Limits of Theory of Mind Modelling in Dialogue-Based Collaborative Plan Acquisition (2024)

Abstract: Recent work on dialogue-based collaborative plan acquisition (CPA) has suggested that Theory of Mind (ToM) modelling can improve missing knowledge prediction in settings with asymmetric skill sets and knowledge. Although ToM was claimed to be important for effective collaboration, its real impact on this novel task remains under-explored. By representing plans as graphs and exploiting task-specific constraints we show that, as performance on CPA nearly doubles when predicting one’s own missing knowledge, the improvements due to ToM modelling diminish. This phenomenon persists even when evaluating existing baseline methods. To better understand the relevance of ToM for CPA, we report a principled performance comparison of models with and without ToM features. Results across different models and ablations consistently suggest that features learnt for ToM tasks are more likely to reflect latent patterns in the data with no perceivable link to ToM. This finding calls for a deeper understanding of the role of ToM in CPA and beyond, as well as new methods for modelling and evaluating mental states in computational collaborative agents.

heading: 1 Introduction
text: Dialogue-based human-AI collaboration is an interaction in which humans and artificial intelligent (AI) agents converse to achieve a shared goal or task (Streeck et al., 2011). When humans collaborate with each other, they rely on two main abilities: Verbal communication and Theory of Mind (ToM), i.e. the ability to infer one’s own and others’ mental states (Premack and Woodruff, 1978). To succeed in collaborating with humans, it is therefore imperative for AI agents to possess similar capabilities (Williams et al., 2022).
†Equal second-author contribution. The project web page is accessible here.
Recent work on this topic has introduced collaborative plan acquisition (CPA) as a promising task for evaluating collaborative abilities in agents (Bara et al., 2023). Starting from asymmetric knowledge and skill-sets of two collaborating agents, the goal of CPA is to infer one’s own missing knowledge (OMK) and the partner’s missing knowledge (PMK) to achieve a shared goal by engaging in a multi-round situated dialogue (see Figure 1). To study CPA, the authors used MindCraft – a multi-modal collaborative dialogue-based benchmark grounded in the sandbox game Minecraft (Bara et al., 2021). They also proposed a sequenceto-sequence CPA model that used visual observations, plan, and dialogue history as input. Their empirical results showed a large difference in performance between predicting OMK and PMK. Furthermore, they found that while including a subset of ToM features improved performance, using all ToM features resulted in nearly the same performance as using none.
In this work, we systematically analyse the limits
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of ToM modelling in dialogue-based collaborative plan acquisition. We first propose to represent plans as directed graphs, each represented by a node feature matrix, a connectivity matrix, and an edge feature matrix. This starkly contrasts previous works (Bara et al., 2021, 2023) that represented plans as lists consisting of materials and tools processed by GRU (Cho et al., 2014). Our novel structured representation allows us to elegantly frame CPA as a link prediction task (Liben-Nowell and Kleinberg, 2007) and apply negative sampling constrained on MindCraft plans’ structure for efficient training. Our proposed representation not only doubles the performance of predicting OMK compared to (Bara et al., 2023) but also bridges the gap to predicting PMK.
However, our evaluations show no significant performance difference when using ToM features – neither for our method nor for the baselines from Bara et al. (2023). We thus conduct extensive analyses using diagnostic probing, correlation analysis, and ground-truth ToM labels as input. Results across different models and ablations consistently suggest that learned ToM features are less associated with mental states and more aligned with revealing latent patterns within the data.
In summary, the contributions of our work are two-fold: (1) We propose a novel graph-based representation of plans for CPA and show that applying graph learning methods simultaneously doubles the performance of predicting OMK and closes the gap to predicting PMK; (2) We report principled analyses across different models and ablations that suggest that learnt ToM features reflect latent patterns in the data with no perceivable link to ToM.

heading: 2 Related Work

heading: 2.1 Dialogue-based Human-AI Collaboration
text: Collaborative dialogue systems are designed to work with humans towards achieving a shared goal (Rich et al., 2001; Bohus and Rudnicky, 2009; Allen et al., 2002; Streeck et al., 2011). Early works were based on scripts (Traum, 2017), employed planning (Papaioannou et al., 2018), or modelled the dialogue as a collection of information states (Larsson and Traum, 2000). More recent work focused on neural sequence-to-sequence models to learn from dialogue corpora (Wen et al., 2015; Dong et al., 2023). Neural approaches have also been explored for collaborative dialogues taking place when participants are working on
a shared artefact within a co-observed environment (Narayan-Chen et al., 2019; Kim et al., 2019; Jayannavar et al., 2020; Bara et al., 2021, 2023). Another line of work explored the role of Theory of Mind (Premack and Woodruff, 1978) in dialoguebased collaboration, focusing on simulated textual environments (Qiu et al., 2022; Zhou et al., 2023), or on human gameplay (Bara et al., 2023).
Our work focuses on the MindCraft environment (Bara et al., 2021, 2023) in which two agents with asymmetric skill sets and knowledge converse to achieve a shared goal in a Minecraft world.

heading: 2.2 Computational Theory of Mind
text: With recent advances in AI, an increasing number of works studied means to equip models with Theory of Mind capabilities based on deep learning approaches (Rabinowitz et al., 2018; Bara et al., 2021; Gandhi et al., 2021; Zhou et al., 2023; Liu et al., 2023; Bortoletto et al., 2024), partially observable Markov decision processes (Doshi et al., 2010; Han and Gmytrasiewicz, 2018) or via Bayesian approaches (Baker et al., 2009; Lee et al., 2019; Buehler and Weisswange, 2020; Fan et al., 2021). Within these, one line of work focused on inferring beliefs, actions, or instructions solely as an observer of agent behaviour (Rabinowitz et al., 2018; Grant et al., 2017; Duan et al., 2022). An emerging second line of work explored ToM from the perspective of interacting agents (Wang et al., 2021; Qiu et al., 2022; Bara et al., 2023), highlighting the significance of ToM in collaborative tasks. Bara et al. (2023) claimed that integrating ToM features improves collaborative plan acquisition (CPA). However, the limits and failure cases of ToM-enabled agents are poorly understood, particularly whether they really model mental states or exploit dataset biases. This work aims to address these concerns and assess ToM modelling on CPA.

heading: 3 Problem Formulation
text: MindCraft (Bara et al., 2021) was introduced as a multi-modal benchmark for studying ToM modelling within collaborative tasks. It involves two players collaborating through dialogue in a 3D block world to craft a target material by manipulating blocks using specific tools (see Figure 3, left). Players initially receive a partial plan as an incomplete directed AND-graph and a tool allowing each to interact with a set of specific blocks. Endowed with complementary knowledge and skill sets, play-
(indicated by ) for a fair comparison with the baseline.
ers must communicate via the in-game chat to craft the target material and reason about each other’s mental states. The ToM tasks introduced by Bara et al. (2021) are specifically designed to capture mental state information pertinent to collaboration. During gameplay, players are presented with popup questions every 75 seconds, each paired by type:
1. Task Status: Predict if one of the two players has created a specific material. For instance, Player 1 is asked: “Has your partner created GOLD_BLOCK so far?” and Player 2 is asked: “Have you crafted GOLD_BLOCK yet?” Possible answers are YES, NO, or MAYBE.
2. Player Knowledge: Predict whether players know how to craft a material or if they believe their partner knows. For example, Player 1 is asked: “Do you think the other player knows how to make BLUE_WOOL?” and Player 2 is asked: “Do you know how to make BLUE_WOOL?” Possible answers are YES, NO, or MAYBE.
3. Player Intention: Predict which material a player is making at the current time step. For example, Player 1 is asked: “What do you think the other player is making right now?” and Player 2 is asked: “What are you making right now?”. Possible answers are the different types of blocks in the game or NOT_SURE.
In this work, we focus on a recent extension of MindCraft by Bara et al. (2023) in which they proposed collaborative plan acquisition (CPA) and
explored the role of ToM modelling in predicting players’ missing knowledge while executing the crafting tasks. CPA is formulated as follows:
Definition 1 Consider a joint plan as a directed AND-graph P = (V,E), where the nodes V denote (sub-)goal materials, and edges E denote temporal constraints between the sub-goals. In a collaborative plan acquisition problem, two agents i and j start with partial plans Pi = (V,Ei), Ei ⊆ E, and Pj = (V,Ej), Ej ⊆ E. Given a sequence of visual observations Oti and a joint dialogue history Dt at time t, agent i has to infer their own missing knowledge Ēi = E\Ei and the partner j’s missing knowledge Ēj = E \ Ej . ToM and CPA tasks are closely related but fundamentally different: ToM tasks focus on exploring players’ beliefs about the game state and their partner’s mental states, while CPA tasks involve predicting missing information from players’ partial plans. Additional details are in §A.1 and §A.2.

heading: 4 Method

heading: 4.1 Baseline
text: As a baseline we used the model proposed by Bara et al. (2023) that embeds dialogue utterances using a frozen pre-trained BERT model (Devlin et al., 2019) and represents each utterance by the features obtained from processing the corresponding [CLS] token using linear layers with tanh activation. A CNN and GRU were used to process the video frames and partial plans, respectively. During training, a model was first trained for each of the three
ToM tasks of §3 as classification tasks, requiring them to predict players’ answers. Afterwards, two separate models were trained on OMK and PMK by feeding the concatenation of the input modalities and the learnt ToM features into an LSTM (Hochreiter and Schmidhuber, 1997) followed by an MLP that outputs softmax scores for each possible missing link.

heading: 4.2 GNN-based Missing Knowledge Prediction
text: Representing Plans as Graphs. We propose a modification to the method by (Bara et al., 2023) that includes representing plans as graph objects and using a GNN-based encoder-decoder together with candidate sampling to predict missing edges (see Figure 2). More specifically, as shown in Figure 3, nodes represent materials, edges connect each material to the prerequisite components for its synthesis, and edge features denote the specific tool needed to interact with the material. This structured representation allows us to more naturally represent the dependencies between materials and information about the tools involved in the crafting process. Most importantly, it allows us to elegantly frame CPA as a link prediction task.
Theory of Mind Modelling. We modified the ToM modelling architecture of Bara et al. (2021) with two key changes: Replacing the GRU plan encoder with GATv2 layers (Brody et al., 2022) and average graph pooling, and substituting the LSTM with a single-block Transformer (Vaswani et al., 2017). The rest of the architecture remains unchanged for a fair comparison.
Missing Knowledge Prediction. By representing plans as graphs we can perform missing knowl-
edge prediction by applying negative sampling – a common technique used for graph completion (Yang et al., 2015; Schlichtkrull et al., 2018). A GNN encoder g first maps each node vi ∈ V to a real-valued vector zi = g(vi) ∈ Rd. We then add Ω negative edges to the original graph. In conventional link prediction, negative edges are sampled randomly starting from the complete graph, and the goal is to classify edges as true or fake. In contrast, our approach begins with an incomplete graph and the task is to predict missing edges. Randomly selecting negative edges poses the risk of missing the edges we aim to predict. Our improved approach uses the plan structural constraints of MindCraft to narrow down the pool of all possible V 2\E{i,j} edges to a set of valid candidates Ω (see Figure 3, right). Specifically, valid candidate start-nodes must have an out-degree smaller than four whereas candidate end-nodes must have an indegree less than or equal to one. We also exclude the starting set of game materials from the candidate end-nodes. We call this technique candidate sampling.
Afterwards, a decoder classifies edges as positive or negative by relying on the node embeddings. In particular, we learn a scoring function s : Rd × Rd → R using a linear layer f that takes as input the concatenation of the two node embeddings corresponding to the candidate edge, and the output c of the sequence model, that serves as a context: s(vi, vj) = ŷij = f(zi⊕zj⊕c), where ⊕ denotes the concatenation operator. In contrast to (Bara et al., 2023) who used an LSTM to process the sequential data, we used a single Transformer block. Finally, we optimise with the binary crossentropy loss function L, which maximises the likelihood of positive edges while minimising that of
Status
Modalities Bara et al. (2023) Ours Human
M 47.7± 0.6 59.9± 0.7 67.0 D+M 45.5± 2.3 59.1± 0.6 67.0 D+V+M 45.2± 1.8 58.9± 0.8 67.0 V+M 47.3± 0.7 59.6± 0.4 67.0
sampled negative edges: L = − ∑
(i,j)∈E log(σ(ŷij))−
∑
(i,k)∈Ω log(1−σ(ŷik))
where σ indicates the sigmoid function. Additional details about the model’s architecture and training are provided in §A.3.

heading: 5 Experiments

heading: 5.1 Theory of Mind Modelling
text: We first report the performance of our model on the three ToM tasks introduced in Section 3. As summarised in Table 1, our model outperforms the baseline1 on all three tasks, underlining the efficiency of the proposed GNN-based approach. Notably, as highlighted in green in Table 1, our model manages to even match human performance in the Knowledge task. However, performance on the other two tasks is still far from a human level, especially on Intention. This might be attributed to the fact that, unlike Knowledge that does not require temporal modelling and could be solved by
1Despite training the baseline model (Bara et al., 2023) using the official code, its performance slightly deviated from the original paper, and discussions with the authors did not yield clarity. See §A.4 for further details and comparisons.
using plan information, both Status and Intention require accurate temporal modelling, which has to be kept coherent across the different input modalities. As can also be seen from the table, ablations of different input modalities have little impact on the final performance of our model and the baseline for all ToM tasks.

heading: 5.2 Collaborative Plan Acquisition (CPA)
text: Subsequently, we evaluate our model on the CPA task following Bara et al. (2023). We always use dialogue moves as input since they were shown to have a positive impact on performance. As can be seen from Table 2, our model consistently achieves overall F1 scores of over 56.6 thereby significantly outperforming the baseline of Bara et al. (2023) in all evaluation settings.
Own Missing Knowledge (OMK). We first analyse the task of predicting one’s own missing knowledge. As can be seen in Table 2, our model manages to double the performance of the baseline2 by consistently achieving F1 scores of over 57%. In stark contrast to the baseline, which performs best when using only ToM features extracted from Intention, our model’s best performance is obtained by additionally incorporating features extracted from Knowledge. The benefit of these features on CPA is expected and intuitively makes sense since Knowledge was the ToM task for which our models achieved human-level performance (see Table 1).
Partner’s Missing Knowledge (PMK). Second, we evaluate the task of predicting the partner’s missing knowledge. In contrast to prior work (Bara et al., 2023), our evaluations reveal a significantly reduced performance gap between predicting the different types of missing knowledge (OMK vs PMK) as can be seen in the second part of Table 2. As highlighted in blue , this can be attributed to our proposed candidate sampling approach that, contrarily to naive sampling, effectively narrowed down the pool of valid candidate edges for one’s own missing knowledge to a similar order of magnitude as that of the partner’s. The difference in performance compared to the baseline is likely due to the choice of cost function used for training.
Statistical Tests. Although our model attained improved results on CPA, especially in predicting one’s own missing knowledge, it did so without
2In this case, the scores are higher than the ones reported in (Bara et al., 2023).
relying much on the learned ToM features. This can be seen from the results of the different ablated versions of Table 2. To study the effect of ToM features on CPA performance, we performed paired t-tests between our model trained without ToM features and versions of our model trained with different sets of ToM features. We can see that the ToM features did not result in any statistically significant performance difference on CPA since all tests resulted in p > 0.05. Notably, performing the significance testing on the baseline model of (Bara et al., 2023) yielded the same behaviour, i.e. p > 0.05 across all model versions. Therefore, we challenge the utility of the ToM features in CPA by posing the question of whether these features represent actual information about mental states or reflect latent patterns in the data. We empirically answer this by performing various principled experiments ranging from diagnostic probing to correlation analysis over substituting ToM features with ground-truth labels.

heading: 5.3 Probing for Theory of Mind
text: Motivated by our results, we formulate the following research question: Does ToM modelling as proposed by Bara et al. (2023) actually capture mental state information? To answer this question, we conducted extensive analyses to study the impact of
ToM modelling on CPA from different angles.

heading: 5.3.1 Diagnostic Probing
text: The ToM features used in CPA are obtained by learning the different tasks of Section 3. As a result, we expect such features to exclusively hold some information about the mental state that other models, when trained on different tasks than ToM, simply lack. To validate this intuitive hypothesis, we used diagnostic probing (Alain and Bengio, 2017; Adi et al., 2017; Conneau et al., 2018; Hupkes et al., 2018) and trained a simple logistic regression (LR) model to perform the three ToM classification tasks. We trained the LR model with different inputs in each experiment and tested its performance on the ToM tasks using the test split. More specifically, we considered four different input scenarios: the vanilla ToM features used in the previous experiments, the hidden representations of the transformer from models predicting OMK and PMK (output of the green model in Figure 2), and finally random noise. As seen in Table 3, a LR model trained on ToM features can perform reasonably well on the three tasks, especially Status. However, when trained with missing knowledge features, i.e. features completely optimised in the absence of ToM, the LR model achieves comparable performance in Knowledge and even better performance in Intention.
These findings open up two possible scenarios: (1) The learnt ToM features are more likely to represent latent patterns in the data with no perceivable link to ToM; (2) ToM capabilities spontaneously emerge from training models on CPA.

heading: 5.3.2 Correlation Analysis
text: In this experiment, we explored whether improvements in CPA tasks correlate with the performance of models on ToM tasks, which are then used to extract ToM features. Intuitively, if the ToM fea-
tures truly benefit the model, we anticipate a strong positive correlation between the performance on the individual task ToM tasks and that of CPA. To validate this, we chose the best-performing model for each ToM feature in CPA and calculated the performance difference relative to the model without any ToM features (refer to Table 2). Next, we calculated the Pearson correlation coefficient to measure the relationship between this difference in performance and the F1 score on ToM tasks. Results for both OMK and PMK are reported in Figure 4. Given that r < 0.3 and p ≫ 0.05 in all cases, we can conclude that there is no correlation between the performance on ToM tasks and improvements on CPA. It is worth noting that for some cases, CPA improved even if the F1 score on ToM was zero (highlighted with red dotted circles in Figure 4).

heading: 5.3.3 Incorporating ToM Ground-Truth
text: In our final experiment, we aim to assess the utility of mental state information in CPA by answering the question: To what extent do models gain from including ground-truth information about mental states? We replicate our experiments from Section 5.2 to explore this. However, instead of the learnt ToM features, we feed models with a onehot encoding of the corresponding ToM questionanswer pair. This encoding process follows the
same methodology employed by Bara et al. (2021). As can be seen from a comparison of Table 4 and Table 2, the baseline and our model trained with ground-truth mental state information consistently under-perform those trained with learnt ToM features on OMK and PMK, respectively. The remaining results are generally on par. Furthermore, upon comparing the initial row in Table 4 with the subsequent rows, we note that incorporating ToM ground-truth yields similar scores to those achieved without, except for the baseline in PMK. This underscores a significant limitation of the ToM task representation: the collected ground-truth mental states are not beneficial for CPA. This finding, in conjunction with our diagnostic probing analysis, suggests that models trained to infer mental states may be learning information more closely associated with other correlations in the data, rather than representing the mental states.

heading: 6 Limits and Future Directions for Neural Theory of Mind
text: A key insight of our work is that current approaches for CPA, rather than learning ToM, seem to merely exploit latent correlations in the data that have little to do with mental states. This is highlighted by the lack of impact of the proposed ToM features on
CPA, as shown in Table 2 and Table 4. This finding is surprising and worrisome at the same time and calls for a fundamental re-assessment of how to equip computational agents with ToM capabilities and how to evaluate them. Despite research on this topic still being in its infancy, the problem of correctly learning neural ToM has recently been put more and more under scrutiny (Sap et al., 2022; Aru et al., 2023). Our results underline in a directly observable way that the acquisition of comprehensive ToM capabilities cannot be reduced to merely passing a specific, narrow set of tasks. The main rationale for this conclusion is that we still do not have a task for which possessing ToM capabilities is both a necessary and sufficient prerequisite for its resolution. Current ToM benchmarks rely on tasks that seem to intuitively require ToM to be solved. However, these tasks can often be solved by just exploiting shortcuts within the data (Le et al., 2019; Aru et al., 2023; Bortoletto et al., 2024). As a result, we posit that directly optimising an agent or system for ToM may not represent an effective approach for progress.
Instead, recent work proposed the use of openended environments to study ToM with the aim of observing whether these capabilities emerge through interactions with other agents (Aru et al., 2023). Minecraft represents a good candidate environment for multi-agent collaboration in an open world. However, the way Bara et al. (2021, 2023) frame MindCraft is still limited to specific tasks and requires extensive data collection efforts. One possible solution could be to transform MindCraft into a reinforcement learning environment with a focus on less constrained collaborative tasks. While Bara et al. (2021, 2023) suggest modelling ToM
as a supervised learning task, the way humans acquire ToM is more nuanced and largely unsupervised (Ruffman, 2023). We believe that the development of open-ended environments combined with learning ToM capabilities in an unsupervised, human-like manner is a more promising direction for future research.
ToM capabilities are deeply linked to language acquisition (Tomasello, 2005). In the context of dialogue-based collaboration, another interesting future direction could be to learn ToM from generation instead of classification (Liu et al., 2023). Current approaches could be further improved by building a more general and robust world model, e.g., by leveraging a pre-trained language or videolanguage model as a more general prior. Finally, in addition to developing suitable environments and learning algorithms, effective and interpretable methods to evaluate whether agents have truly learned ToM will be crucial. We see three exciting directions in this regard: probing (Niven and Kao, 2019), mechanistic interpretability (Wang et al., 2023), and concept learning (Oguntola et al., 2021; Chen et al., 2020). The work of Oguntola et al. serves as an inspiring example, where agents learn human-interpretable concepts that represent beliefs about other agents in a simple multi-agent reinforcement learning setting.

heading: 7 Conclusion
text: In this work, we demonstrated that applying taskspecific constraints to plan graphs reduces significantly the performance gap between predicting OMK and PMK in MindCraft. At the same time, improvements from ToM modelling diminish, raising concerns about current approaches. Our ex-
periments and analyses consistently suggest that current ToM modelling approaches learn features that likely reflect latent patterns in the data, with no perceivable link to ToM. This finding calls for a deeper understanding of the role of ToM in CPA and beyond, as well as for new methods to model and evaluate mental states in collaborative agents.

heading: 8 Limitations
text: We identify two main limitations of our work. First, our strategy of selecting candidate edges for own missing knowledge prediction is specific to the structure of the task as presented by Bara et al. (2021). While we recognise the task-specific nature of our strategy, it is crucial to note that Bara et al. (2023) also leverages task-specific constraints by assuming that the partner’s missing knowledge is present in one’s own. However, our approach can still be used in other settings without the assumption that one’s own missing knowledge covers that of the partner. Crucially, our approach does not challenge or undermine the fundamental conclusions drawn about modelling and evaluating ToM. Neither does it serve as the cause for the diminishing improvements on CPA observed when including ToM features.
Second, our current analysis is limited to the MindCraft dataset. To the best of our knowledge, it is the only environment that studies the role of ToM in CPA making it the natural candidate for our analysis. However, our work lays the basis of a systematic study of ToM in CPA in general and can also inform future work targeting new environments or datasets.

heading: 9 Ethical Impact
text: Our work is foundational, far away from particular applications or any potential societal impact. However, it is important to keep in mind that claims about modelling and predicting mental states potentially have huge ethical impact. Caution is imperative when dealing with sensitive aspects of individuals’ inner experiences and emotions. Mishandling such information could lead to privacy breaches, potential stigmatisation, or the misuse of personal data. Additionally, there is a risk of reinforcing biases or misinterpreting complex psychological nuances, which may have unintended consequences on individuals’ well-being. Lastly, resonating with our findings, the use of models that predict mental states by merely exploiting heuris-
tics and spurious patterns in the data rather than genuinely modelling Theory of Mind introduces significant ethical challenges. Therefore, ethical considerations and responsible practices are crucial to ensure a respectful and appropriate use of technology in this domain.

heading: 10 Acknowledgements
text: M. Bortoletto and A. Bulling were funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No 801708. L. Shi was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – EXC 2075 – 390740016. The authors thank the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for supporting C. Ruhdorfer. The authors would like to especially thank Hsiu-Yu Yang, Manuel Mager, Pavel Denisov, Ekta Sood, and Anna Penzkofer for their support and the numerous insightful discussions.

heading: A Appendix

heading: A.1 MindCraft
text: MindCraft (Bara et al., 2021) is an interactive environment based on Minecraft in which the objective of each game is to create a randomly generated goal material. Some starting materials are already present in the environment, and the others are created by the players by:
• Mining: hit a specific block with a tool to create a new block. This allows to generate infinite new blocks of a certain type and move them around.
• Combining: fuse two materials to obtain a new one.
Players are free to navigate in the environment, move blocks around and chat. Being the field of view first-person, players have partial observability of the environment.
Players possess asymmetric knowledge and skill sets, where each player is provided with a partial plan (such as a partial knowledge graph or recipe) along with a specific tool to interact with certain blocks. Their knowledge and skills are complementary: Player 1’s plan contains the information missing in Player 2’s plan, and vice versa. Likewise, Player 1 can interact with blocks that Player 2 cannot, and vice versa. This inherent asymmetry encourages communication between players and the need to reason about each other’s mental states.
Bara et al. (2021) introduced three ToM question answering tasks that are specifically designed to capture mental state information that is pertinent to collaboration. Players are presented with three questions, each paired by type: if one player is asked about their partner’s beliefs, the other player is presented with the same question regarding their own beliefs (with respect to the same question):
1. Task Status: Predict if a specific material has been created by one of the two players. For example, if Player 1 is asked: Has the other player made GOLD_BLOCK until now?, then Player 2 is asked: Have you created GOLD_BLOCK until now?. Possible answers are YES, NO, or MAYBE. This task probes players’ belief of the game state.
2. Player Knowledge: Predict whether a player knows how to create a specific material or if they believe their partner knows. For example,
if Player 1 is asked: Do you think the other player knows how to make BLUE_WOOL?, then Player 2 is asked: Do you know how to make BLUE_WOOL?. Possible answers are YES, NO, or MAYBE. This task probes players’ belief of their and their partner’s current knowledge.
3. Player Intention: Predict which material a player is making at the current time step. For example, if Player 1 is asked: What do you think the other player is making right now?, then Player 2 is asked: What are you making right now?. Possible answers are the different types of block in the game or NOT_SURE.
Mental state annotations are collected using periodic pop-ups that interrupt the game every 75 seconds.
Computational models are trained and evaluated by predicting the answer to the ToM tasks from a player’s perspective, given a history of observations, the chat dialogue, the perceived actions in the shared environment, and the partial plan. Models are trained to minimise the cross entropy loss. They output c logits, with c being the number of possible classes: three for Status and Knowledge, and 22 for Intention (21 possible materials + NOT_SURE). Models’ final prediction is obtained by taking the argmax of the logits.

heading: A.1.1 Data Modalities
text: The MindCraft dataset comprises various modalities, including first-person video streams for each player, chat dialogue and corresponding dialogue moves, and players’ plans. Bara et al. (2021) established a timestep of ∆t = 1 second, ensuring that each timestep has an associated video frame. However, not all timesteps include dialogue utterances or questions, as players do not necessarily exchange messages every second and questions pop-up every 75 seconds. The players’ plan is static and known from the beginning of the game. The models generate predictions at timestep t, coinciding with when questions are posed to the players. These predictions rely on the player’s plan, video stream, and dialogue history (if available) up to time t.

heading: A.1.2 Dataset Statistics
text: Bara et al. (2021) report that the original MindCraft dataset includes 100 games, with an average of 20.5 dialogue exchanges per game, for a total of 2091 exchanges. Games last between 1 minute and
22 seconds to 27 minutes and 26 seconds, with the average game lasting 7 minutes and 23 seconds. A total of 12 hours, 18 minutes, and 33 seconds of in-game interaction was recorded. Between 5 and 10 objects are used in a game, and between 7 and 11 steps are necessary in each game to achieve the goal. The dataset is randomly partitioned into 60% for training, 20% for validation, and 20% for testing, with the condition to keep similar distributions of game lengths.

heading: A.2 Collaborative Plan Acquisition
text: Bara et al. (2023) extended MindCraft by collecting 60 additional game sessions and defined an additional task: collaborative plan acquisition (CPA). In CPA a model has to predict, from a player’s perspective, its own missing knowledge (OMK) and the other player’s missing knowledge (PMK). CPA was introduced to explore the role of ToM modelling in predicting players’ missing knowledge while executing the crafting tasks. CPA is formulated as follows:
Definition 1 Consider a joint plan as a directed AND-graph P = (V,E), where the nodes V denote (sub-)goal materials, and edges E denote temporal constraints between the sub-goals. In a collaborative plan acquisition problem, two agents i and j start with partial plans Pi = (V,Ei), Ei ⊆ E, and Pj = (V,Ej), Ej ⊆ E. Given a sequence of visual observations Oti and a joint dialogue history Dt at time t, agent i has to infer their own missing knowledge Ēi = E\Ei and the partner j’s missing knowledge Ēj = E \ Ej .
Predictions for OMK and PMK are made at t = T , where T is the final timestep of the game.
While intrinsically linked, ToM and CPA tasks exhibit a fundamental distinction: ToM tasks directly explore players’ beliefs regarding the game state and their partner’s mental states, whereas CPA tasks involve predicting the absent information from players’ partial plans. In ToM tasks, the ground truth is based on players’ beliefs, which may be true or false, whereas in CPA tasks, the ground truth is formally determined by Ēi = E\Ei for OMK and Ēj = E \ Ej for PMK. Bara et al. (2023) discuss the partial overlap between Task Knowledge and PMK, highlighting their difference: Task Knowledge probes whether a single piece of knowledge is known by the partner, while PMK involves predicting whether the partner shares each piece of the player’s knowledge.

heading: A.2.1 Data Modalities
text: CPA is conducted in the MindCraft environment, therefore the data modalities utilised mirror those in the ToM tasks: first-person video streams for each player, chat dialogue along with corresponding dialogue moves, and the players’ plans. In addition to the aforementioned modalities, models for CPA receive ToM features extracted from the sequence-to-sequence model trained on the ToM tasks discussed in §A.1. These ToM features are tensor representations of dimension 1024 that are incorporated into the model’s input. A timestep of ∆t = 1 second is maintained. In contrast to the ToM tasks, CPA models generate predictions at timestep t = T , i.e., at the end of each game.

heading: A.2.2 Formalising ToM Tasks
text: Based on the formalism introduced for CPA, we can formalise the ToM tasks as follows:
1. Task Status: Predict if a specific material Vk ∈ V has been created by one of the two players.
2. Player Knowledge: Predict whether a player knows how to create a specific material Vk, i.e.,
{enVk}n>1 ?∈ Ei
or if they believe their partner knows, i.e.
{enVk}n>1 ?∈ Ej ,
with eVk ∈ E being an edge with end-node Vk and n being the number of materials needed to craft Vk.
3. Player Intention: Predict which material Vk ∈ V a player is making at the current time step t.

heading: A.3 Technical Details

heading: A.3.1 GNN Plan Encoder
text: We propose a modification to the method by Bara et al. (2023) that includes representing plans as graph objects and using a GNN-based encoderdecoder together with candidate sampling to predict missing knowledge, i.e., missing edges (see Figure 2).
In the encoding phase, given a graph, we compute the node embeddings using GATv2 convolutions (Brody et al., 2022). The node features (one-hot encoding of materials) are first projected using a single linear layer with hidden dimension 128, followed by GELU activation and dropout. The same procedure is applied to edge features
(one-hot encoding of tools). Then the first GATv2 convolution is applied, which has hidden dimension 128, four heads, GELU activation and dropout. The final node embeddings are generated by a second GATv2 convolution with output dimension 128 and one head.
In the decoding phase, we evaluate potential missing edges by scoring them against the relevant node embeddings and the context vector. This involves combining the two node embeddings associated with the edge and the context vector, then passing the resulting concatenation through a linear layer with an output dimension of one. The output logits are subsequently fed into a sigmoid function with a threshold of 0.5 to determine whether the edge exists or not.

heading: A.3.2 Transformer
text: We use a single-block Transformer (Vaswani et al., 2017) with output dimension 1024 as sequence-tosequence model. The input consists of concatenated features from various modalities, such as video, dialogue, plan graph, and dialogue moves (and ToM features in the case of CPA), as depicted in Figure 2. Our Transformer incorporates positional encoding (Vaswani et al., 2017) and utilises
a causal attention mask to ensure that each token attends only to previous tokens during self-attention computation. We utilise eight attention heads to compute attention scores over the concatenated input features, including ToM features for CPA tasks. This ensures that the model attends to ToM features. Following the baseline models (Bara et al., 2021, 2023), our models utilise zero-padding when an input modality is absent.

heading: A.3.3 Training
text: Models are trained using PyTorch (Paszke et al., 2019) with 1, 42 and 123 as random seeds. All models were trained on a single GPU card, taking approximately 60 minutes for the baselines (17,946,302 parameters) and our models (9,222,100 parameters) on ToM. For CPA, training takes approximately 60 minutes for the baselines (33,698,691 parameters) and 20 minutes for our models (13,364,641 parameters). For the baselines (Bara et al., 2023), we used default parameters reported in the code. For our models, we used the Adam optimiser (Kingma and Ba, 2015) with β1 = 0.9, β2 = 0.99, ϵ = 10−8, and a learning rate of η = 1 ·10−4. We did not perform any exhaustive hyper-parameter tuning but just tried a set of reasonable values: {1 · 10−5, 5 · 10−4, 1 · 10−4, 5 · 10−4}.

heading: A.4 Comparison to Bara et al. (2023)
text: Although we trained the baseline of (Bara et al., 2023) using the official code3 with default hyperparameters, its performance slightly deviated from the original paper. We contacted the authors asking for clarifications and details that are not documented in the paper/code. Discussions with them did not yield a clear answer, and they were unable to provide their model files. Therefore, in Table 1 and Table 2 we provided results obtained from our runs, reproducible by using our code provided as supplementary material. In the interest of completeness, we include a comparison between our results and those reported by Bara et al. (2023) in Table 5 for ToM tasks and in Table 6 for CPA tasks. On the ToM tasks, the scores achieved by our model are generally on par with those reported by Bara et al. (2021). On CPA, our model still outperforms the baseline of Bara et al. (2023) that, based on the originally reported scores, on average performs slightly worse in some tasks (see Table 6, Overall).
3https://github.com/sled-group/ collab-plan-acquisition
ToM Features Overall OMK PMK
Status Knowledge Intention Bara et al. (2023) Ours Bara et al. (2023) Ours Bara et al. (2023) Ours
44.1± 0.6 56.9± 0.6 16.7± 0.1 57.6± 0.8 71.4± 1.0 56.2± 0.3 ✓ 45.9± 1.5 57.3± 0.6 20.4± 1.4 58.0± 0.8 71.3± 1.6 56.5± 0.3
✓ 47.2± 1.1 57.0± 1.4 20.1± 1.4 58.4± 0.5 74.3± 0.7 55.5± 1.9 ✓ 47.4± 1.4 57.2± 0.5 19.8± 1.7 57.9± 0.7 75.0± 1.0 56.5± 0.3
✓ ✓ 47.0± 1.4 56.6± 1.4 20.9± 1.2 57.7± 0.5 73.1± 1.5 55.5± 1.9 ✓ ✓ 45.9± 1.2 57.5± 0.6 19.8± 0.8 58.4± 0.8 71.9± 1.5 56.5± 0.3 ✓ ✓ 46.9± 1.5 57.5± 0.6 20.3± 1.8 58.5± 0.8 73.4± 1.2 56.4± 0.1 ✓ ✓ ✓ 45.5± 0.3 56.7± 0.7 17.4± 0.1 57.1± 1.9 73.5± 0.5 56.6± 0.2
Table 6: Performance comparison on CPA when training with learnt ToM features. F1 scores for the baseline are reported from the original paper (Bara et al., 2023) rather than from our execution of the official code.
gold shovel and gold pickaxe i have iron shovel iron and soul sand for redstone do you now how to make diamond block? yep lime and redstone make diamond
Has the other player made WHITE_WOOL until now? NO Do you think the other player knows how to make LIME_WOOL? YES What do you think the other player is making right now? NOT_SURE Have you created WHITE_WOOL until now? NO Do you know how to make LIME_WOOL? YES What are you making right now? DIAMOND_BLOCK
how do we make a diamond block? we need another redstone redstone and lime
Has the other player made REDSTONE_BLOCK until now? YES Do you think the other player knows how to make DIAMOND_BLOCK? NO What do you think the other player is making right now? REDSTONE_BLOCK Have you created REDSTONE_BLOCK until now? YES Do you know how to make DIAMOND_BLOCK? YES What are you making right now? LIME_WOOL
can you put the lime wool on this redstone block? we made the goal material yay lets go
Player 1
Player 2
It is important to node that our main contributions remain unaffected by this mismatch: First, our improvement on OMK stands, both if we compare our baseline results and those reported in Bara et al. (2023). Notably, our results for the baselines (∼ 0.28) are higher than the ones in the original paper (∼ 0.21). Second, our analyses are not contingent on absolute results but rather on the relationship with the ToM tasks.

heading: A.4.1 Qualitative Example
text: Figure 5 shows the chat from a game in which our ToM model cannot solve the Player Intention ToM task. However, on the same game, integrating the corresponding ToM features into the CPA model enhances the performance on the PMK task by approximately 10 points. This particular game
instance is highlighted by the dotted red circle in the rightmost plot of Figure 4. We speculate the ToM model’s struggle with the Player Intention task may arise from the initial game part where players’ beliefs are misaligned, which could result in a false belief (cf. Figure 5). Despite this, the CPA model still benefits from the inclusion of ToM features, suggesting that ToM models may actually be learning information that is more closely associated with other correlations in the data, rather than representing the mental states.

heading: A.5 Tools
text: We performed our data analysis using NumPy (Harris et al., 2020), Pandas (pandas development team, 2020; McKinney, 2010), and SciPy (Virtanen et al., 2020). Figures were made using Matplotlib (Hunter, 2007).
A.6 Infrastructure We ran our experiments on a server running Ubuntu 22.04, equipped with NVIDIA Tesla V100-SXM2 GPUs with 32GB of memory and Intel Xeon Platinum 8260 CPUs.

heading: Future Work
text: However, our work lays the basis of a systematic study of ToM in CPA in general and can also inform future work targeting new environments or datasets