Inference of Evolving Mental States from Irregular Action Events to Understand Human Behaviors

We first thank reviewer 1Fue for the meticulous analysis and insightful comments, especially for the questions about details of our model and potential extension, which benefit us to further clarify our paper. We would like to address the concerns one by one.

In response to your mentioned weaknesses:

W1: Compared to traditional imitation learning models, our proposed model integrates human mental processes into behavior generation. In contrast to thought clone models that rely on supervised learning and necessitate actual human thought data for training, our method enables the inference of unobserved mental processes from observed human actions in an unsupervised manner. Our approach eliminates the need for human thought data, which is often difficult to acquire in real-world scenarios.

Moreover, both imitation learning and thought cloning typically operate in discrete-time settings, neglecting the irregular occurrence nature of human thought processes reflected in irregular event-to-event time intervals. Our model, on the other hand, addresses mental event inference in a continuous-time framework, capturing the evolving nature of these processes over time.

In terms of interpretability, our approach, with the incorporation of logic rules, excels in explaining the intricate triggering mechanisms between mental processes and action processes. In contrast, imitation learning and thought cloning models lack this capability.

W2: In the revised paper, we have outlined the computational requirements in Appendix J and presented scalability and computational cost experiments in Appendix H. In scalability experiments, we have expanded our evaluation to include two additional synthetic datasets and two real-world datasets with varying sample sizes. The new synthetic datasets encompass intricate rules and enlarged latent state domains. Additionally, we augmented the data sequences for the Hand-Me-That and Car-Following datasets to assess our model's scalability to handle extensive real-world datasets. Here, we present our experimental results from both small and large datasets to showcase our findings.

For small-scale real-world dataset, our model adeptly handles challenges posed by small datasets. Even with a dataset size of only 1000 samples, our model delivers satisfactory results. For the Hand-Me-That dataset with 1000 samples, the ER% and MAE are 73.25% and 1.22. For the Car-Following dataset with 1000 samples, the ER% and MAE are 35.38% and 2.12, which are comparable with the majority baselines trained with larger sample size.

For large-scale real-world dataset, the ER% and MAE decrease to 68.19% and 1.13 for Hand-Me-That dataset with 5000 samples. And these two metrics decrease to 30.18% and 1.69 for the Car-Following dataset with 5000 samples. Even on large-scale datasets, our algorithm converges relatively quickly with current computational infrastructure, indicating the ability of our proposed model to handle large-scale real-world datasets. This is attributed to our backtracking mechanism's ability to adjust the number of backtracking rounds as the data volume grows, and the constraints of rule length to reduce search space, thereby mitigating computational complexity to some extent.

Across all four datasets, model's prediction performance enhances as sample sizes increase, while maintaining acceptable time costs, showcasing its good scalability.

W3: Although we incorporate rule templates as priors to utilize rich domain knowledge of the application, our rule-generation algorithm is inherently capable of learning rules from scratch, even in scenarios with limited prior knowledge. By leveraging column-generation framework, the algorithm can autonomously discover and refine new rules, with its accuracy improving as more data becomes available. Additionally, standard techniques such as constraining rule lengths ensure computational efficiency and prevent an excessively large search space.

In practice, we can employ two complementary strategies tailored to different problem settings: autonomous rule learning for data-rich domains and template-guided learning for scenarios with limited data but abundant prior knowledge.

In our response to Reviewer orep, W7, we have evaluated the effectiveness of our model in scenarios with and without predefined rules, across different sample sizes. Please refer to the table for detailed experiment results and corresponding analysis. Briefly, with same training samples, not providing prior rule templates during training leads to basically satisfactory model performance, but increased training time. When increasing the training sample size without prior rule templates, the model exhibits a notable improvement in converged negative loss and prediction accuracy, approaching or even matching the model performance achieved with prior rule templates on a smaller dataset, showing good ability to adapt to data lacking prior knowledge.

Continuing with W3: Moreover, many works also extract prior logic rules from expert knowledge, regulations, or statistical findings to guide models across various domains and tackle challenges posed by limited data [1, 2, 3, 4]. In high-stakes scenarios, incorporating prior knowledge enables our model to align well with human cognition and learning processes and tackle limited data issues.

[1] Liu, J., Wang, H., Cao, Z., Yu, W., Zhao, C., Zhao, D., ... & Li, J. (2023). Semantic traffic law adaptive decision-making for self-driving vehicles. IEEE Transactions on Intelligent Transportation Systems.
[2] Li, Shuang, et al. "Temporal logic point processes." International Conference on Machine Learning. PMLR, 2020.
[3] Zhang, Yizhou, Karishma Sharma, and Yan Liu. "Vigdet: Knowledge informed neural temporal point process for coordination detection on social media." Advances in Neural Information Processing Systems 34 (2021): 3218-3231.
[4] Marinescu, Radu, et al. "Logical credal networks." Advances in Neural Information Processing Systems 35 (2022): 15325-15337.

W4: Thanks for your advice! We have adapt the suggested models to our datasets with same sample size as in Table 1 and Table 2. We use the metric of success rate (SR) as the key comparison metric. For these models, we hide the event time point information but retain the ordering of events and event type information. Then we can use these models for predicting next action tasks. Given that the Thought Cloning model [6] relies on human thought data (which our model does not require), we assume that the thought event occurs immediately before each action.

In our synthetic dataset experiments, our model outperforms all baselines in terms of success rate. Due to the absence of human thought data for fair comparison, the thought cloning model performs less effectively on all real datasets compared to other models. For the Hand-Me-That dataset, FISER achieved the highest success rate, with our model and the Rule-based ToM model achieving similar success rates. On the Car-Following and Epic-Kitchen datasets, our model achieves success rates close to FISER and outperforms other models. Specifically, on the Car-Following dataset, our model achieves a success rate of 67.28%, higher than FISHER's 66.67%. On the Epic-Kitchen dataset, our model achieves a success rate of 59.74% close to FISHER's 61.28%. Additionally, on the MultiTHUMOS dataset, our model attains the highest success rate.

Encouragingly, our model has demonstrated competitive performance on both synthetic and real-world datasets. Moreover, it has an additional advantage of predicting future event times, including the timing of goal achievement in the baseline scenarios we examined, a capability absent in other models. Furthermore, in addition to Rule-based ToM, the other two models also lack interpretability compared to our rule-based predictions. Our model can effectively enhance our understanding of the underlying reasons for predictions through logic rules.

[6] Hu, S., & Clune, J. (2024). Thought cloning: Learning to think while acting by imitating human thinking. Advances in Neural Information Processing Systems, 36.
[7] Cao, C., Fu, Y., Xu, S., Zhang, R., & Li, S. (2024). Enhancing Human-AI Collaboration Through Logic-Guided Reasoning. In The Twelfth International Conference on Learning Representations.
[8] Wan, Y., Wu, Y., Wang, Y., Mao, J., & Jaques, N. (2024). Infer Human's Intentions Before Following Natural Language Instructions. arXiv preprint arXiv:2409.18073.

Dear Reviewer 1Fue,

We would like to express our gratitude once more for the constructive feedback and prompt response to this paper. We will also ensure the extra results and discussions will be updated in the revised manuscripts.

Warm regards,

The Authors

We are grateful for your careful review! We will address your concerns from the following aspects.

In response to your mentioned weaknesses:

W1 & W3: Although in our current work we incorporate rule templates as priors to harness domain knowledge, our rule-generation algorithm is inherently capable of learning logic rules from scratch, even in scenarios with limited prior knowledge. Utilizing the column-generation framework, the algorithm autonomously uncovers and refines new rules, with its accuracy improving as more data becomes available. Additionally, standard techniques such as constraining rule lengths ensure computational efficiency and prevent an excessively large search space.

In practice, we can employ two strategies tailored to distinct scenarios: autonomous rule learning for data-rich domains and template-guided learning for scenarios with limited data but ample prior knowledge.

In our response to Reviewer orep, W7, we evaluate the effectiveness of our model in scenarios with and without predefined rules, across different sample sizes. Please refer to the table for detailed experiment results.

The results demonstrate that under the same training sample cases, not providing prior rule templates during training leads to basically satisfactory prediction accuracy and convergence negative loss, but increased training time. When increasing the training sample size without prior rule templates, the model exhibits a notable improvement in converged negative loss and prediction accuracy, approaching or even matching the model performance achieved with prior rules on a smaller dataset. Therefore, with ample data, our model can deliver strong performance even without prior knowledge.

If the quality or quantity of predefined rules is low, the presence of the backtracking mechanism can also help improve model performance. In our response to Review 1Fue, Q1, we have added more experiments to assess the effect of the backtracking mechanism and predefined rule templates. The results indicate that reducing the quantity of predefined rules, coupled with appropriately configured backtracking rounds, can still yield a higher converged negative loss and prediction accuracy comparable to cases with more predefined rule templates and less backtracking rounds.

W2 & Q4: Thanks for your advice! Adding a priority filtering mechanism would be a promising approach to improve the efficiency of the backtracking mechanism. We can establish predefined filtering mechanisms based on logic rules to selectively discard certain events during the backtracking process with tunable probability thresholds. This approach may enhance efficiency while maintaining exploration capabilities.

During the rebuttal phase, we have incorporated ablation studies to evaluate how the number of backtracking rounds and the prior logic rule templates affect the model performance and computational efficiency. Please refer to our reply to Review 1Fue, Q1 for the detailed experimental results.

Due to the sparse nature of mental events, in most cases, the backtracking mechanism does not trigger a resampling process. Therefore, the introduction of a backtracking mechanism will not excessively deplete computational resources. The experimental results also confirm this point, by setting a reasonable number of backtracking rounds, we enhance model performance with only a slight increase in computational time. Additionally, increasing the number of backtracking rounds does not excessively raise computational cost.

Considering the impact of prior rule templates, when holding the backtracking rounds unchanged, reducing the provided prior rule templates can somewhat diminish model performance. However, under the same set of provided prior rules, such as offering only one prior rule, increasing the backtracking rounds from 1 to 3 elevates the converging negative loss from -22.72 to -18.43. Therefore, the results demonstrate that the presence of the backtracking mechanism helps mitigate the decrease in model performance caused by the lack of well-defined prior rules.

In response to your questions:

Q1: Firstly, we want to clarify that the probabilities of our model's latent mental processes and the intensities of the action processes are non-negative. Considering the resolution of the discretized time grid is not infinitesimal, theoretically, infinite loops should not occur. Moreover, we have considered multiple possible ways to improve the accuracy of the backtracking mechanism:

• Logic-based Event Selection: we can filter some events based on the learned or predefined logic rules.
• Learn from Failures: we can maintain a history of failed sampled events to avoid making the same mistakes again.
• Conflict-Directed Backtracking: we can backtracking more than one level if inference and prediction are not stable.

Q2: In Appendix B, we have provided details of our rule generator. For the rule generation process, we first extract temporal logic rule templates from prior knowledge, such as expert knowledge. We can also learn temporal logic rules starting from a blank template. Then we use the column generation algorithm to generate temporal logic rules. The algorithm alternates between the rule generation stage and the rule evaluation stage [1]. In the rule evaluation stage, we solve the restricted master problem which evaluates the current rules (updates rule base and rule weights) by maximizing the likelihood:

$\text{Restricted Master Problem}: \mu^*_k, w^*_k = argmin -l(\mu, w) + \Omega(w),\ s.t.,\ w_f \geq 0, f \in F_k$

where $F_k$ is the current rule set, $l(\mu, w)$ is the log-likelihood derived by Equation (3) in our paper, and $\Omega(w)$ is a convex regularization function on the rule length.

In the rule generation stage, we solve the subproblem to search and construct a new temporal logic rule based on the given template (or blank template).

$\text{Sub Problem}: min_{\phi_f} -\frac{\partial l(\mu, w)}{w_f} + \frac{\Omega(w)}{w_f} |_{\mu^*_k, w^*_k}$

The rule generator module act as a plug-in module, if prior rule templates were given, we can consider adding and removing predicates and corresponding temporal relations to refine the prior knowledge in sub-problem. Or freeze the rule generator module and solely rely on the prior knowledge to guide the generating process. If prior rule templates were not given, we can still use the rule generator to search the rule from scratch.

[1] Li S, Feng M, Wang L, Essofi A, Cao Y, Yan J, & Song L (2021, October). Explaining point processes by learning interpretable temporal logic rules. In International Conference on Learning Representations

Q3: For different situations or datasets, our proposed model needs to specify different logic rule templates for different datasets which should be easily obtained from common sense, expert knowledge, government regulations, and literature references. Simultaneously, in cases where we lack sufficient prior knowledge, our model can also learn rules from blank templates, without the need of predefined rules.

In high-stakes scenarios, it is common that many existing works predefine various logic rules as prior knowledge across different domains to boost model performance. For instance, in [2], traffic laws were formalized using linear temporal logic based on government regulations and expert knowledge. In [3], domain knowledge summarized by human experts in the form of first-order logic rules was incorporated to model event dynamics via intensity function. The proposed model in [4] encoded prior knowledge as temporal logic and power function, facilitating the learning of neural point process models for inferring coordinated behaviors in social media. Additionally, [5] utilized imprecise expert knowledge in first-order logic formulas to specify a set of probability distributions over all its interpretations. Similar to these work, our proposed model also incorporates prior knowledge in first-order logic form for different scenarios.

[2] Liu, Jiaxin, et al. "Semantic traffic law adaptive decision-making for self-driving vehicles." IEEE Transactions on Intelligent Transportation Systems (2023).
[3] Li, Shuang, et al. "Temporal logic point processes." International Conference on Machine Learning. PMLR, 2020.
[4] Zhang, Yizhou, Karishma Sharma, and Yan Liu. "Vigdet: Knowledge informed neural temporal point process for coordination detection on social media." Advances in Neural Information Processing Systems 34 (2021): 3218-3231.
[5] Marinescu, Radu, et al. "Logical credal networks." Advances in Neural Information Processing Systems 35 (2022): 15325-15337.

Thank you for your reply and I will keep my scores.

Dear Reviewer gQch,

We deeply appreciate your positive comments and valuable feedback. We will also ensure to incorporate the improvements in the final version.

Warm regards,

The Authors

We thank reviewer 4kqs for the time of reviewing and the constructive comments! We will address your concerns below.

W1: Paper Clarity: We apologize for any unclarity in our paper. In the revised version, we have included more in-depth insights into the underlying mechanisms, motivations, and interconnections among the various modules of the model. The updated paper has been re-uploaded.

W2: Generative v.s. Predictive: First, generative models are highly effective for predictive tasks, often complementing predictive approaches, particularly in sequential settings (e.g., deep autoregressive models, which are generative models, used for predicting future sequences).

Our model employs a generative approach for both actions and mental states, serving distinct purposes. For actions, the generative process predicts future events by sampling from their conditional probability distribution, enabling accurate forecasting of behavior. For mental states, the generative approach facilitates learning and inference by sampling latent trajectories from an approximate posterior distribution, as the true posterior lacks a closed form. These sampled trajectories allow the model to marginalize over the posterior effectively, supporting both the understanding of latent cognitive processes and the prediction of observable actions.

W3: Insight for Backtracking Mechanism: In a nutshell, the primary motivation behind incorporating the backtracking mechanism is to prevent the omission of the crucial yet sparse mental events. In real-life scenarios, human behavior evolves with changing thoughts. Considering the example mentioned in Section 3 Discrete-Time Renewal Process in our paper, if someone is thinking about starting an exercise routine, typically, they are likely to promptly begin exercising. However, if they experience a shift in mindset, such as feeling tired, they might struggle to maintain a consistent exercise routine. Therefore, these shifts in thinking are typical and should be noted, as humans frequently ponder prior thoughts before making definitive decisions.

We introduce a backtracking mechanism based on this human cognitive and behavior logic. When sampling actions, it's hard to ensure that new thoughts won't arise between consecutive actions. Hence, the backtracking mechanism is utilized to examine if new thoughts have emerged during this time interval. If so, these are considered and actions are resampled. Through iterative backtracking, sampled actions can be refined continuously and newly emerged thoughts are not overlooked, enhancing adaptability to real-time fluctuations in human behavior.

W4: Generating from the Candidate Pool vs. Novel Action/Mental Events: In our framework, actions and mental states are generated within a predefined candidate pool, reflecting a closed problem where all possible actions and mental events are specified in advance.

While our current approach is grounded in a closed setting, the framework could be extended to open-ended problems by introducing predicate invention mechanisms for generating novel mental states. We agree with the reviewer that such an extension would make the model more flexible and more capable of handling dynamic, real-world scenarios.

W5: Our claim about understanding: Even within the closed problem setting, we assert that our framework can still understand human behavior. This understanding is achieved in two significant ways:

• Learning Rule Content: The model uncovers the underlying structure of human decision-making by learning the content of behavioral rules—how actions are generated and how they depend on inferred mental states.
• Personalized Rule Usage: Beyond the rules themselves, the model also learns individual preferences in applying these rules. By modeling the conditional probability of actions and mental states, the framework understands the evolution of human thoughts and captures how different humans prioritize and weigh various rules, reflecting personalized behavioral patterns.

Dear Reviewer 4kqs,

We thank reviewer 4kqs for the prompt response to this paper. We wonder whether our response has addressed your concerns.

In our response, we have:

(1) improved the writing of our paper and uploaded the revised version.
(2) clarified the distinct roles of generative process in predicting action events and inferring latent mental events.
(3) detailed the high-level motivation behind the proposed backtracking mechanism and highlighted its alignment with human cognitive and behavioral logic.
(4) clarified that our framework understands human behavior by learning rule content, modeling probability of actions and mental states, and capturing personalized rule usage.

We sincerely inquire if reviewer 4kqs has any additional concerns, and we are more than willing to provide corresponding response. Thank you!

Best regards,

The Authors

We sincerely thank you for your insightful reviews! We hope our response below addresses your concerns.

W1: We apologize for any ambiguity in our paper. In the revised version, we have improved clarity by offering deeper insights into the proposed model and enhancing the logical flow between sections. The revised version has been uploaded.

W2: Thank you for pointing it out! We have revised the sentence to "Define an action set…" in the updated version.

W3: We use the hazard function to model the instantaneous event probability because it effectively captures dynamic event likelihoods over time.

By definition, the hazard $h(t):=\frac{p(t)}{S(t)}$, where $p(t)$ represents the probability of an event occurring at the specific time $t$, and $S(t)$ is the survival function, indicating the probability that no event has occurred up to time $t$.

The reason we use the hazard function to model event rates is that it effectively captures the evolution of action or mental states based on the elapsed time since the last event. Moreover, the hazard function can be adapted by incorporating historical or external features, enhancing the model's flexibility to account for varying dynamics.

We use a discrete-time hazard function to model the occurrence probability of hidden mental events and a continuous-time hazard function to model the occurrence rate of action events.

• Justification for discrete-time hazard function: By discretizing time and utilizing the renewal process framework, we gain computational tractability, making it feasible to infer latent mental states over time.
• Justification for continuous-time hazard function: The continuous-time hazard function allows us to model real-time event predictions for action events, accommodating their continuous and dynamic nature.

This dual approach ensures an effective and computationally efficient model for both mental and action events. We have added this detailed explanation in our revised paper, please refer to Section 3.

W4: The resetting of the survival process after an event is intrinsic to the renewal process definition. According to renewal property: In a renewal process, the occurrence of an event marks the end of one cycle and the start of another. As defined in Equation (1), the survival function $S\left(t_{\xi}\right)$, which represents the probability that no mental event has occurred up to time $t_{\xi}$, is reset to 1 immediately after an event.

Equation (2) defines the event probability $p_{\xi}=S\left(t_{\xi-1}\right)-S\left(t_{\xi}\right)$, which approximates the likelihood of an event occurring in the interval $V_{\xi}$. After an event, $S\left(t_{\xi}\right)$ resets to 1 at the next interval, ensuring that both the survival and event probabilities reflect the reset process. We have also added the corresponding analysis in Section 3 in our revised paper.

W5: We use the embeddings for the observed action time as defined in Equation (4) to capture the information of the action sequence on the spanning time horizon and address irregularities. The embedding method we used in our paper is commonly employed in attention mechanisms for processing sequential event data [1, 2]. This temporal encoding preserves sequence order, encodes temporal information, handles irregular time gaps, aids the attention mechanism in capturing long-range dependencies between events, and reduces symmetry in self-attention mechanisms.

[1] Zuo, S., Jiang, H., Li, Z., Zhao, T., & Zha, H. (2020, November). Transformer hawkes process. In International conference on machine learning (pp. 11692-11702). PMLR.
[2] Yang, C., Mei, H., & Eisner, J. (2021). Transformer embeddings of irregularly spaced events and their participants. arXiv preprint arXiv:2201.00044.

W6: We sample the mental event type according to Equation (8) using the Gumbel-Softmax trick [3], which is a method used to approximate the sampling of discrete variables with a continuous relaxation, enabling the backpropagation of gradients through the sampling process. This trick ensures end-to-end differentiable during the training of neural networks involving discrete outputs, such as when sampling discrete mental event types in our scenario. The reason for using log probabilities is to ensure numerical stability. In mathematically form, this trick can be written as $y_i = \frac{\exp((\log(\pi_i) + g_i) / \tau)}{\sum_{j=1}^k\exp((\log(\pi_j) + g_j)/\tau)}, \text{for}\ i=1,...,k$ where $g_i$ is the Gumbel noise, $\pi_i$​ is the probability of category $i$, and $\tau$ is the temperature parameter that controls the smoothness of the softmax. Our Equation (8) is based on this initial formula.

[3] Jang, E., Gu, S., & Poole, B. (2016). Categorical reparameterization with gumbel-softmax. arXiv preprint arXiv:1611.01144.

W7: Although in our current work we incorporate rule templates as priors to leverage the rich domain knowledge of the application, our proposed rule-generation algorithm is inherently capable of learning logic rules from scratch, even in scenarios with limited prior knowledge. By leveraging the column-generation framework, the algorithm can autonomously discover and refine new rules, with its accuracy improving as more data becomes available. Additionally, standard techniques such as constraining rule lengths ensure computational efficiency and prevent an excessively large search space.

In practice, we can employ two complementary strategies tailored to different problem settings: autonomous rule learning for data-rich domains and template-guided learning for scenarios with limited data but abundant prior knowledge.

To assess our model's efficacy in scenarios without predefined rules, we have conducted an ablation study in Appendix I to evaluate its performance without prior logic rule templates. Below, we present expanded results on Syn Data-1 across various sample sizes.

With 2000 training samples and no prior rule templates provided, there was a minor accuracy decrease in the prediction task, but the model still achieved an ER% of 43.76% and an MAE of 2.58. Increasing the training samples to 5000 without prior rule templates led to an improvement in the model's negative loss at convergence from -19.24 to -18.25. The model's performance in the prediction task also improved, with the ER% and MAE reaching 42.33% and 2.39, respectively. Encouragingly, these results closely approach those achieved with 2000 samples and provided prior rule templates. These results showcase that our model provides viable strategies for handling scenarios where prior knowledge is lacking. Furthermore, with sufficient data, our model can achieve good performance even in the absence of prior knowledge.

For scenarios with limited data but ample prior knowledge, we can employ an alternative strategy to integrate prior knowledge. In Appendix.H, the results of the scalability experiment demonstrate that our model can handle limited data issues. For instance, with prior rule templates provided, reducing the sample size from 2000 to 1000 resulted in only a slight increase of 2.25% in ER% and 0.19 in MAE for Syn Data-3, and a 2.36% increase in ER% and 0.25 in MAE for Syn Data-4 (Syn Data-3 and Syn Data-4 are datasets with more complex ground truth rules and larger domains for latent mental states). These results demonstrate the robustness of our model with small datasets.

Overall, We can appropriately select remedies for providing prior knowledge to the model based on varying dataset sizes and levels of prior knowledge.

W8: Thanks for your suggestion! In our experiment, we use metrics such as training negative loss, training time, and prediction accuracy to select appropriate resolution of a discretized time grid. The choice of resolution balancing accuracy and sample efficiency. For example, in experiment on Syn Data-1, we use grid search for the resolution and the results are as follows:

From the results one can see that under current selection of 0.50, the proposed model achieves the second highest negative loss. Reducing the resolution to 0.25 only marginally increases the negative loss to -16.90, but extends the model convergence time by 1.70 hours. Conversely, while increasing the resolution can only slightly shorten training time. Moreover, it only slightly increase the model's converged negative loss and result in a decline in prediction accuracy when using the well-trained model for prediction tasks. This could be due to missing some crucial latent mental events. Hence, balancing between accuracy and computational efficiency, we opt for the current resolution of 0.5. This strategy is applied consistently for other datasets to determine the resolution.

Dear Reviewer orep,

We thank reviewer orep for the time of reviewing and the constructive comments. We really hope to have a further discussion with reviewer orep to see if our response resolves the concerns.

In our response, we have:

(1) enhanced clarity, delved deeper into the model, and improved coherence across sections in our paper. We have also uploaded the revised version.
(2) explained the hazard function and reset mechanism in discrete-time survival processes, elucidated the embedding technique for temporal event sequences, and detailed the gumbel-softmax trick.
(3) clarified that our model excels in autonomous rule learning for data-rich domains, and template-guided learning for scenarios with limited data but abundant prior knowledge. Additionally, we extended the ablation study to evaluate our model's effectiveness in scenarios lacking prior knowledge, showing its ability to perform well even in the absence of prior knowledge within a reasonable training timeframe.
(4) clarified that we determined the resolution of the discretized time grid based on metrics like training loss, time, and prediction accuracy, supported by corresponding experimental results.

We genuinely hope reviewer orep could kindly check our response. If reviewer orep has any further questions, we are more than willing to response. Thanks!

Best regards,

The Authors

Dear Reviewer orep,

Thank you very much for your commitment and effort in evaluating our paper. We understand that this is a hectic time, and we are writing to gently remind you about providing your insights on our rebuttal. As the discussion phase is drawing to a close, your feedback would be invaluable to us.

Should you have any further thoughts or recommendations about our work, we are eager to discuss them with you.

We eagerly await your reply.

Thank you once again,

The Authors

Dear Esteemed Reviewer orep,

We are grateful to you for generously dedicating time and effort to evaluating our paper. As the deadline of reviewer-author discussion is fast approaching, we are becoming increasingly concerned about the absence of feedback or response from you.

We fully recognize and appreciate the significant efforts and time constraints faced by reviewers. We have responded to your major concerns about the "efficiency of prior logic rules", "selection of resolution of discretized time grid", and "clarification about hazard function, temporal embedding, and gumbel-softmax trick" point-by-point in the response sections.

Nevertheless, considering the critical role of the rebuttal phase in the review process, we are worried that the lack of interaction with you could potentially affect the fair and thorough assessment of our work. If you have any further concerns, please let us know and we are willing to response!

Warm wishes,

The authors