Source-linked AI summary
Compositionality and Generalization in Emergent Languages
Rahma Chaabouni, Eugene Kharitonov, Diane Bouchacourt, Emmanuel Dupoux, Marco Baroni
TL;DR
The paper investigates whether emergent languages can refer to novel composite concepts and whether they do so through compositional strategies resembling human language. Using disentanglement-inspired measures, it finds that large input spaces promote generalization, compositionality is not required for it, and compositional languages are easier for new agents to learn and transmit.
Problem
The paper asks whether emergent communication codes can refer to novel composite concepts and whether this ability relies on human-like compositionality.
Method
The authors introduce disentanglement-inspired measures of order-dependent and order-independent compositionality for emergent languages.
Results
Sufficiently large input spaces produce generalizing languages, but compositionality does not correlate with generalization, while compositional languages are easier for new agents to learn.
Takeaways & Limitations
Compositionality is not necessary for generalization, but languages that develop it are more likely to be learned and transmitted across agents, including agents with different architectures.
Takeaways & Limitations
The authors caution that conclusions about generalization should be replicated under different conditions and that small input environments can misrepresent neural networks’ abilities.
Abstract
from arXiv · showhide
Natural language allows us to refer to novel composite concepts by combining expressions denoting their parts according to systematic rules, a property known as \emph{compositionality}. In this paper, we study whether the language emerging in deep multi-agent simulations possesses a similar ability to refer to novel primitive combinations, and whether it accomplishes this feat by strategies akin to human-language compositionality. Equipped with new ways to measure compositionality in emergent languages inspired by disentanglement in representation learning, we establish three main results. First, given sufficiently large input spaces, the emergent language will naturally develop the ability to refer to novel composite concepts. Second, there is no correlation between the degree of compositionality of an emergent language and its ability to generalize. Third, while compositionality is not necessary for generalization, it provides an advantage in terms of language transmission: The more compositional a language is, the more easily it will be picked up by new learners, even when the latter differ in architecture from the original agents. We conclude that compositionality does not arise from simple generalization pressure, but if an emergent language does chance upon it, it will be more likely to survive and thrive.
1 Introduction
The paper asks whether emergent languages can refer to novel composite concepts compositionally and develops measures suited to unknown, graded forms of composition. It finds that large input spaces promote generalization, but compositionality and generalization are not correlated, while compositionality improves language transmission.
- Compositionality lets language systematically combine expressions for parts to refer to novel composite concepts.
- Existing generalization-based measures reveal whether unseen composites are handled correctly, but not how that ability arises.
- Topographic similarity is more informative than generalization but remains agnostic about the underlying type of composition.
- The paper introduces disentanglement-inspired measures for order-dependent and order-independent compositional strategies.These strategies assess whether symbols or symbol-position pairs independently refer to primitive meanings.
- Sufficiently large input spaces yield generalizing emergent languages, yet compositionality does not correlate with generalization.Compositionality is nevertheless associated with easier learning by new agents, including agents with different architectures.
2 Setup
The study uses a reconstruction signaling game in which a sender encodes composite attribute inputs and a receiver reconstructs them from fixed-length messages. Experiments vary attribute dimensions, value counts, channel capacity, recurrent agents, and training procedures.
- A sender receives an input and emits a fixed-length symbol sequence, while a receiver uses that message to reconstruct the input.Success occurs when the receiver’s reconstructed input equals the sender’s input.
- Each input concatenates 2–4 attributes, each taking 4–100 possible values, creating composite input spaces.Attributes are represented as one-hot vectors and can describe object properties such as color and shape.
- The sender’s channel has enough capacity to express the entire input space, with vocabulary sizes of 5, 10, 50, or 100 and message lengths of 3, 4, 6, or 8.
- Both agents use single-layer GRU cells with 500-dimensional hidden states, and the sender generates messages symbol by symbol.At test time, symbols are selected greedily rather than sampled.
- The receiver predicts one probability vector per attribute, and training uses average cross-entropy with a hybrid backpropagation and REINFORCE procedure.The hybrid procedure is chosen for more robust convergence, with standard variance-reduction tricks.
3 Measurements
The paper measures compositionality with topographic similarity and two disentanglement metrics, then evaluates generalization on held-out attribute combinations. The measures target different structural properties and are only moderately related.
- Topographic similarity: Topographic similarity is the Spearman correlation between pairwise input distances and message edit distances.It detects whether similar meanings have similar forms but is agnostic to the specific compositional mechanism.
- Disentanglement measures: Positional disentanglement measures whether symbols in particular positions univocally refer to values of specific attributes.It uses mutual information and does not require preidentifying which positions encode each attribute.
- Disentanglement measures: Bag-of-symbols disentanglement measures whether symbols independently refer to meanings when symbol order is irrelevant.It captures permutation-invariant languages using symbol counts rather than positions.
- Metric comparison: The three metrics have Spearman correlations of 0.08 for topsim/posdis, 0.38 for topsim/bosdis, and 0.31 for posdis/bosdis.All correlations are statistically significant at p < 0.01.
- Generalization: Generalization is measured by test accuracy on inputs whose attribute combinations were withheld from training.The split uses 90% training and 10% test items, and only converged runs above 99.9% training accuracy are evaluated.
4 Generalization emerges “naturally” if the input space is large
Emergent languages almost perfectly generalize to unseen combinations when the input space is sufficiently large, regardless of whether size grows through more attributes or values. Larger, varied input spaces and adequate channel capacity support convergence and near-perfect accuracy.
- ρ = 0.86 (p ≈0) between input size |I| and test accuracy, with almost perfect generalization at sufficiently large |I|.The result is robust to how input size is increased and to agent-capacity variations.
- Changing the number of attributes or values to obtain the same |I| does not significantly affect accuracy.Bracketed settings with the same input size show no significant difference under t-tests with p > 0.01.
- Training data supports generalization when attribute values occur with a large range of values from other attributes, signaling composite inputs.The effect persists when the number of distinct training examples is fixed but combinatorial variety changes.
- Small input environments can understate generalization because agents may develop ad-hoc strategies that overfit training data.The paper recommends repeating such experiments with much larger and more varied input spaces before attributing failures to architectures or training methods.
- For configurations with |I| ≥625, converging runs require an average minimum channel-capacity ratio |C|/|I| of 5.9 (s.d.: 4.4).Successful languages are therefore not as compact as a minimal fully compositional solution, and |C| must exceed a large threshold for near-perfect accuracy.
5 Generalization does not require compositionality
Generalization to unseen composite inputs does not require compositional language structure: highly accurate runs span widely varying compositionality scores. Compositionality may help generalization, but it is not necessary for it.
- Significant correlations between test accuracy and compositionality occurred in only 4 of 141 settings.The analysis computed Spearman correlations separately across converging runs for each configuration and metric.
- At test accuracy above 98%, posdis ranged from 0.02 to 0.72, bosdis from 0.03 to 0.4, and topsim from 0.11 to 0.64.Thus, languages with very different compositionality scores can communicate new attribute combinations accurately.
- Highly compositional languages never occupied the low-accuracy top-left quadrant of the compositionality-versus-generalization plots.Among languages with metric values above 0.5, the proportion reaching test accuracy above 0.80 was 0.90 for posdis, 0.50 for bosdis, and 0.11 for topsim.
- A near-perfect language with accuracy above 99% used a medium posdis score of 0.70 rather than the theoretical maximum of 1.Its three-position code assigned positions 2 and 3 primarily to attributes 2 and 1, while position 1 supplied complementary information.
- Preserving position 2 alone predicted most att2 values, while preserving position 3 alone predicted almost 90% of att1 values.Preserving position 1 alone failed for both attributes, but position 1 combined with either position 2 or 3 yielded 100% accuracy for the corresponding attribute.
- The analyzed language used positional specialization with complementary ambiguity rather than a perfectly one-to-one symbol-to-attribute code.Positions 2 and 3 used 96 and 98 symbols respectively, below the 100 symbols required for perfect one-to-one strategies; position 1 disambiguated them.
6 Compositionality and ease of transmission
Although generalization pressure alone does not produce compositionality, compositional languages are easier for new agents to learn. This transmission advantage persists across receiver architectures of different complexity.
- The study extends an established language-transmission result from hand-crafted languages to spontaneously emerging languages.The experiments selected highly generalizing sender-receiver pairs, retrained new receivers three times per game, and measured test accuracy and learning speed.
- The transmission test used GRU receivers with hidden sizes 500 and 50, plus a two-layer feed-forward network with hidden size 500.This design probes language transmission across models with different complexity.
- New Receivers trained from scratch showed strong positive correlations between compositionality and both learning speed and generalization accuracy.The experiments froze the Sender and varied the newly trained Receiver’s architecture and random initialization.
- Correlations reached almost 0.90 for learning speed and 0.80 for generalization in new Receivers.These results support the hypothesis that compositional emergent languages are simpler for new agents to understand.
7 Discussion
The discussion argues that richer input environments promote generalization, but generalization can arise without compositionality. Compositionality instead helps emergent languages transmit to new learners and architectures, although the proposed measures often resemble topographic similarity.
- The natural emergence of generalization: Generalization strongly correlates with input-environment variety, cautioning against judging neural networks from small, carefully constructed input pools.The authors state that this result should be replicated under different conditions.
- Generalization without compositionality: There is virtually no correlation between generalization to novel composite inputs and compositionality in emergent messages.Some systems generalize without being compositional according to the paper’s intuitive measures.
- Compositionality and disentanglement: The paper connects its compositionality measures to disentanglement in representation learning, but they usually do not behave significantly differently from topographic similarity.The authors present this similarity as a sanity check and as a limitation of the new measures.
- What is compositionality good for?: Positional disentanglement is sufficient but not necessary for generalization, whereas less informative topographic similarity provides no such guarantee.Bag-of-symbols disentanglement is associated with generalization to a lesser extent.
- Compositionality and disentanglement: The authors suggest adapting disentangled-representation methods to encourage more compositional emergent languages.This is presented as future work rather than an established result.
8 Supplementary material
The supplementary material describes the explored input and message-space settings and reports constraints on emergent compositional languages. It also uses miniature languages to show that the proposed compositionality metrics distinguish different structural properties.
- Experimental settings: The experiments require |C| ≥ |I| so agents have enough distinct messages to refer to all inputs.The study also samples settings with comparable numbers of configurations and sufficiently large message spaces.
- Experimental settings: Unless explicitly stated otherwise, each experimental setting uses 10 different initializations.
- Experimental results: For large |I|, GRU agents need |C| strictly larger than |I|, suggesting perfectly nonambiguous compositional languages may be impossible there.The proposed perfectly nonambiguous language would map each message symbol to one attribute value and each attribute value to one message symbol.
- Metric illustrations: The miniature-language analysis fixes iatt = 2, ival = 4, clen = 3, and cvoc = 8, with bijective input-message mappings.Lang1, Lang2, and Lang3 are used to illustrate different metric behaviors.
- Metric illustrations: Lang1 is perfectly positional-disentangled with posdis=1, although topographic similarity is below 1 because two symbols encode one attribute.This shows that topographic similarity penalizes the absence of a one-to-one attribute-position mapping.
- Metric illustrations: Lang2 and Lang3 have equal topographic similarity but differ in compositional structure: Lang2 is more positional-disentangled, whereas Lang3 is perfectly bag-of-symbols-disentangled.
8.3 Generalization for different agents’ capacity
Generalization depends on the size and combinatorial variety of the input space, rather than simply on agent capacity or the number of training examples.
- Capacity and input size: Larger input spaces support generalization, whereas agents trained on small spaces do not generalize reliably.The experiments compare (iatt=2, ival=10) with (iatt=2, ival=100) across different GRU capacities.
- Capacity and input size: Changing GRU capacity does not eliminate the contrast between small and large input spaces.The reported capacity experiments include differently sized GRU agents, with comparable results replicated using differently sized LSTMs.
- Input-space density: 92.7%, 66.7% and 22.8% test accuracy were obtained at input densities 1, 0.51 and 0.25, respectively.All conditions used 10000 sampled points, 90% for training and 10% for testing, while ensuring every attribute value appeared during training.
- Input-space density: Generalization therefore reflects input density and combinatorial variety, not only the number of training examples.Lower density leaves fewer combinations represented despite the same number of sampled instances.
8.5 Impact of channel capacity on generalization
Channel capacity has little aggregate effect on generalization, but sufficiently large input spaces require capacity above a threshold for near-perfect performance.
- Aggregate effect: ρ = 0.14: Aggregating across input sizes, channel capacity has only a small effect on generalization.The relationship is reported using a Spearman correlation across the tested settings.
- Capacity threshold: For large |I|, agents need |C| > |I| to achieve almost perfect generalization.The threshold appears when studying settings in which generalization is observed.
- Capacity threshold: Having |C| >> |I| does not harm generalization.This contradicts earlier claims that excessive channel capacity could impair generalization.
- Compositionality measures: topsim and bosdis show clear negative correlations with |C|, despite the expectation that compositionality measures should be channel-independent.The passage presents this as a concern about interpreting these measures across channel capacities.
8.7 Analysis of example medium- and low-posdis languages
The medium-posdis and low-posdis languages both use positional information, but the medium-posdis language is more disentangled and more robust to some ablations.
- Language comparison: Both languages achieve excellent generalization, while low-posdis has very low posdis of 0.05.The languages arise from a setting with two 100-valued attributes and three 100-symbol message positions.
- Mutual information: The low-posdis language has an almost uniform mutual-information profile, indicating highly entangled information across positions and attributes.The corresponding mutual-information values are summarized in Table 5.
- Vocabulary usage: Medium-posdis uses 91, 96 and 98 symbols across positions, while low-posdis uses 99, 99 and 100.Both languages use most of the available 100-symbol vocabulary, but medium-posdis is slightly more parsimonious.
- Ablation studies: Ablating untouched positions can preserve partial information for medium-posdis, whereas virtually any ablation strongly affects low-posdis accuracy.Shuffling positions damages both languages, showing that both exploit positional information.
8.8 Effect of channel capacity on ease of transmission
More compositional emergent languages are generally easier for new receivers to learn, with the transmission advantage varying across channel capacities and receiver architectures.
- Transmission: Retraining performance and compositionality measures show significantly positive correlations in most channel-capacity conditions.Table 7 measures new Receiver Learning Speed and Generalization for (iatt=2, ival=100).
- Transmission: The correlation is higher for larger Receivers and for languages with shorter messages.Shorter messages correspond to smaller clen.
- Transmission measures: Across the reported measures, posdis has corr=-0.094, topsim has corr=-0.208, and bosdis has corr=-0.574 in the shown channel-capacity condition.The displayed correlations are associated with the reported transmission analysis.