographic similarity, EL can generalize to novel combinations of concepts when the input space is rich enough. Andreas [ proposed new compositionality metric,

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tree reconstruction enror (TRE), measuring how well a representation model can be approximated by compositional operator and learnable primitive representations. While claimed as a general compositionality metric with learnable compositional operator, some pre-commitment to a restricted composition function is essentially inevitable. Similar to [6. 1 also studied the relationship between TRE and generalization. While they work on simple attribute data and evaluate on the tasks for emergent language learning, we use image data and are motivated by learning useful representations for downstream tasks. Furthermore, unlike all previous work, we studied the compositional general- ization representations from both disentanglement and emergent language models with a unified setup.
Conclusions and Discussions
We proposed a protocol to evaluate the compositional generalization of unsupervised representation learning models that have a built-in inductive bias for compositionality: disentanglement models and emergent language (EL) learning. Our evaluation emphasizes using small number of labeled samples to train simple models for downstream tasks. The interesting finding that latent variables the bottleneck do not work as well as "pre" and "post" representations reminds us to be careful when concluding that a model performs poorly when its latent representation does not perform well. For disentanglement models, we observe that generalization performance is not well correlated with existing disentanglement metrics. This finding demonstrates the gap between pursuing better disentanglement metrics and more generalizable representations in previous studies. Similarly, the existing compositionaliiy metries for EL, e.g. topographical similarity, cannot represent the generalization of learned representations. However, under the same setup, EL models, which were not initially proposed for unsupervised representation learning. induce representations with surprisingly strong compositional generalization and are robust to the change of dataset and hyperparameters.
We focus on unsupervised learning algorithms that are specifically designed for compositional representation to answer whether they lead to better generalization (which was an assumption made by a great deal of prior work). A broader evaluation on other representation learning approaches e.g. self-supervised learning [8] [8] would be interesting for future work. We hope that our study draws more attention to the study of compositional generalization and emergent language models as way of learning representations. Interesting future directions include working on more challenging datasets, e.g. images of multiple objects; testing other downstream tasks, e.g. visual question answering; testing different model architectures, c.g. Transformers 477; and developing better pre-training tasks beyond auto-encoding. Recent work showing that emergent language (Atatent) can be used corpus to pretrain a language model [48] also suggests that emergent language may be a better visual representation choice in vision-language models.
Acknowledgement
We thank Nikhil Kandpal for giving feedback on the draft of the paper. Zhenlin Xu was supported by the Royster Society of Fellows Dissertation Completion Fellowship during this work.
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Checklist
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14


Reviews:
[{"review_id": "zaXlrc9KUCK", "reviewer": "Reviewer_mvHF", "summary": "The authors study the compositional generalization performance of several approaches which aim to learn compositional representations including those focused on disentanglement and those based on emergent language. They propose a new metric to measure compositional generalization, specifically exploring novel combinations of previously-observed concepts. They find that, perhaps counterintuitively, often the features immediately before or after the latent variable perform better on generalization metrics. They evaluate on multiple instances of each model and also analyze the relationship between the generalization performance metrics and ones commonly used to evaluate disentanglement ", "questions": "“we find that the previously proposed metrics for evaluating the levels of compositionality are not correlated with actual compositional generalization in our framework” - Why might this be? The paragraph on Implications in Sec 4.2 discusses certain conclusions which cannot necessarily be drawn, but what does it imply if “compositionality exhibited in representations learning …  may not match with [the] human definition”? If they are different, how might they be different?", "limitations": "The limitations section in the Appendix is reasonable and complete.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths: \n- The results are non-obvious and have implications for other representation learning research which, for autoencoders, often (though not always) focuses evaluations on the latent representations.\n- The experiments are thorough, covering a broad range of interesting questions, and well-grounded in disentanglement literature. In particular, this sheds some important light on questions left open by the widely-referenced Locatello et al. 2018., as discussed in Section 5.\n- The metrics are reasonable, the datasets are standard for the disentanglement literature (though more would always be welcome), and the models are also reasonably chosen. \n\nWeaknesses:\n- Given the paper’s title and claims, other kinds of representation-learning approaches would have been reasonable (e.g. encoder-only self-supervised techniques like SimCLR or BYOL, masked autoencoders, decoder-only ones like InfoGAN coupled with projection). However, the results carry useful implications even without this.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "_nbEBNqZM5J", "reviewer": "Reviewer_tbrQ", "summary": "The paper aims to investigate the compositional generalization performance of the representation learned from unsupervised learning, focusing on disentanglement and emergent language (EL). In contrast to previous works that measure compositional generalization on the learning task, the authors propose a two-stage evaluation protocol that does the same but on downstream tasks by introducing a simple header on top of the learned representation. Through experiments on two image tasks, they find that (1) representations from layers before or after the model bottleneck result in better compositional generalization (4.1); (2) previously proposed compositionality or disentanglement metrics do not always correlate with better performance (4.2); (3) EL appears to be more powerful than disentanglement models in such generalization (4.3). An ablation study follows to confirm the function of EL (e.g., hyperparameters).", "questions": "1). In addition to the explored factors on lines 88-90, varying the model structure as the backbone of both encoder and decoder is needed.\n\n2). Can EL predicts correctly for failed cases of disentanglement models, or the opposite?\n\n3). Is there a case that leads to higher compositionality metrics but lower compositionality?\n\n4). Other than dSprites and MPI3D-Real, I'm curious about whether the same findings can be observed from any application tasks.\n", "limitations": "I did not see a discussion regarding the limitations.", "rating": 5, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:1). This paper focuses on the valuable problem of systematic generalization (i.e., generalization from learned concepts to unseen compositions) that plays a crucial role in improving the generalization of models and the following interpretation. 2). The work is well-motivated and focuses on compositional representation learning. The introduced evaluation protocol sounds reasonable and may be helpful for the followers to refer to. 3). The experimental results on two benchmarks are encouraging and supported by a further ablation study. The findings may benefit the usage of learned representations and distinguish the advance of EL over disentanglement models in compositional generalization.\n\nWeaknesses:1). Technically speaking, the contribution of this work is incremental. As an analysis paper, its technique depth is shallow. 2). The reported experimental results appear to evidence the findings, while the encoder and decoder are fixed. More model structures. (e.g., transformers) should be taken into consideration to support the findings. 3). The work ends with the ablation study on EL; however, more studies and case analysis are necessary to underline the difference between the two learning methods (e.g., a failed case of disentanglement models but correctly inferred by EL).", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "HNPsC5B6Ivp", "reviewer": "Reviewer_KMyy", "summary": "**Main goal:** Come up with an evaluation methodology to evaluate compositional generalization (how consistently object attributes are expressed in representations obtained from test data) and use it to evaluate disentanglement and emergent language techniques to obtain insights about the representations that get learned. \n\n**Summary of the proposed evaluation pipeline for measuring compositional generalization:**\n  1. Use the training set to learn representations in an unsupervised manner (using e.g. variation methods, or emergent language teqhniques)\n  2. Using a small portion of the training data annotated with object attributes, train a simple (e.g. linear) probe to extract the attributes from the representations. \n  3. Check if the probe still works on unseen data. \n\n**Findings:**\n* If one commits to a linear probe to measure compositional generalization, then using bottleneck representations doesn't yield the best generalization results - using the layer before and after work better. \n* Emergent language models yield better compositional generalization (when one uses a linear probe). \n* Compositional generalization doesn't correlate well with other metrics that quantify disentanglement. \n\n\n################\n\n**Post rebuttal update** I thank the authors for their response. I've increased my score.\n\n################", "questions": "* Learning the linear probe from limited training labels: I don't quite understand why one would use a limited number of training examples so train the probe. Isn't higher == better, as long as we don't mix test data? \n* Line 52: Could you provide citations for the claim that today's SOTA unsupervised disentanglement models are built on top of variational generative models? \n* Could you discuss the results you obtain with gradient boosted trees a bit more? Do they agree with what you get with a linear probe? What are the main disagreements? ", "limitations": "A central limitation of the submission is that the proposed compositional generalization strategy isn't validation to fully capture compositional generalization. While high scores likely indicate strong compositional generalization, it's not clear whether low scores indicate lack of it. The paper would likely be stronger with sanity check experiments to validate the proposed eval methodology.", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "STRENGTHS\n**Interesting research direction:** Trying to directly measure compositional generalization is interesting - usually this skill is presumed in downstream evaluations. Coming up with a robust way of measuring this would be quite valuable. \n**Useful signal for designing better techniques/algorithms:** As long as the proposed evaluation strategy is validated to genuinely capture compositional generalization, it can be a very useful tool in algorithm design by providing quantitative feedback. \n\nWEAKNESSES\n**Limitations of linear separability as a measure of compositionality:** Linear separability of object attributes (i.e. the crux of the proposed evaluation scheme) might not be the best way to capture how \"compositional\" a given representation is. It is perhaps not surprising that the bottleneck representations perform worse at this: representations in higher dimensions are easier to separate. I understand that the proposed metric measures more than just separability by evaluating the learned probe on a held-out test set. However, since linear separability is a necessary condition for this type of probe to generalize in the first place, I fear the conclusions drawn from this evaluation methodology might be a bit misleading. \n**Affect of the probe model on results** This is a slightly general comment than the above one: how can we disentangle the inaccuracies caused by the probe itself form actual compositional generalization? This seems crucial to discuss here. \n  * (Sanity check experiment) For example, if one generated a dataset of perfectly disentangled representations (not necessarily linearly separable) and used the proposed evaluation pipeline, would the proposed metric identify these representations as having 'high compositionality'? Having a sanity check experiment like this to test the proposed evaluation metric seems important. \n  * (Another sanity check experiment) Another useful sanity check experiment could be checking how well the trained downstream probe works \"in-distribution\". That is, train the downstream probe with, say half the training data and evaluate it on the other half of the training data (not the test data). Does the probe generalize then? Are the results qualitatively different than if you evaluate on the unseen test set? \n**Narrow evaluation:** It'd be interesting to see if the current takeaways hold for other types of models and datasets. For example, how about the Slot Attention model (https://arxiv.org/abs/2006.15055), on the CLEVR dataset? \n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "CMXxIvO-07", "reviewer": "Reviewer_JnAD", "summary": "In this paper, the authors study the compositional generalization ability, i.e. unseen feature combination of elementary combinations, of beta-(TC)VAE and emergent language with Gumbel-softmax training. Both of the methods have been argued for their ability to disentangle features in the representation. However, the results on the two image datasets the authors did experiments on showed that the latent representations learned by beta-(TC)VAE do not generalize well and existing metrics show a different trend than their proposed metric, while emergent language is better and allowing flexible length and stochastic sampling are essential to the better performance. ", "questions": "Have you done any study on the relationship between message lengths of instances and instance novelty? It would be very interesting to see the characteristics of language use. For example, for more novel combinations (less maximum overlap with training instances) maybe longer sequences should be used to describe. ", "limitations": "Yes. The authors didn't discuss any negative societal impact, but I don't think there's any major negative societal impact in this paper that should be addressed. ", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n\n1. It is interesting to see that despite being argued for strong disentanglement, beta-VAEs still cannot generalize well compositionally with the heuristic regularizations. Pointing out the discrepancy between these two metrics is essential for researchers to understand the capability of these latent variable models.\n2. It is also interesting to see that using flexible length discrete channel works better than the continuous channel. \n\nWeaknesses:\n\nI think the major weakness is the lack of discussion about evaluating compositional representation. Previous work, e.g. [1], has studied the latent structure of representations and methods to evaluate the compositional structure of them through simple compositional networks. I think this paper is in spirit similar to [1], and the difference and similarity should be addressed. \n\n[1] Measuring compositionality in representation learning. 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Author rebuttal:

Decision: Accept