Speaking Your Language: Spatial Relationships in Interpretable Emergent Communication
Authors: Olaf Lipinski
Adam Sobey
Federico Cerutti
Timothy J. Norman
Venue: NeurIPS 2024 poster (2024)
Keywords: Emergent Communication
Spatial References
Spatial Deixis
NPMI
NLP
Primary area: reinforcement_learning

Abstract: Effective communication requires the ability to refer to specific parts of an observation in relation to others. While emergent communication literature shows success in developing various language properties, no research has shown the emergence of such positional references. This paper demonstrates how agents can communicate about spatial relationships within their observations. The results indicate that agents can develop a language capable of expressing the relationships between parts of their observation, achieving over 90% accuracy when trained in a referential game which requires such communication. Using a collocation measure, we demonstrate how the agents create such references. This analysis suggests that agents use a mixture of non-compositional and compositional messages to convey spatial relationships. We also show that the emergent language is interpretable by humans. The translation accuracy is tested by communicating with the receiver agent, where the receiver achieves over 78% accuracy using parts of this lexicon, confirming that the interpretation of the emergent language was successful.

Speaking Your Language: Spatial Relationships in Interpretable Emergent Communication
Olaf Lipinski!" Adam J. Sobey2:1 Federico Cerutti
Timothy J. Norman' University of Brescia
University of Southampton "The Alan Turing Institute
(o ho.lipinski,tt t. j.rmmmaann)) norman)@sotoon ac. uk asobey@turing ac. uk federico cer.rctiirruttiiiibeee... it
Abstract
Effective communication requires the ability to refer to specific parts of an ob- servation in relation others. While emergent communication literature shows success in developing various language properties, no research has shown the emergence of such positional references. This paper demonstrates how agents communicate about spatial relationships within their observations. The results indicate that agents between parts of their observation, achieving over 90% accuracy when trained in a referential game which requires such communication. Using a collocation measure, we demonstrate how the agents create such references. This analysis suggests that agents use a mixture non-compositional and compositional messages to convey spatial relationships. We also show that the emergent language is interpretable by humans. The translation accuracy tested by communicating with the receiver agent, where the receiver achieves over 78% accuracy using parts of this lexicon, confirming that the interpretation of the emergent language was successful.
develop a language capable of expressing the relationships
1 Spatial referencing in emergent communication
Emergent communication allows agents to develop bespoke languages for their environment. While there are many successful examples of efficient (Rita al. 2020) and compositional (Chaabouni et al. 2020) languages. they often lack fundamental aspects seen in human language, such as syntax (Lazaridou and Baroni 2020) recursion (Baroni 2020). It is argued that these aspects of communication are important to improve the efficiency and generalisability of emergent languages (Baroni 2020 Boldt and Mortensen 2024 Rita et al. 2024). However, the current architectures, environments, and reward schemes are yet to exhibit such fundamental properties.
One such aspect is the development of deixis (Rita al. 2024), which has been described way of pointing through language. Examples of temporal deixis include words such as "yesterday" or "before." and spatial deixis include words such "here" "next to" (Lyons 1977). In emergent communication, Lipinski et al. (2023) investigate how agents may refer to repeating observations, which could also be viewed from the linguistic perspective investigating temporal deixis. However, while there are advocates to investigate how emergent languages can develop key concepts from human language (Rita et 2024), no work has demonstrated the emergence of relative references to specific locations within an observation, or spatial deixis.
Spatial references would be valuable in establishing shared context between agents, increasing munication efficiency by reducing the need for detailed descriptions, and adaptability, by removing the need for unique references per object. For example, instead of describing new, previously
Corresponding author: o. w.Iippnnkk1sstoon..cc uc.uk
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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unseen object, such as "a blue vase with intricate motifs on the table," one could simply use spatial relationships and say "the object left of the plate." Spatial referencing streamlines communication by leveraging the shared environment as reference point. In dynamic environments where objects might change positions, spatial references enable agents to easily track and refer to objects without having to update their descriptions. This enhances communication efficiency and improves interaction and collaboration between agents. These elements may also help the evolved language become human interpretable. allowing the development of trustworthy emergent communication (Lazaridou and Baroni 2020; Mu and Goodman [202T).
This paper therefore explores how agents can develop communication with spatial references. While Rita et al. (2024) posit that the emergence of these references might require complex settings, we show that even agents trained in a modified version of the simple referential game (Lazaridou et al. 2018 Lewis. 1969) can develop spatial references F]] This resulting language is segmented and analysed using collocation measure, Normalised Pointwise Mutual Information (NPMI) adapted from computational linguisties. NPMI allows us to measure the strength of associations between message parts and their context, making it valuable tool for gaining insights into the underlying structure of the emergent language. Using NPMI, we show how the agents compose such spatial references, providing the first hint of syntactic structure, and showing that the emergent language can be interpreted by humans.
Development of a spatial referential game
Current emergent communication environments have not produced languages incorporating spatial references. To address this, we present a referential game (Lazaridou et al., 2018) environment where an effective language requires communication about spatial relationships.
2.1 Referential game environment
In the referential game, there are two agents, a sender and a receiver. The sender observes a vector and transmits its compressed representation through discrete channel to the receiver. The receiver observes a set of vectors and the sender's 's message. One of these vectors is the same as the one the sender has observed. The receiver's 's goal is to correctly identify the vector the sender has described, among other vectors referred to as distractors. The simplicity of the referential games enables the reduction of extraneous factors which could impact the emergence of spatial references, such as transfer learning of the vision network or exploring action spaces in more complex environments.
In this work, the sender's 's input is an observation in the form of vector Vo E (, ... 59]. The vector o always composed of integers. The observation includes a -1 in only one position, e.g., O3 -1 for o [r, x, -1, xz ær. to indicate the target integer for the receiver to identify. o represents a window into a longer sequence 8, which is randomly generated 59}
[01, O2, 03, 04, 05). where
using the integers (0. 59) without repetitions. This sequence is visible to the receiver, but not to the sender. As the target's 's position in the sequence is unknown to the sender, it has to rely on the relative positional information present in its observation, necessitating the use of spatial referencing.
Due to the window into the sequence being of length 5, is necessary to shift the window when approaches either extent of the sequence. The window is then shifted to the other side, maintaining the size of 5. For example, given a short sequence = [,,5,2 2, 12, 10, 4, 3, 15, 16, 13, 14, 6, 9, 8, 11, if the selected target is 1, since there are no integers to the right of 1 the vector o would be o [6, 9, 8, 11, -1] where is shifted to the left as it approaches this rightmost extent of the sequence.
Due to the necessity of maintaining the window size, some observations provide additional positional information to the sender agent. Given the same example sequence 8, we can categorise all obser- vations into 5 types. The begin and begin+l, 1, where the target integer is either at. or one after, the beginning of the sequence, i.e.. o = [-1, 1, 5, 2, 12, 10] or o = [7, 11, 2, 12, 10). The end and end-1, where the target integer is either at, or one before, the end of the sequence, i.e.. = [6, 8, 11. -1] or o [6, 9, 8, 11, 1). The most common case is the middle observation, where the target integer is anywhere in the sequence, excluding the first, second, second to last, and last positions, e.g., = [12, 10,- 3, 15). Given window of length 5, only 4 specific target integer positions per sequence can result in the other observations (begin, begin+ 1, end-1, and end). All other target
"Our code is available GitHub at aatagss//gghhu..cooooopnss//t//s

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integer positions within the sequence fall into the middle category, as they do not occupy the first, second, second last, or last positions. Consequently, the majority of the target integer positions result in middle type observation.
The sender's output is message defined vector m [m,, m2, ma). where m E {1... 26). 26 is chosen to allow for high degree of expressivity, with the agents being able to use over 17k different messages, while also matching the size of the Latin alphabet. Since such a vocabulary size is enough to convey any information in natural languages like English, we consider that this should also apply the agents. The vector m is always composed of 3 integers.
The receiver's input is an observation consisting of three vectors: the sender's message m, the sequence 8, and the set of distractor integers together with the target integer td. The distractor integers are randomly generated, without repetitions, given the same range of integers as the original sequence 8, i.., {0... 59), excluding the target object itself. Given environment with 3 distractors, td could be [d1, f, d2, da), where t is the target object and d1, d2, d3 are distractor objects. The position of the target object in td is randomised.
For example, given the sequence 8 = 7,5, 2, 12, 10, 4, 3, 15, 16, 13, 6,,6,9,8, 11, 11. and the sender's observation
[4, 1, 16, 13). the vector ld could be td [7. 15, 11,9). with 15 being the target that the receiver needs to identify. The sender could produce a message m [3, 1, 1], which would mean that the target integer is after the integer 3. This message would then be passed to the receiver, together with 8 and td. The receiver would then have to correctly understand the message (i.e., that the target is after 3) and find the integer 3 together with the following integer in the sequence 8. Having identified the target 15 given the message m and the sequence 8, it would output the correct position of this target in the td vector, i..,, 2, since tdz 15.
2.2 Spatial reference formalisation
To provide generalisation of our results, we formalise what we refer to spatio-temporal references. Let O represent an abstract observation that an agent perceives from its environment, 0 R", where m represents the dimensions of the observation. For 3D observation, m could be = j x & x d. matrix of d = values, which, for example, could be an RGB
Such an m could represent a j picture, with j x k pixels and one value for each of the RGB colours (d = 3). The m dimensions can represent the spatial, temporal, or other positions.
Let Op and O₂ be the coordinates of some elements in O, represented by an m-tuple of natural numbers (11, (g...Fmm and (3/1 U2- respectively. Op represents the reference point and O represents a target point.
Then, the relative distance function d(Op, O,) returns m-tuple of integers (21, 2m ). such that x x4 - yi- This relative distance function allows for unambiguous identification of the target object Oz, given that the position of Op is known.
We define the spatio-temporall referent expression as mapping of the value of d(Op, Oz), the reference point Op. and their context O, to specific linguistic symbolic phrase that describes the relationship between Op and O,, This mapping can be represented as:
(O, (O,((OpOO,). Op) Phrase(O, O,),
where the resulting expression Phrase d d(Op. Oz), 0p) is description of the reference point Op and its relative distances to the target point O,, given the context O.
The version of spatial referencing in our environment is specific case of the general spatial reference formalisation, where the observation O is represented as dimeesnnsional tensor, and the target point O is always indicated by the value -1 within the tensor. The sender's 's task is to describe the relative position of the target O within this sequence, using message that effectively communicates the spatial relationship between chosen O, and the target O,,
3 Agent Architecture
The agent architecture follows that of the most commonly used EGG agents (Kharitonov et al. 2019). This architecture is used to maintain consistency with the common approaches in emergent
communication research (Chaabouni et al. 2019 2020 Kharitonov et al. 2019 Lipinski et al. 2023
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Sequence Window [122-1.4.5]
Final hidden states, for each element the sequence
Target and Distractors [5,10.7.3]
Full sequence (12.3.4..66.88...0
Sequence of Character Probabilties
GRU
Intial Hidden State GRU
Repeat until max len reached
Object Embedding Linear
GRU 2 (Combine)
GRU
Message Gemeration
Hidden to Vocab Linear
Softma-Softmax
Objeett Embedded
Final hidden element in the sequence
Embedding from Linear
Halaen
Matrix Mulliply torch.matmul
Integer Guess
Sequence Characler Probabilties
(a)
The sender architecture.
(h) The receiver architecture.
Figure 1: The sender and receiver architectures. Adapted from (Lipinski et al. 2023)
increasing the generalization of the results presented in this work. All environmental observations, i.e., O, 8, and td, are passed in as sealars, as one-hot encoding of the observation vectors leads to agents memorising the dataset.
Ueda and Washio 2021
The sender agent, shown in Figure Ia receives a single input, the vector o, which is passed through the first GRU of the sender. The resulting hidden state is used as the initial hidden state for the message generation GRU (Cho et al. 2014). The message generation GRU is used to produce the message, character by character, using the GumbellSofftaa reparametrization trick (Jang et al. 2017) Kharitonov et al.] 2019 Mordatch and Abbeel 2018). The sequence of character probabilities generated from the sender is used to output the message m..
is input to the receiver agent, shown in Figure Tb. together with the full sequence and the target and distractors td. The message is processed by the first receiver GRU, which produces a hidden state used the initial hidden state for the GRU processing the sequence s. This is the only change from the standard EGG architecture (Kharitonov et al. 2019). This additional GRU allows the receiver agent process the additional input sequence s, using the information contained within the message m. The goal of this GRU is to use the information provided by the sender to correctly identify which integer from the sequence s the target integer. The final hidden state from the additional GRU is multiplied with an embedding of the targets and distractors, to output the receiver's prediction. This prediction is in the form of the index of the target within td.
Following the commonly used approach (Kharitonov et al. 2019 agent optimisation is performed using the Humbel-Softman reparametrization (Jang al. 2017 Mordatch and Abbeel 2018). allowing for direct gradient flow through the discrete channel. The agents" loss is computed by applying the cross entropy loss, using the receiver target prediction and the true target label. The resulting gradients are passed to the Adam optimiser and backpropagated through the network. Detailed training hyperparameters are provided in Appendix A
4 Message interpretability and analysis using NPMI
To analyse spatial references in emergent language, a way to identify their presence is essential. In discrete emergent languages, interpretation typically done by either using dataset labels in natural language (Dessi et al.) 2021). by qualitative analysis of specific messages (Havrylov and Titov 2017). However, both of these techniques require message-meaningg pairs, and so neither would be able to identify the presence of spatial references, as the labels for spatial relationships that the agents refer to would not necessarily be available. One approach that could overcome this problem is emergent language segmentation using Harris' Articulation Scheme, recently employed by Ueda al. (2023). [eda et al. (2023) compute the conditional entropy of each character in the emergent language, segmenting the messages where the conditional entropy increases. However,

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even after language segmentation, there is no easy way to interpret the segments, as no method has been proposed to map them to specific meanings.
We present an approach to both segment the emergent language and map the segments to their meanings. We use collocation measure called Normalised Pointwise Mutual Information (NPMI) (Bouma 2009), often used in computational linguistics (Lim and Lauw] 2024, Thielmann et al. 2024 Yamaki al. ).23). is used to determine which messages are used for which observations
and to analyse how the messages are composed, including whether they are trivially compositional
(Korbak et al. 2020 Perkins 202T Steinert- Threlkeld, 2020). By applying a collocation measure to different parts of each message as well as the whole message, we can address the problems of both segmentation and interpretation of the message segments. This approach allows any part of the message to carry a different meaning. For example, if an emergent message contains segments that frequently appear in contexts involving specific integers, NPMI can help identify these segments and their meanings based on their statistical association with those integers.
NPMI is a normalised version of the Pointwise Mutual Information (PMI) (Church and Hanks 1989), which is a measure of association between two events. PMI is widely used in computational linguistics, measure the association between words (Han al. 2013 Paperno and Baroni 2016). Normalising the PMI measure results in its codomain being defined between -1 and I, with indicating a purely negative association (i.e., events never occurring together), 0 indicating no association (i.e., events being independent), and 1 indicating a purely positive association (i.e., events always occurring together). Normalised PMI used for convenience when defining threshold which we consider a message or n n-gram to carry a specific meaning, as the threshold can be between 0 and 1, instead of unbounded numbers in the case of PMI. F
To determine which parts of each message are used for a given meaning, two algorithms are proposed.
1. PMIne The algorithm to measure non-compositional monolithic messages, most often used for target positional information (e.g., begin+/ (Section ); and
2. PMI, the algorithm to measure trivially compositional messages and their n-grams, used to refer to different integers in different positions.
visual representation of the different types of messages that the algorithms can identify is provided in Figure 2 The PMIne algorithm can identify any non-compositional messages, while the PMI, algorithm identifies both position variant and invariant compositional messages. The positional variance of the emergent language means that the position of an 7-gram in the message also carries a part of its meaning. In this work, n--grmm refer to a contiguous sequence of n integers from the sender's 's message. Consequently, in one message there are 3 unigrams (m1, M2, ms),, two bigrams ([m1, m2]. [m2, mal), and one trigram (i.e., the whole message [m], m2, mml)
Figure 2 shows that in the position invariant case, the bigram [5, 6] always carries the meaning of While in the position variant case, the bigram [5, 6] in position 1 of the message means 4, but [5, 6] in position 2 of the message means 8. This can also be interpreted as the position of the bigram containing additional information, meaning a single "word" could be represented as a tuple of the bigram and its position in the message, both contribute to its underlying information. Non-compositional messages are monolithic, i.e., the whole message carries the entire meaning. For example, message [5, 6, 8) means the target is in the first position, while [5, 6, 6 means the target is one to the right of 9, even though the two messages share the bigram [5, 6].
The PMI,e algorithm The PMIne algorithm calculates the NPMI per message by first building a dictionary of all counts of each message being sent, together with an observation that may provide positional information (e.g., begin+/) or refer to an integer in given position (e.g., 1 left of the target). The counts of that message and the counts of the observation, including the integer position, are also collected. For example, consider the observation
[4, 1,, 15, 16, 13]. For the corresponding message m, the counts for each integer each position relative to the target would increase by I (i.e.. fef] 1, [15] also be increased. Given these counts, the algorithm then estimates the probabilities of all respective events (messages, positional observations, and integers in given positions) and calculates the NPMI measure.
etc.). The count for the message signifying begin+/ would
*Our implementation of NPMI is not numerically stable due to probability approximation, sometimes exceeding the [-1,1] co-domain. We provide more details in the code.
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Message
Observation
Compositional Position Invariant
[5. 8]
[4, 8]
[10, 5, 6]
[X. 4,4111 X
[X, 2, -1 X
[ -1, 4, X]
Compositional Position Variant
[5, 8]
[8, 5,
(10, 5, 6]
[X. 4, 4,,1, x,
[X, 8, -1, X, X]
XX, X, -1, 8, X]
Non Non-Compositional
[5, 6, 8]
[5. 6. 6]
[5. 2]
H1, x, X, x
[X. 9, -1, x, x]
[X, -1, X, X
Figure 2: Examples of the different types of message compositionality that are possible to identify using the PMI algorithms.
The PMI, algorithm The PMI, algorithm first creates a dictionary of all possible n- n-grams, given the message space (m) and maximum message length (3). The list of all possible n-grams is pruned to contain only the n-grams present in the agents' language, avoiding unnecessary computation in the later parts of the algorithm. Given the pruned list of n-grams, the algorithm checks the context in which the n-grams have been used. The occurrence of cach n-gram is counted, together with the n-gram position in the messages and the context in which has been sent, or the integers in the observation. The n-gram position in the message is considered to account for the possible position variance of the compositional messages.
Consider the previous example, with o = [4, -1, 15, 16, 13] and a message m = [11, 13, 5]. For all n-grams ([11). [13], [5], [11, 13). etc.) of the message, all integers are counted, irrespective of their positions (i.e., cownt.. [4] 1, counts [05]+s[15]+++ 1,, efc.).
Given these counts, the PMI, algorithm estimates the NPMI measure for all n-grams and all integers in the observations. These probabilities are estimated from the dataset using the count of their respective occurrences divided by the number of all observations/messaees,
Once the NPMI measure is obtained for the n--ram-inneeee pairs, the algorithm calculates the NPMI measure for n-grams and referent positions or the positions of the integer in the observation the message refers to. For example, given an observation an n-gram which has been identified as referring to the integer 15, the rest of the message (i.e., the unigram or bigram, depending on the length the integer n-gram) is counted as a possible reference to that position, in this case, to position right1, or 1 to the right of the target. This procedure follows for all messages, building count for each time an n-gram was used together with a possible n-gram for integer. These counts are used to calculate the NPMI measure for n-gram and position pairs.
[4, -1, 15, 16, 13), if the message contains
The PMI, algorithm also accounts for the possible position invariance of the n-grams, i.e., where in the message the n-gram appears. This is achieved by calculating the respective probabilities regardless of the position of the n-gram in the message, by summing the individual counts for each n-gram position.
Pseudocode We provide condensed pseudocode for both algorithms in Algorithm I In the case of the PMI the n-grams in the pseudocode would be whole messages, i.e., trigrams. This base pseudocode would then be duplicated, interpreting the context either observation that may provide positional information (e.g., begin+ /) or an integer.
For the PMI, algorithm, only the unigrams and bigrams would be evaluated. The base pscudocode would also be duplicated, once for the integer in given position, and second for the referent position. Each would be used as the context in which to evaluate the NPMI for each n-gram. A detailed commented pseudocode for both the PMIne and PMI, algorithms is available in Algorithm 2 and Algorithm 3 in Appendix respectively.
Both algorithms use two hyperparameters: confidence threshold l, and top_n ly. The confidence threshold refers to the value of the NPMI measure at which a message or n--gram can be considered to refer to the given part of the observation unambiguously. To account for polysemy (where one symbol can have multiple meanings), the agents single n-gram to refer to multiple integers.

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Algorithm 1: PMI Algorithm Base
Gather
context_ccontas joint_ n_grams;
for each n-gram y in position p and context e do
P(g.p) = ngram_counts||
total n-grams"
P(c) = context_countete total contexts'
5
P(g.p:c) = joint_ ()] total n grams'
NPMI(g. p; log2 Plg.p.c) P(c) -loga Plg.p.c)*
end
return NPMI;
This is given by the second hyperparameter, top_n, n. which sets the degree of the polysemy, or the number of integers to be considered for given n-gram.
5 Spatial referencing experiments
The agent pairs are trained over 16 different seeds to verify the results" significance. All agent pairs achieve above 98% accuracy on the referential task, showing that the agents develop a way to communicate about spatial relationships in their observations. The analysis provided in this section is based on the messages collected from the test dataset after the training has finished.
The two hyperparameters, te and t, (Section 4. governing the NPMI measure have been determined through a grid search to maximise the understanding of the emergent language, by maximising the translation accuracy. The results in this section are obtained using the hest-performing values for each of the hyperparameters. We provide the values for the grid search Appendix A
5.1 Emergence of non-compositionall spatial references
Using the PM algorithm, detect the emergence of messages tailored convey the positional information contained the observations. As mentioned Section 2 sender observations which require shifting convey additional information about the position of the target within the sequence. In over 90% of agent pairs, these observations are assigned unique messages, used only for each kind of observation, i.e., begin, b end-1 and, end.
In 20% of runs which develop these specialised messages, the same repeating character is used to convey the message. The characters used for these observations reserved only for these kinds of observations. For example, in one of the runs the agents use character 11 to signify the beginning of the sequence, with the character 11 being used only in two contexts: the messages [11, 11, 11 to signify begin, or as message [0, 11, 11] to signify begin+ 1, In other cases, characters are fully reserved for specific messages. e.g., 22 is used only for end, in the message [22, 22, 22].
The emergence non-composiiional references used for other observations also detected using the PM In algorithm. Such messages refer to specific integer in specific position of the sender observation, e.g., 05 10. While we allow for polysemy of the message in our analysis using t [1, 2, 5, 10, 15), observe the highest translation accuracy with t_ indicating that the non-compositional messages do not have any additional meanings.
5.2 Emergence of compositional spatial references
Using the PMIc algorithm, we also detect the emergence of compositional spatial references for 25% of agent pairs. Such messages are composed of two parts, positional reference and an integer reference. The positional reference specifies where a given integer can found in the observation, in relation to the masked target integer 1. The integer reference specifies which integer the positional mean that
reference referring to. For example, one pair of agents has assigned the unigram the target integer is to the right of the given integer, and the bigram [0, 2| to mean the integer 18.
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Table 1: Average emergence and vocabulary coverage of all message types.
Message Type
Avg. % Emergence
Avg. % of Messages
Non-Compe Con-Compositional Positional
99.3% (100%-93.755%
1% (3%-0%%
Non-Comppe Compositional Positional Reserved
18. 75% (18.75%-18.75)
1% (3%-0%)
Non-Comea ConnCompositional Integer
45.1% (100%-0%)
10% (15%-0%)
Compositional Integer
100% (100%-100%)
34% (9977%-0%)
Compositional Positional
25% (27%-0%)
56% (100%-0%)
Together, a message can be composed [7.0. 0, 2), which means that the target integer for the receiver to identify is 2 to the right of the integer 18, i.e., [18, X, -1, X, X]. This allows the sender to identify the target integer exactly, given the sequence 8.
In Table 1 we summarise the emergence of each type of message across all runs, together with the percentage of the vocabulary that they represent. The entries in the table are composed of average percentages, across all in and le choices. In the parentheses, we show the maximum and minimum values across all in and be choices. The average % of emergence represents the absolute % of runs which developed that message type message feature. For all messages, the average % of messages which are of a given type or exhibit a given feature is only counted for in runs where these features emerged.
5.3 Evaluating interpretation validity and accuracy
To ensure the validity of our message analysis, we present two hypotheses which, if supported by the results, would indicate that the mappings generated by the NPMI measure are correct.
Hypothesis (HI) If the correlations exist and do not require non-trivial compositionality (Perkins) 2021p, and are not highly context-depender (Nikolaus) 2023). then the evaluation accu-
racy should be significantly higher than chance, or above 20% when using the identified mappings.
Hypothesis (H2) If the positional components of compositional messages are correctly identified and carry the intended meaning, then their inclusion should result in an increase in accuracy.
Given the messages identified by the NPMI method, we test HI and H2 by using a dictionary of all messages successfully identified, given value of both NPMI hyperparameters i, and 4,- A dataset is generated to contain only targets which can be described with the messages present in the dictionary.
For the non-compositional messages, the dataset is generated by selecting message from the dictionary at random, and creating an observation that can be described with that message. Given non-compositional message that corresponds to the target being on the right of the integer 15, an observation o = [1, 15, -1, 5, 36) would be created. Analogously, for non-compositional positional messages such begin an observation
[-1, 15, 8, 36] would be created.
For the compositional messages, we create the observations by randomly selecting positional component and an integer component from the dictionary. For example, given the unigram 7 meaning that to the left of the target, we could select the bigram [8, 14] corresponding to the integer 30. The observation created could then be [30, 8, 1,, 36, 5). The dataset creation process for the compositional messages also checks the observations can be described given the two n-grams in their required positions within the message.
To test H2, a dataset is created using only the integers that can be described by the dictionaries, randomly selecting integer components from the dictionary, and creating the respective observations. This process also accounts for the required positions of the message components so that a message describing the observation can always be created. For example, if the unigram 9 described the integer 11, and the bigram [5. 1] described the integer 6, corresponding observation could be
[11,6, 6, -1 1, 8, 9. The positions of the integers in the observations are chosen at random. By generating both compositional datasets using stochastic process, we do not assume a specific syntax. Rather, the syntax can only be identified by looking at messages understood by the receiver.
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Table Accuracy improvements using the NPMI-based dictionary, = denotes the 1-sigma standard deviation. Von-Conpositional Positional refers to messages such as begin or end, Non- -on-Coopositional Integer refers to the non-compositional monolithic messages describing both the position and the integer, Compositional-NP refers to messages only containing the identified integer components, and the Compositional-P which refers to messages containing both the identified integer and positional components.
Dict Type
fn
te
Average Accuracy
Maximum Accuracy
Non-C Non-Compositionall Positional 1
0.9
90% +3%
94%
Non-Compositional Integer
1
0.5
36%
+0.4%
37%
Compositional-NP Compositional-P
1
0.5
22% + 2%
28%
1
0.5
30% + 21%
78%
These datasets, together with their respective dictionaries, are then used to query the receiver agent, testing if the messages are identified correctly. We run this test for all of our trained agents, with the dictionaries that were identified for each agent pair. We provide the details in Table 2
Using just the non-compositional positional messages, we observe significant increase in the perfor- mance of the agents, compared to random chance accuracy of 20% %. This proves H1, showing that at least some messages do not require complex functions to be composed, be interpreted. As the accuracy for these messages reaches over 90% on average, we argue that the NPMI method has captured almost all the information transmitted using these messages.
contextual information to
As mentioned in H2, we examine the impact of the positional components and whether they earry the information the NPMI method has identified. We, therefore. separate the compositional anal- ysis into two parts: Compositional-NP, where the positional components are replaced with and Compositional-P, which includes the identified positional components. In the Compositional-NF case, the agents achieve a close to random accuracy, whereas, in the Compositional-P case, agents achieve above random accuracy, with some agent pairs reaching over 75% accuracy. This proves H2 correct, showing that the NPMI method has successfully identified the positional information contained in the messages, together with the integer information.
Discussion
Having successfully verified both H1 and H2, confirmed the validity of the language analysis. We also verify the generalisation ability of the agents, by evaluating varying training and evaluation sequence lengths, vocabulary sizes, and hidden size in Appendix C
To provide human interpretability of the emergent language, we use the NPMI method to create a dictionary providing understanding of both the positional and compositional messages. We present an excerpt from an example dictionary Table 3 With human interpretability, we can gain deeper understanding of the principles underlying the agents' communication protocol.
We posit that the emergence of compositional spatial references points a first emergence of simple syntactic structure in an emergent language. Both of the n-grams in our example from Section 5.2 also shown in Table 3 are assigned specific positions in the message by the agents. The unigram 7 must always be in the first position of the message, while the bigram [0. 2] must always be in the second position. The emergence of this structure shows that even though referential games have been considered obsolete in recent research (Chaabouni et al. 2022; Rita et al.) 22024), careful design of the environment may yet elicit more of the fundamental properties of natural language.
We hypothesise that the emergence of non-compositional spatial references tailored to specific obser- vations, such as begin+ is due observation sparsity: Compositionalitty would bring no benefit since the observations which they describe are usually rare, representing 1-2% of the dataset and are monolithic, i.e., begin, begin+ end-1, 1, and end. We therefore argue that the emergence of non- compositional references in these cases is advantageous, since these messages are easily compress- ible. Since these messages are monolithic, they could be compressed to a single token/character in
t for the referent position n-grams is set 0.3

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simple encoding schemes. In contrast, compositional messages require at least two tokens/characters. one for each integer/positional component. With a linguistic parsimony pressure (Chaabouni et al.) 2019, Rita et al.) 2020) applied, these messages could be more efficient at transmitting the information contained within these observations than compositional ones.
Table 3: Example dictionary of the agents' messages and their meanings
Message
Type
Meaning
[11, 11, 11] 01,
Non- Con-Compositionall
Positional
begin begin+1
Non-Con Compoooooiiii Positional
[10, 10, 10
Non- Non-Coopositionall Positional
end-1
18, 18 18
Non-Compositional Positional
end
12, 16, 14
Non- Non-Compositional Integer
15 is 1 left of target
11, m2, ma]
Compositional Positional
? is 2 left of target
[,, ma
Compositional Positional
? is 2 right of target
m1, 0, 17]
Compositional Integer
Integer
mi, 0, 2]
Compositional Integer
Integer 18
m1,8, 8, 14]
Compositional Integer
Integer 30
7 Limitations
The accuracy for the Con-Coopositional Integer, and Compositional-P messages averages about 33%. While still above random, showing that some meaning captured in non-compositional messages, points to there being more to be understood about these messages. We hypothesise this may be due to the higher degree of message pragmatism, context dependence (Nikolaus) 2023). J Our method of message generation, using randomly selected parts, may not be able to capture the complexity of the messages. For example, the context in which they are used might be crucial for some n-grams, requiring the use of a specific n-gram instead of another when referring to certain integers, or when specific integers are present in the observation. Just like in English, certain verbs are only used with certain nouns, such as "pilot a plane" vs "pilot a car". While the word "pilot" in the broad sense refers to operating a vehicle. is not used with cars specifically. This may also be the case for the emergent language. For compositional messages, an additional issue may be that some messages are non-trivially compositional, using functions apart from simple concatenation to convey compositional meaning (Perkins) 2021). making them impossible to analyse with the NPMI measure. However, these issues may be addressed by scaling the emergent communication experiments as the languages become more general with the increased complexity of their environment (Chaabouni et al. 2022
Conclusion
Recent work in the field of emergent communication has advocated for better alignment of emergent languages with natural language (Boldt and Mortensen] 2024 Rita et al.) 2024). such as through the investigation of deixis (Rita al.) 2024). Aligned this approach, we provide a first reported emergent language containing spatial references [Lyons] 1977). together with a method to interpret the agents' messages in natural language. We show that agents can learn to communicate about spatial relationships with over 90% accuracy. We identify both compositional and non non-compositional spatial referencing, showing that the agents use a mixture of both. We hypothesise why the agents choose non-compositional representations of observation types which are sparse in the dataset, arguing that this behaviour can be used to increase communicative efficiency. We show that, using the NPMI language analysis method, we can create human interpretable dictionary, of the agents' own language. We confirm that our method of language interpretation is accurate, achieving over 94% accuracy for certain dictionaries.
10

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Acknowledgments and Disclosure of Funding
This work was supported by the UK Research and Innovation Centre for Doctoral Training Machine Intelligence for Nano-electronic Devices and Systems [EP/S024298/1].
The authors would like to thank Lloyd's Register Foundation for their support.
The authors acknowledge the use of the IRIDIS high-Performance Computing Facility, and associated support services at the University of Southampton, in the completion of this work.
For the purpose of open access, the authors have applied CC-BY public copyright licence to any Author Accepted Manuscript version arising from this submission.
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A Training Details
The computational resources needed reproduce this work are shown in Table 4 with the hyperpa- rameters in Ta and T The T shows resources required for all training and evaluation. mixture of Intel Xeon Silver 4216s and AMD EPYC 7502s. The GPUs
The processors used used were a mixture of NVIDIA Quadro RTX 8000s, NVIDIA Tesla V100s, and NVIDIA A100s. These nodes used in our experiments were hosted on the IRIDIS cluster. The development process consumed more compute, which we estimate would have added 10 CPU and GPU hours, to account for experimentation.
Table 4: Compute resources
Resource
Value (1 Run)
Value (Training Total)
Value (Evaluation & Analysis)
Nodes
CPU
16 cores
128 cores
cores
GPU
8
Memory
50 GB GB 2 hours
400 GB
120 GB
Storage
32 GB
32 GB
Wall time
240 hours
24 hours
Table 5: Hyperparameters
Parameter
Value
Epochs
1000
Optimizer
Adam
Learning Rate
0.001
Gumbel-Softtax Temperature
[1.0]
Training Dataset Size
200k
Test Dataset Size
20k
No. Distractors
No. Points
[20,40,60, 100]
Message Length
Vocabulary Size
[13,26,52]
Sender Hidden Size
[64,128]
Receiver Hidden Size
[64]
Table 6: PMI Grid Search Parameters
Parameter
Values
[0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9] [1, 2, 3, 5, 10, 15]
bn
B
Dataset Details
To train and evaluate the agents, we use datasets consisting of 200,000 samples for training, 200,000 for validation, and 20,000 for testing. Each dataset generated independently, with sequences created randomly. Given the sequence length of 60 and the fact that no integers are repeated, the number of possible permutations 60! 8 1081, which vastly exceeds the number of samples we generate. We further ensure that there is no overlap between datasets by empirically checking the overlap rates across 1,000 randomly generated datasets, confirming an overlap rate of 0%.
C Generalisation
To generalise the results presented this paper, we also run additional tests, varying the vocabulary size, training sequence length, evaluation sequence length, and the hidden size of the agents, as
13

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outlined in Appendix A We observe no performance decline with either increasing or decreasing the vocabulary size or the training sequence length, given that the agents have enough capacity within their network to still learn the longer sequence lengths. We observe a decline in task accuracy at sequence lengths of 100, when the agents have hidden size 64. However, increasing the hidden size to 128 brings the training and validation accuracy back to over 90%.
When agents evaluated on sequence lengths that are different from the ones they were trained on, we observe small performance decline for small differences in sequence lengths. We present the average accuracies for the base case (Sequence shortened by 0), as well as the average difference in accuracy as compared to the baseline for different sequence lengths in Table 7 significant difference if the agents are evaluated on sequences that over 50% shorter than the ones they were trained on. We hypothesise that this is due to the agents missing certain integers that they used more often than others, therefore reducing their accuracy. However, even the worst case, the accuracy remains above 70%.
We observe
Table 7: Evaluation of different sequence lengths
Training sequence length
Sequence shortened by
-5
-10
-20
-40
20
98.68%
-0.53%
-7.50%
N/A
N/A
40
95.59%
0.05%
-0.75%
-5.55%
N/A
92.98%
0.30%
-0.30%
-2.47%
-15.8%
100
86.23%
0.34%
-0.03%
-1.26%
-5.2%
D Algorithm Descriptions
For pscudocode we will be using the Python assignments convention, i.e., and + equivalent, and x+=1 is equivalent to x +- x ++ The algorithms presented are for top_r = 1. To improve the computational efficiency. the probability of the integer appearing is statically defined 6o for top_n = 1, or in Equation (T) for top_n_ > 1. the case top_n > 1 we use the probability for the integer per Equation [ account for the polysemy. i.e., the probability for any of top integers occurring in the observation. The lower part of the binomial is 4, as there are 4 integers that can be sampled from the 60 possible integers, instead of as exclude the target integer.
(00)
(60 (100-op_x
p(integers)
Additionally, in the PMI. algorithm, we specify probability equal 0.98 Line 74 and Line 77 This is simplification of the calculation for clarity of the pseudocode. This probability is instead obtained using the count of given type of observation, divided by the number total observations. This calculation is performed for each type of observation, i.e., begin, begin+/, end, end-1 and middle. The probability of the middle observation is very close 1, being on average 0.98, while the other probabilities are on average 0.005. Since the middle observation is most common, we included its value in the pseudocode.
14

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Algorithm 2: The PMIne algorithm
Data: 0 M
# All observations together with messages
Data: L len(O_M
Total number of observations with messages # List of positional observations
Data: 5 [begin, begin + 1, end - 1, endd]
Result:
pmine dict;
2 for o, m E $ O_M do
pmine [m] [coutt += 1
Message occurrences
for pos E 5
o pos then pritne pos [cunt|] += 1; pminge m pos] += 1;
# Positional observations count Message sent with positional observation
end
end
10
for integer E do punine mm] (integer_pos) (integer) +=
11
# Message sent with integer given position
12
end
13
end
14
for pos E S do
15
posilzatal = pmmt no 1uss|
Count of positional observations
16
p(pos) positeotal.
Estimate observation probability
17
for m E pm [m]
18
Mittal = prnine [m]] coontt]
Total count of message
19
MStotal = pmi ml [pos]
Total count of message with positional obs # Estimate message probability Estimate joint probability
20
p(m) L
meora!
21
p(m, pos) mösnnal
22
h(m,poo) = log2 (p(m, pos))
pmi(m,, pos) logz( p(m..pos)
23
p(m))p(pps)
npmii(m, pos) pmn mmi(m.ppo))
24
pomm
25
pmiie m [M]]] = npmiim, pos);
end 26
end
28
pos E pmmine [m]
29
for integer pmmine [m]] [pos] do
30
p(pos) 6m
Estimated observation probability for 60 integers
31
Mittal = pmnine [m] [counn)))]:
Total count of message
32
MStotal pminn [m] [pos] [integer]: Total count of message with integer in given position # Estimate message probability
33
p(m) L
Menta!
34
p(m, pos) miintal
Estimate joint probability
35
himm,pos) = log, (p(m, pos)):
36
pmi(m,,pos = logu( p(m,,poe)
p(on)p(pos) );
npmii(m, pos) pmi(m,,po))
37
h(m.ppo)
38
pmine im] [pos] [integer|[ = mpmi(m,,ps))
end
end
15

---

Algorithm 3: The PMI, algorithm
Input: to;
# Confidence value # All ohservations together with sent messages Total number of observations with sent messages # List of all message r-grams present in O O_M
Data: O_M;
Data: L= =-en(O_MM);
Data: ngrams:
Result: pmi.[m][[PM]
pmi dict;
# First we identify r-grams corresponding to integers.
2 for ngram E rigrams do for m E O_M do
if ngram E m then
pmni[ngramm] [cownd] +=
# Total ra-gram occurrences
pmniengrram tanggrm__poseeee +=
# re-gram occurrences including n-gram
position
for integer do pmii|ngram] jinteger][count] += 1; n-gram with integer in given position
pmii[ngram (ngram_pos pingggerrrr//// += 1 n-gram in given position sent with integer given position
end 10
end 11
end
13 end
# Calculate integer NPMI.
14 for ngram E nigrams do
## Position variant NPMI.
15
for pos E [mnic[ngrami]naa (nggaraammlngaam_poo do
16
p(integer) = 00
Estimated observation probability for 60 integers
17
integer, = max (mm [intttgrggeooooottt/
# Find integer with highest
co-ocurrence given position
18
ngrampos = pmide [ngmenggrm]]]
p(ngrampos) = ngrampes
19
p(ngrampor integer) = pmii, [ngram [nggamm]|ggaaannn [ngram pos] [integer] [count]
20
L hingram inleger) logg (p(ggpp((nm)p)m integer))s
21
pmiinggrampo. integer) = log2( p(agrampos integer)
22
p(ngram,.s))r )lintegerr
23
npmii(ngram integer) intggramna..ittegrrr
24
ppcrraammppppp__a (integer] = mpmilnggram integer);
end
Position invariant NPMI.
integer maz (pmi. [ngram] [integer] [nttim/ [count)) Find integer with highest co-ocurrence p(integer) 00
26
27
Estimated observation probability for 60 integers
ngramrotal = pmi (ngram] [arram][coumil [count]]
28
29
p(ngram) Lx(a-len( lent (ngram))
ngramentel
n n-gram length it could appear times per message
pingram, inleger) = pmnig [ngram) lintegrr
30
31
hnggram, integer) = log, (p(ngram, integer)); pmi(ngram, integer) =
log p(ngram (nttger) pmagram po plinteger) integer))
32
33
upmi(ngram, integer) K(ngram,integee
34
pmiiangrame (waaangrramnnggeeeee = rpmmi(ngram, integer);
end
16

---

Algorithm 4: The PMI, algorithm cont.
# Now we identify n-grams corresponding to referent positions.
36 ngrampr dict;
# Prune n-grams with NPMI below
37 for nggram E pmic do for integer pmiio[ggramm] do if pmiilngramm [integer] < te then
38
40
del [ngramm (integer: end
42
for pos E pmniengramm] do for integer pmiiengramm]laaa do
44
if pmiiengramm] [pos] [integer] te then
end end [nnnen/ngg del pmi: (mgramm [ppos]][ppp]]]] [iteger);;
46
47
end 49
end
end
# Find messages with integer n-grams for ngraam E pmnee [ngram] do for o, E O_M do
# Position variant re-ram if pmnc (ngrami] [pos] then if ngram E mm[pos] then
53
54
new new_ngram
# Get leftover n-gram patggramm[pssssittggggoo msg): Get the possible referent position
ngram;
pr (omii (tpppmmmmmaamplpppm ngramp ngrampr [new__gran [pos] [counnt + 1 # Count leftover n-gram occurence
[cr]oottt]]]] 1: Count leftover n-gram occurence
in given positions end end
59
60
# Position invariant n-gram else
61
62
if ngram m then
new_ngram pr pos(pmi. [ngram]] [integer) msg):
ngram:
# Get leftover n-gram Get the possible referent position
ngrampr (newongwwwnnnnnnnnnnee (arrro/m///[//oond]-
Count leftover n-gram occurence
ngramp (new [new_ngram [pos] (or 1 Count leftover n-gram occurence
in given positions
67
end
68
end
end
70 end
17

---

Algorithm 5: The PMI, algorithm cont.
# Calculate referent position NPMI. for ngram E ngrampp do
for pr nggramprr [ngramm]]]] [pr] do # Position variant NPML.
for pos ngrampr [ngrami] [ngramm [pos] [pr] do
p(pr) 0.98;
Estimated observation probability for given position
ngrammpps nggrmmpr [ngram] pos] prr][ p(ngrampos) ngrammpo pon:ramppss: pr) ngrampp [ngram]]
pos] [count))]
h(ngram pos: pr) log, (p(ngrampos integer));
pmi(ngramppos pas pr) logz( por Jp(pr) );
pingram (or)
npmi(ngrammpor poss pr)
prmil (nggaangaaas
h( h(ngrammgoo..rr)
[pos] [pr]
npmmn (ngranngsppppss pr);
76
end
# Position invariant NPMI.
77
p(pr)= = 0.98;
# Estimated observation prohability for given position
78
ngram = max maz(nggra ppgrampr [ngram] [pr][[oom]]]]]
# Find highest positional reference count
p(ngram) = ngram.
79
80
p(ugram, pr)
ag Ingram] [count).
E
81
h(ngram, pr) = log, (p( (ngrom, integer)) ));
82
pmiingram, pr) = loga( (ingram))pppr) );
pingram.pr)
npmi(ngram, pr) = pmiingrammppr
83
h(ngrammpr))
[ngramm [pr] = rupmiingramm 85 end
84
end
18

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NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: We claim that demonstrate how agents can communicate about spatial relationships, and how such language can be interpreted. These claims are supported by our results Section 3
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No
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The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
is fine to include aspirational goals as motivation as long as is clear that these goals not attained by the paper.
2. Limitations
Question:
Does the paper discuss the limitations of the work performed by the authors?
Answer:
[Yes]
Justification: discussion of the limitations provided in Section
Guidelines:
The answer NA means that the paper has limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create a separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (c.g.. independence assumptions, noiseless settings, model sell-speciiiatiinn asymptotic approximations only holding locally). ). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution low or images are taken in low lighting. Or speech-to-tex, system might not be used reliably to provide closed captions for online lectures because it fails handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and faimesss.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, a worse outcome might be that reviewers discover limitations that aren't 't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community, Reviewers will be specifically instructed to not penalize honesty concerning limitations.
3. Theory Assumptions and Proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and complete (and correct) proof?
19

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Answer:
[NA]
Justification:
We present no theoretical results or proofs.
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced in the statement of any theorems.
The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged to provide a short proof sketch provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should be properly referenced.
4. Experimental Result Reproducibility
Question: Does the paper fully disclose all information needed to reproduce the main ex- perimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
Answer: [Yes]
Justification: The architecture and training details are described in Section and Appendix A respectively. The NPMI measures are described Section 4 together with more detailed
pseudocode in Appendix D
Guidelines:
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Reviews:
[{"review_id": "3CJQwIUwcb", "reviewer": "Reviewer_YdNg", "summary": "This paper shows that emergent communication can learn spatial references. They first create a modified referential game which requires the agents to communicate by messages that indicate the relative position of a number. The proposed agent architecture shows that the GRU-based agents can achieve good performance. The analysis uses NPMI to identify the meaning of the ngrams in the message (i.e., the correlation between the ngram and the referred positions). This paper further shows that the mapping generated by NPMI is correct by generating additional datasets based on the identified dictionaries to show that both non-compositional and compositional messages carry the intended meanings.", "questions": "- In the experiment, the observation is always fixed length which makes the communication easier. What happens when the observation is longer? I can imagine if the longer sequence contains the same number at different positions, it will introduce some ambiguity in the messages.", "limitations": "- The experiment is based on one-dimensional sequences, the types of spatial references are limited in this case. It will be helpful if the author can discuss how it can extend to more complex types of spatial references.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- This paper proposes a novel spatial game to study the emergence of spatial references.\n- This paper shows that NPMI is an effective measure to decompose the messages by finding correlations with the intended meanings.", "weaknesses": "- The paper is not very easy to follow especially the definition and design of different types of sequences, examples of the messages, and how the hypotheses are tested. The presentation can still be improved.\n- It is unclear how much the test set overlaps with the training set when measuring the accuracy. There is no control of generalization tests such as varying full sequence length or observation of certain patterns of sequences. So, it is hard to understand if the learned messages are effective or memorization of part of sequences in training. For example, does the ngram that means “leftmost” can effectively communicate in a longer sequence?\n- The design of the game put high communication pressure on the agents. The agents need to develop messages conveying relative positions in order to succeed. How does the success relate to the communication protocol, for example, when the message length is longer, is it still necessary to develop messages that convey relative positions? It is unclear about the role of channel bandwidth, effective communication, and developed messages.\n- The test in Compositional-NP is to generate the dataset by removing the positional component of the message. This is an extreme case of H2. In reality, the message is most likely to be corrupted rather than removed. To reject the null hypothesis, it will be more convincing to have a corrupted message version.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "# Response to Reviewer YdNG\nWe would like to thank the reviewer for their insightful comments and feedback. We appreciate that the reviewer found our game setting novel and the measure effective.\n\nWe address the concerns and weaknesses raised below.\n\n## Weaknesses\n> The paper is not very easy to follow especially the definition and design of different types of sequences, examples of the messages, and how the hypotheses are tested. (...)\n\nBased on your and the other reviewers' comments, we will improve the presentation for the camera-ready version of the paper. We will include the formalisations of the definitions, rephrasing the hypotheses, additional information about the dataset splits, and the types of different sequences tested. \n\n> It is unclear how much the test set overlaps with the training set when measuring the accuracy. There is no control of generalization tests such as varying full sequence length or observation of certain patterns of sequences. (...)\n\nThe test set does not overlap with the train set or the validation set. Therefore, as our agents achieve high accuracy on the validation set, we can conclude that the results are not a case of overfitting. We will add the dataset split and overlap information in the revised version.\n\nWe tested train sequence lengths between 20 and 100 and observed that agents can still learn to achieve the same accuracy as in the original task. The only differences are that longer sequences take longer to converge and require a larger hidden size.\n\nLonger sequences in the test dataset will be difficult to reliably evaluate after the training has finished due to the lack of trained weights for either the sender or the receiver to process given integers. This is a similar issue to extending the context windows in LLMs. However, sequences shorter than the ones present in the training dataset can be evaluated, and would contain integers that the agents would have the corresponding weights for. Our preliminary tests suggest that the agents can understand shorter sequences than the ones they were trained on. They can still achieve the same high accuracy as on the sequences from the training set. We only observe at most a 5-10% decrease in accuracy when the training and test sequences are significantly different lengths (60 vs 20 respectively). We hope this alleviates some concerns about the generalisation of our approach.\n\nBoth tests will be expanded and included in the revised version of the paper.\n\n> The design of the game put high communication pressure on the agents. The agents need to develop messages conveying relative positions in order to succeed. How does the success relate to the communication protocol, for example, when the message length is longer, is it still necessary to develop messages that convey relative positions? (...)\n\nChannel bandwidth will indeed play a role in how the agents learn. Increasing the channel bandwidth to the point that the agents can describe the observation in full will nullify any development of spatial referencing.\n\nHowever, this is not the focus of this work. We show that the agents can communicate about spatial relationships, how such messages can be composed, and that this does not require as much bandwidth as transferring the complete observation. Therefore, analysing the bandwidth of the channel was outside the scope of this paper.\n\n>   The test in Compositional-NP is to generate the dataset by removing the positional component of the message. This is an extreme case of H2. (...)\n\nWe apologise for the confusion. We think that our test already represents your suggestion. When the positional components are removed from the messages, any part of the message that does not convey information about an integer is replaced with $0$ instead of truncation. This ablation test is the most straightforward way of rejecting the null hypothesis of whether the positional components were correctly identified. We will clarify this in the camera-read version.\n\n## Questions\n> In the experiment, the observation is always fixed length which makes the communication easier. What happens when the observation is longer? (...)\n\nAs mentioned in our response to the weaknesses, we notice no differences when the observation length is increased.\n\nHowever, including integer repetitions would be challenging for the current setting and would require a careful design of the dataset. It would not provide additional information about the emergence of spatial deixis. If repetitions were allowed, there could be cases where the sender's observations could be duplicated multiple times in a single sequence. This would make the task of the receiver nearly impossible to accomplish, and would lead to training instability. Instead, to allow for repetitions, the sequence window would have to be extended, or the dataset generation would have to be designed to ensure that the sequence windows cannot be repeated while maintaining the possibility of single integer repetitions.\n\nTo illustrate this, consider a sequence $S = [1,2,3,4,5,1,2,4,4,5]$, where each integer can be repeated multiple times. If the observation to the sender is $o_s=[1,2,-1,4,5]$, then it is impossible for the receiver to correctly predict the target number, as both $3$ and $4$ are valid answers.\n\nAfter applying such restrictions, the dataset allowing repetitions would most likely lead to the same results as the one presented in this paper. Possible differences include the sender having to refer to 2 integers in a single message to identify the referent position in the sequence precisely.\n\n## Limitations\n> The experiment is based on one-dimensional sequences, the types of spatial references are limited in this case. It will be helpful if the author can discuss how it can extend to more complex types of spatial references.\n\nThank you for this suggestion. We discuss the formal extension of our setting in our response to Reviewer `vZ26`.", "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": "KUqFu9Tidq", "reviewer": "Reviewer_VwFJ", "summary": "The authors design a referential game environment intended to motivate the emergence of spatial references, cast in the form of a task where the target integer must be selected from an integer sequence.  The character vocabulary for the message is smaller in size than the set of integers in the list, and this necessitates an alternative to directly specifying the target integers.  Using a traditional GRU-based speaker/listener architecture, the model achieves high task accuracy.  Using existing information theoretic measures the authors are able to roughly decode the semantics of the messages and show some degree of compositionality in the messages.", "questions": "- There are some fairly trivial solutions to this problem.  It seems compositional integer style gets at this -- are there cases where compositional integer would fail?  I'm not seeing the need to learn a spatial solution to this problem when it seems that a two-character code could cover all possible target integers.  Does this vary as the length of sequence or size of alphabet are increased/decreased?\n\n- Similarly, is there any reason to motivate the choice of vocabulary size with respect to latin alphabet?  The chunks of the messages are more akin to words than characters.  To me it just read as an attempt to have a connection to human language, but that relationship was not meaningful.\n\n- It is mentioned that the hyperparameters for MI are optimized for translation accuracy.  I can make some guesses as to what might be done here, but it wasn't clear to me exactly what is being compared here.", "limitations": "Some limitations have been discussed, though limitations of the experimental design (such as 3 character messages, \"nouns\" being integers and therefore being able to reference without features, etc.) are not.  The authors mention some doubts in previous work regarding the value of referential game -- I think this is precisely one of the ways that these doubts emerge, i.e., \"we try very hard to setup a task where success must be achieved in this way, and the model finds it\".  These sorts of limitations may not be addressable in the scope of the paper, but they are also not mentioned.  There are no negative societal impacts from such work.", "rating": 5, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 2, "strengths": "- The experimental design is simple but I think straightforward and correct for what the authors want to test.\n\n- Similarly, it appears from the analysis in sections such as Table 2 that the resulting messages do seem to exhibit a variety of communication strategies, including the desired type in some messages (compositional positional)\n\n- The approach of decoding the meaning and segmentation of the messages via NPMI (though I would have also liked to see some discussion of where this would/would not be appropriate in terms of a general evaluation metric for EC.  It seems some strong expectation over what the emergent language needs to say may be necessary?  In this case, the presence of the integers, for instance)", "weaknesses": "- Overall I find the biggest weakness to be in the scope of the paper and the degree to which the design of the environment caters to the type of messages the authors want to elicit here.  It comes across as a toy problem, and through the lens of the field as a whole, I think it raises the question of whether there is sufficient novelty in making such small and targetted tweaks to the referential game formula.\n\nThis might be best highlighted by revisiting the motivating example, such as \"a blue vase with intricate motifs on the table\".  Why refer to this as \"the vase over there\" or \"that vase near you\"?  There are pressures in the referential game to draw out these spatial references, but these feel artificial and devoid of broader understanding about linguistic pressures when we compare them to the pragmatic concerns that would motivate a spatial reference (and what type of spatial reference) in the motivating example.\n\nI also think claims are over-stated.  The authors claim this is the first paper in EC to have syntax and make comparisons to SVO ordering.  This comes across as a flimsy attempt to connect to human language and to signal a degree of progress in the complexity of ECs, but a lengthier discussion is warranted.  Syntax can't be treated as something that does or does not exist, but rather, discussion of what formal language class the emergent language falls into would be relevant, and nothing here would necessitate a CFG or the degree of syntax that is meaningful when it comes to discussing natural language.\n\nDespite the simplicity I do see value in this work but I would have liked to have seen a less contrived environment with a more difficult learning problem / substantial scope in the necessary semantics to feel comparable to the degree of contributions typical of a paper at this venue.  I think it would be far more appropriate at a more targetted venue where it can also recieve appropriate attention and discussion.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "# Response to Reviewer VwFJ\nWe would like to thank the reviewer for the insightful feedback and detailed criticism. We also appreciate that the reviewer found our experimental setup and analysis interesting.\n\nTo address the points raised by the reviewer:\n\n## Weaknesses\n> Overall I find the biggest weakness to be in the scope of the paper and the degree to which the design of the environment caters to the type of messages the authors want to elicit here. It comes across as a toy problem, and through the lens of the field as a whole, I think it raises the question of whether there is sufficient novelty in making such small and targetted tweaks to the referential game formula. (...)\n\nWe address this weakness in detail in the general response.\n\n> I also think claims are over-stated. The authors claim this is the first paper in EC to have syntax and make comparisons to SVO ordering. This comes across as a flimsy attempt to connect to human language and to signal a degree of progress in the complexity of ECs, but a lengthier discussion is warranted. (...)\n\nWe agree that the claim of SVO ordering may be an overstatement, so we have removed it from the paper. Instead, we point to a possible syntactic structure, but make no comparisons to natural language syntax, as also suggested by reviewer `vZ26`.\n\n## Questions\n> There are some fairly trivial solutions to this problem. It seems compositional integer style gets at this -- are there cases where compositional integer would fail? I'm not seeing the need to learn a spatial solution to this problem when it seems that a two-character code could cover all possible target integers. Does this vary as the length of sequence or size of alphabet are increased/decreased?\n\nWe apologise for the confusion — the compositional integers style does include spatial referencing, where one character represents an integer, and the other the relative position of that integer. It represents a spatial solution. Simply representing the target integer is impossible, as the sender does not know the target integer, so that cannot be transmitted. If the sender, instead of using the compositional message, always transmits the identity of the integer one to the left of the target, we would still consider this a spatial solution. The spatial deixis is implicitly agreed between the sender and the receiver. Indeed, for our setting, a two character code, which includes spatial referencing, would be enough to convey all information. However, without explicit or implicit spatial referencing, we do not identify a feasible solution to this environment.\n\nWe do not observe any differences in terms of the performance of our agents when the train sequence length is increased/decreased, except for the convergence speed and need to adjust the hidden layer sizes, as noted in our response to Reviewer `YdNG`. Similarly, there is no observable difference for changes in the alphabet sizes, up to a point: there must be enough characters, and the message space must be large enough for the sender to be able to describe its observations. In the case of making the message space too small, the sender cannot convey enough information about its observations to the receiver. If the message space is too large, the sender can just encode the complete observation, bypassing the need for communication.\n\nWe will include this information in the revised version of the paper.\n\n>  Similarly, is there any reason to motivate the choice of vocabulary size with respect to latin alphabet? The chunks of the messages are more akin to words than characters. To me it just read as an attempt to have a connection to human language, but that relationship was not meaningful.\n\nThe choice of vocabulary size was arbitrary, with $26$ providing high expressivity and presenting a good starting point. If such a vocabulary is enough to convey information in natural languages like English, this should also apply to the agents. We have additionally run preliminary tests with smaller and larger sizes of the vocabulary and found no impact on the agent performance.\n\n> It is mentioned that the hyperparameters for MI are optimized for translation accuracy. I can make some guesses as to what might be done here, but it wasn't clear to me exactly what is being compared here.\n\nWe apologise for the lack of clarity. The optimised hyperparameters are $t_c$ and $t_n$, on which a grid search is performed. We create all possible permutations of the tuple ($t_c$, $t_n$), for $t_c \\in [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]$ and $t_n \\in [1, 2, 3, 5, 10, 15]$. Then, we select the best tuple of hyperparameters regarding the measured translation accuracy on the test dataset. We will clarify this in the camera-ready version.", "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": "RGr2jt0fsK", "reviewer": "Reviewer_JyuC", "summary": "This paper proposes a new communication game in the emergent communication framework to analyze the emergence of _deictic reference, i.e. expressions akin to demonstratives like \"this\" and \"that\".  These are important expressions in natural language and especially in this emergence literature, since their meaning is context-dependent and \"functional\", i.e. cannot be reduced to objective properties of the object of reference. The paper also introduces an application of normalized pointwise information to the analysis of the emergent communication protocol in order to identify holistic messages (where a message refers to an entire meaning) and compositional ones (where certain n-grams and/or positions refer to specific \"components\" of the meaning).  Both of these are welcome contributions and will be of interest to many people working on emergent communication.  The core idea in their game is to use integers within longer sequences as the object of reference, provide a _partial observation_ of the true context to the sender (so that absolute positional information cannot be used) and to _mask out_ the target object in a sequence (so that the integer itself cannot be used); what remains as possible information to convey are things like \"two to the right of 13\".", "questions": "* Why did you choose a fixed-length of 3 for the messages (as opposed to either a single token, or variable-length)? \n* Line 92 and 114: should \"target integers\" and \"targets\" both be singular?  There's one target integer, correct?  Or is the plural here just over a batch of examples?  If the latter, the wording is a bit confusing since the worked case in the paper is just one example (\"batch size 1\" so to speak). \n* Can $PMI_c$ and $PMI_{nc}$ be seen as one metric, with the latter a special case of the former (i.e. for the full tri-grams)?  The discussion just before Section 5 seems to suggest so, so I would encourage more elaboration on whether these are really two separate degrees or not.  For instance: does high $nc$ entail low $c$, and vice versa?\n* \"The analysis provided in this section is based on the messages collected from the test dataset after the training has finished\".  What was the train/test split here?  Appendix A provides model / optimizer hyper-parameters, but what are the game/environment/data choices?\n* Can the observations in Section 5.1 and 5.2 be made more quantitative?  I would appreciate a more detailed analysis of the types of composition observed, their frequency, and other factors like that.\n* H2 and Table 1: while the Comp-P case is above chance, if the NPMI method correctly identified \"genuinely compositional\" messages, we would expect nearly perfect accuracy in this case, right?\n* Very minor typographic point: I think that the \"n\" in \"$n$-gram\" and similarly in the main text should be in math mode.", "limitations": "Yes", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "* A carefully designed emergent communication scenario which requires something like spatial deixis to emerge for successful communication.  This is an important component of human language that goes beyond what has been done in existing literature.\n* Interesting and useful application of NPMI for the analysis of (non-)compositionality of the resulting messages.\n* Engages well with existing literature to situate the new contribution of this paper.\n* Results also show a robustness to things like random seed, which is not always the case in emergent communication.", "weaknesses": "* Some experimental details could be more carefully reported and some analyses could be more systematic/quantitative (see questions below).\n* The artificial messages used to validate their NPMI metric does not yield results as strong as one would like (as discussed in the Limitations section); this makes it not entirely clear that the metric does what its intended to do.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "# Response to Reviewer JyuC\n\nWe thank the reviewer for their comprehensive comments and thoughtful critique. We appreciate that the reviewer has found our paper interesting and that the investigation of deictic references is perceived to be of high value.\n\nTo address the points raised by the reviewer:\n\n## Weaknesses\n\n> Some experimental details could be more carefully reported and some analyses could be more systematic/quantitative (see questions below).\n\n> The artificial messages used to validate their NPMI metric does not yield results as strong as one would like (as discussed in the Limitations section); this makes it not entirely clear that the metric does what its intended to do.\n\nBoth answered below.\n\n## Questions\n\n> Why did you choose a fixed-length of 3 for the messages (as opposed to either a single token, or variable-length)?\n\nThe choice was motivated by our goal of analysing the spatial deixis and the analysis method. A single token would not be able to be segmented and could not show any possible compositionality. While it would be possible for the agents to use a single token to convey the same information, assuming a large vocabulary size, such tokens could not be interpreted as easily. Additionally, allowing for variable length messages increases the computation cost of the analysis. As our method checks all possible $n$-grams used by the agents, increasing the message length would correspondingly increase the number of $n$-grams needing to be generated. The special case handling of each message would also add overhead. However, extending our setting to variable-length messaging, both the training and analysis code, is entirely possible and feasible.\n\n> Line 92 and 114: should \"target integers\" and \"targets\" both be singular? There's one target integer, correct? Or is the plural here just over a batch of examples? If the latter, the wording is a bit confusing since the worked case in the paper is just one example (\"batch size 1\" so to speak).\n\nThank you for pointing this out. There is indeed only one target integer. The camera-ready version will correct this wording.\n\n> Can $PMI_c$ and $PMI_{nc}$ be seen as one metric, with the latter a special case of the former (i.e. for the full tri-grams)? The discussion just before Section 5 seems to suggest so, so I would encourage more elaboration on whether these are really two separate degrees or not. For instance: does high $nc$ entail low $c$ , and vice versa?\n\n$PMI_c$ and $PMI_{nc}$ can be viewed as complementary metrics. High $nc$ values for certain messages do not necessarily entail low $c$. While in practice the two metrics do align in opposition, there could be cases where if a compositional message is most often used only in a specific context, it could have both high $nc$ and $c$ values. For example, a message $[1,9,10]$, where $1$ is a positional component, and $[9,10]$ are integer components, could always be used whenever the integer represented by $[9,10]$ is in a given position. Then, even though the agents use compositional rules to create this message, it would also be classed as high $nc$, since its parts are never observed separately. It would also have a high $c$, as the aforementioned $n$-grams are also associated with the given integer and position.\n\nAs mentioned, in practice, compositional parts of the compositional messages will be frequently used in different messages, lowering the value for $nc$.\n\n> \"The analysis provided in this section is based on the messages collected from the test dataset after the training has finished\". What was the train/test split here? Appendix A provides model / optimizer hyper-parameters, but what are the game/environment/data choices?\n\nThe datasets used are: training 200k, validation 200k, test 20k. We generate each dataset separately instead of splitting a singular dataset into the 3 used. We are confident that this approach does not present any issues with overlap, as all sequences are randomly generated. Considering the sequence length of 60, since there are no integer repetitions, the number of permutations is $60! \\approx 8 \\times 10^{81}$, far outnumbering our number of generated samples. We also empirically confirm this by checking the overlap across 1000 randomly generated datasets, finding an overlap rate of 0%.\n\nWe will provide additional information about the environmental and dataset choices in the appendices of the revised version.\n\n> Can the observations in Section 5.1 and 5.2 be made more quantitative? (...)\n\nWe assume this is similar to the comment by Reviewer `vZ26`. We provide this additional quantitative information in table format in the general response. It will also be included in the camera-ready version.\n\n> H2 and Table 1: while the Comp-P case is above chance, if the NPMI method correctly identified \"genuinely compositional\" messages, we would expect nearly perfect accuracy in this case, right?\n\nIf the compositional messages were context-free and composed only by concatenation of the positional components, we would indeed expect nearly perfect accuracy.\n\nThe lower accuracy for the Comp-P case might be due to contextual information not accounted for by our creation of the messages or the possibility that some messages may require slightly more complex composing methods. For example, if a certain integer component representing $5$ is only used when $6$ is also present in the observation, our method of creating the messages would fail. Accounting for such context dependence is not encoded in the message segmentation or generation process. Similarly, if there are \"synonyms\" for meanings such as \"1 to the left\" that are only used in certain contexts, this would also not be accounted for in our methods.", "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": "1WQkvViO3O", "reviewer": "Reviewer_vZ26", "summary": "This work investigates the presence of spatial deixis (e.g., spatial references in language dependent on the context of the utterance) in a signalling game within the paradigm of emergent communication.\nIt begins by introducing a variant of the signalling game which requires the sender to communicate the relative position of some element in a sequence of integers visible to the receiver.\nAnalysis of the semantics of the emergent communication is performed primarily through looking at normalized point-wise mutual information.\nThese analyses show that the emergent communication regularly uses spatially-referent messages (or sub-message units), validating the presence of spatial deixis in the environment.", "questions": "- The biggest question regarding the paper for me is how do we make the jump for the simple example of deixis presented in the empirical investigation of the paper to a more robust form of deixis.  It is not wrong (and likely correct, in fact) to have started out with a toy problem, but I believe there either needs to be empirical work and/or some light theoretical work on what exactly is meant by \"deixis\" in this paper, how the environment investigated satisfies that definition, and how this is relevant for further environments.  I might raise my score if the authors could respond with a slightly more formal characterization of deixis and how it maps both to the current environment and more sophisticated, \"natural\" environments (e.g., embodied multi-agent environment).\n- In the environment, are the integers actually represented as integers in the neural network or are they encoded as one-hot vectors?  If they are OHVs, it is not clear that it is the case; if they are not OHVs, it seems like an odd design choice to feed a scalar into an NN when it is representing something categorical.\n- How are the various inputs to the receiver agent actually fed into the network.  Are they just concatenated \"temporally\" and given as a sequence to the GRU?\n\n\n### Comments\n\n- The fact that this paper is inducing a segmentation of emergent communication is (minor) contribution in and of itself, so I think it deserves a mention in the introduction.\n- The \"td\" variable needs to be introduced before the example; I am assuming it is the list of distractors plus the correct answer, but it should be stated explicitly when defining the vectors earlier.\n- Table 2: Don't reuse X; use other variables.\n- Include the actual URL for the (Anonymous) GitHub so that it is obvious it is a link.\n- I don't understand the point being made at Line 337.\n- I do not think it is appropriate to specifically mention \"SVO\" as an interpretation of the language since there is no clear way to distinguish between nouns, verbs, subjects, or objects; I think it is fine to say that there is syntactic structure, but I a skeptical of there being evidence to make any claim further than that here.", "limitations": "N/A.", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 2, "strengths": "In conjunction with standard criteria, there are three characteristics that are particularly important for emergent communication research: reusability (how easily can another researcher use the products of this research), generalizability (how much do the findings of this research apply broadly to our knowledge of emergent communication), and directedness (does this research contribute concretely to particular questions in emergent communication research).\n\n### Quality\n- (major) The experimental design is of good quality; the methods are in line with the standards of the field.\n### Clarity\n- (major) The language of this paper is easy to read and illustrates the central points effectively.\n### Reusability\n- (major) The provided code appears to be of good quality (have not attempted to run it); this work would be very easy to reuse in subsequent experiments.\n### Generalizability\n- (minor) The environment is relatively simple, with few confounding factors, making it easier to draw conclusions about more general tendencies in EC.\n### Directedness\n- (major) This paper is directed toward an important goal in emergent communication: discovering/engineering more human-like features in EC, namely deixis or context-dependent reference.\n- (minor) Secondarily, this paper also demonstrates some degree of compositional semantics and syntactic features.", "weaknesses": "### Quality\n- Nothing of note.\n### Clarity\n- (minor) One or two more of the points in Section 5 need to be illustrated (likely with just a table); although the text is mostly clear, some tables which aggregate what is said there would make referencing the paper much easier.\n- (minor) It is a little bit confusing that your hypotheses are what you expect to be false; it might be clearer to state hypotheses in positive (even if the statistical test you are using is rejecting a null hypothesis of a random baseline).\n### Reusability\n- Nothing of note.\n### Generalizability\n- (major) It is not clearly the case that the environment addresses deixis in a way that applies to emergent communication environments more generally (see first question for more).\n- (major) There is not much discussion on how the deixis investigated in this paper is applicable to emergent communication more generally.\n### Directedness\n- Nothing of note.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "# Response to Reviewer vZ26\n\nWe thank the reviewer for the insightful feedback and constructive criticisms. We appreciate that the reviewer found our experimental design and overall approach to be of high quality and relevant to the field of EC. We also appreciate that the code was found to be of high quality.\n\nTo address the comments of the reviewer:\n\n## Questions\n\n> The biggest question regarding the paper for me is how do we make the jump for the simple example of deixis presented in the empirical investigation of the paper to a more robust form of deixis. (...)\n\nLet $O$ be the observation available to an agent. Let $O_p$ be a point in the observation from which the relative position will be described. For example, $O_p$ can represent the agent position or the position of an object. Let $O_t$ be the target object to which the relative position is being described, for example, a different object or agent. Let $d(O_t)$ denote the relative distance of $O_t$ to the reference point $O_p$. $\\theta(O_t)$ is defined as the angle between $O_p$ and $O_t$, using for example the vector angle.\n\nThe spatial deixis could then be defined as a mapping of tuples $(d, \\theta)$ to specific $n$-grams. For example, a tuple $(2,\\pi)$ can be mapped to the $n$-gram $15$ from this paper, representing \"2 to the left\". This, combined with specifying the $O_t$, completes the message, which in this paper could be $[15,0,2]$ to mean \"$O_p$ is to 2 to the left of 15\".\n\nThe version of deixis presented in this paper is a special case of this general deixis, where $O$ is a 1D tensor, $O_p$ is prescribed to be always $-1$, and the $\\theta$ can only take values of $\\pi$ and $0$, as we operate in 1D. However, the concepts presented can be easily extended to the case of 2D or 3D tensors and observations, and when the agent chooses both $O_p$ and $O_t$. When extended to multi-agent settings, the agents may need to additionally specify their position, or both $O_p$ and $O_t$ in their messages, since their observations may have different relative positions.\n\n> In the environment, are the integers actually represented as integers in the neural network or are they encoded as one-hot vectors? (...)\n\nThe integers in the environment are indeed represented as scalars. Based on your comment, we have run additional tests of the OVH approach and found that it performed significantly worse. Instead of learning to communicate about their observations, the agents appeared to be memorising the dataset, increasing accuracy on the training set but staying at random on the validation dataset. Instead, in the scalar approach, the agents learn to communicate, increasing their accuracy on the validation set. This test was performed on agents with the same hidden sizes, except for the layers processing the one-hot vectors. It may be the case that with more tuning of the layer sizes the OVH approach would work, but this is outside the scope of this paper. An additional advantage of using the scalar approach are savings in terms of the number of trainable parameters (98.8K vs 72K), with about a 27% reduction in size. \n\n> How are the various inputs to the receiver agent actually fed into the network. (...)\n\nLet $B$ be the batch size, $T$ the temporal/sequence length dimension, $C$ the hidden size of the GRU and Linear layers (which are the same), $N_v$ the vocabulary size of the agents, and $N_l$ the message length.\n\nThe output of the sender agent is in the form of $[B,N_l,N_v]$ , or $B$ tensors, each representing the probability of a character being in a given position of the message, as per the Gumbel-Softmax reparametrisation.\n\nThis is fed into the receiver agent, to `GRU 1` in Figure 1, from which only the hidden states for the last character probabilities are collected, i.e., only the hidden states after each message has been processed in full. This results in a tensor of shape $[1,B,C]$, where $1$ represents the number of layers of the GRU.\nThis tensor can then be used as the initial hidden state for `GRU 2` in Figure 1.\n\n`GRU 2` receives the sequences in the form of $[B,T,1]$, with $T$ being our sequence length, and the $1$ representing the scalar values. We again collect only the final hidden states for each element, resulting in the output of shape $[1,B,C]$.\n\nThe $td$ vector is passed through a linear layer, in shape $[B,5,1]$, with $5$ representing the 4 distractors and 1 correct target. Similarly to the `GRU 2` input, we use scalar values. The linear layer outputs a tensor of shape $[B,5,C]$.\n\nFinally, the `GRU 2` output is matrix multiplied with the $td$ embeddings. We first permute the `GRU 2` output tensor, creating a tensor of shape $[B,C,1]$.\nThen the two tensors are multiplied, i.e., $[B,5,C] \\times [B,C,1]$, resulting in a tensor of shape $[B,5,1]$, which is then squeezed to produce the batch of target predictions $[B,5]$.\n\n## Comments\n\n> I don't understand the point being made at Line 337:\n\nWe apologise for the confusion. We argue that non-compositional messages are easily compressible, when they would be transmitted in a real-world setting, with limited bandwidth. For simple encodings, since these messages are monolithic, they could be compressed to a single token/character. In contrast, compositional messages require at least two tokens/characters, one for each integer/positional component. We will clarify this in the revised version.\n\n> I do not think it is appropriate to specifically mention \"SVO\" as an interpretation of the language since there is no clear way to distinguish between nouns, verbs, subjects, or objects. (...)\n\nWe have removed the claim of SVO ordering from the paper. Instead, we discuss a possible syntactic structure, but make no comparisons to natural language syntax or concepts, as reviewer `VwFJ` suggested.", "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:
# General Response

We would like to thank the reviewers for their constructive comments. 

We address some common themes in the general response, with more detailed comments in each reviewer rebuttal. Where it was needed, the quoted parts of the review texts were shortened to (...) for brevity. We welcome the reviewers' comments on any major unaddressed points in the discussion. We will be able to answer anything that was missing from our rebuttal.

We have also noted any typographical and layout comments, and assure the reviewers that they will be corrected in the revised version.

## Generalisation

Reviewers `YdnG` and `VwFJ` argue that the settings presented, and the results, are simple and not generalisable. 

We agree that the environment present is quite simple. However, we disagree that this represents a weakness of our results. We see this as a good starting point, with any extraneous confounding factors removed, as reviewers `vZ26` and `JyuC` noted. By using a simple environment, we can show more precisely which factors affect the emergence of spatial referencing strategies. Using a more complex setting at such an early stage of research into deictic phrases in EC could potentially lead to confusing and not generalisable results. For example, using a vision network, or complex tasks, could lead to a generally low accuracy of the agents, which would not necessarily imply that spatial deixis are impossible, or require different approaches. Instead, it could point to an issue with the pretrained vision network, training the vision network, or the size of the agent's network being too small/large for the task given. We therefore consider that starting with the simple environment and showing how such spatial references can emerge, leads to useful insights, paving the way for future research in more complex settings with more complex architectures.

### Generalisation tests

We would also like to thank the reviewers for suggesting additional generalisation tests, allowing us to expand the analyses. We have run these preliminary tests, with the initial results showing that our methods generalise to training on both longer and shorter sequences. We also show that the agents can communicate even when presented with shorter sequences than the ones they were trained on. This indicates that the learned spatial references are transferrable to different environments, including OOD settings. These generalisation tests will be expanded on in terms of robustness and sample size, and featured in the camera-ready version of our paper.

## Presentation

All reviewers requested that the paper provide more information and formalisation, especially regarding the definitions and dataset details. We will include this in the camera-ready version. We will also be adding a more formal definition of deixis, as presented in our response to Reviewer `vZ26`. 

Additionally, Reviewers `vZ26` and `JyuC` requested additional information for Section 5 of the paper. We present this in the table below. The entries in the table are composed of average percentages, across all $t_n$ and $t_c$ choices. In the parentheses, we show the maximum and minimum values across all $t_n$ and $t_c$ choices. The average \% of emergence represents the absolute \% of runs which developed that message type or message feature. For all messages, the average \% of messages which are of a given type, or exhibit a given feature, is only counted for in runs where these features emerged.

 This table will also be added to the camera-ready version.

| **Message Type**                                     | **Avg. \% Emergence**  | **Avg. \% of Messages** |
|-----------------------------------------------------|----------------------------------|---------------------------|
| Non-Compositional Positional      	       | 99.3\% (100\%-93.75\%) | 1\% (3\%-0\%)       	|
| Non-Compositional Positional Reserved | 18.75\%            	              | 1\% (3\%-0\%)       	|
| Non-Compositional Integer                       | 45.1\% (100\%-0\%) 	 | 10\% (15\%-0\%)     	|
| Compositional Integer             	        | 100\%              	            | 34\% (99.7\%-0\%)    	|
| Compositional Positional          	        | 25\% (27\%-0\%)    	| 56\% (100\%-0\%)     	|

Meta-review: The paper proposes a variant of the referential game in which agents must learn to perform a simplified form of spatial deixis, by referring to a target item in terms of its relative position. The authors perform an information-theoretic analysis suggesting that the agents develop a language that is successfully incorporating deixis and is partially compositional.

The reviewers appreciated the interest and novelty of the research question. There were several concerns about generalization, for example in terms of length of the sequences, and a more general worry that the paper is only considering a toy setup for deixis, which might not be sufficient to build upon in future research.

There was a lively and constructive discussion, in which the authors addressed the length generalization issue, and they worked towards a formalization of deixis that establishes a clearer link between the paper setup and the general notion of deixis in linguistics.

The authors have addressed the main concern of the reviewers, and I think the revised paper will be a nice addition to the literature on emergent communication.
Decision: Accept (poster)