Active Target Discovery under Uninformative Priors: The Power of Permanent and Transient Memory

Thank you for your insightful feedback. We are excited to see that you found our conceptual framework highly original and based on strong theoretical guarantees. We appreciate your recognition of our inspiration from neuroscience's dual-memory systems. Thank you for your attention to our comprehensive experiments on challenging tasks, alongside robust baselines and ablations. Next, we clarify all your concerns.

Q1: What happens when a weak pre-trained diffusion model is used for the permanent memory? I believe this could be addressed by adding some flexibility in altering this part of memory, in a conservative way.

A1:

Discussion on Weak prior (Permanent Memory):

Thank you for your insightful questions.

• When an extremely weak prior is used as the permanent memory, according to Equation (6), adapting to a new domain essentially reduces to learning the task from scratch through the transient memory alone. In this case, as indicated by Equation (7), the $h$-model no longer serves as a corrective mechanism; instead, under a partially observable environment, the entire responsibility for modeling the posterior shift falls on this lightweight module. However, this is beyond the capacity of such a lightweight module by design.

• Furthermore, following your questions, we did few additional experiments under remote sensing scenario, where we deliberately replaced the permanent memory with a diffusion model that could only output noise without any meaningful semantic structure. On top of this setup, we implemented EM-PTDM and observed the following phenomenon: even $h$-model was updated under partial observations, its limited capacity made it insufficient to compensate for the lack of a meaningful prior. As a result, all of the unexplored regions of the posterior estimation remained dominated by the weak prior—essentially resembling noise—leading to poor global environment estimation. This supports the claim that an extremely weak or non-semantic prior forces the transient memory to handle an unrealistically large modeling responsibility, which goes beyond its design capability. We appreciate your insightful question and will include qualitative visualizations alongside the quantitative results presented in the following table to provide a thorough analysis of these aspects in the revised draft. Thank you for your thoughtful feedback.

Analysis of Weak Permanent Memory: Performance Comparison on DOTA

Q2: I believe the statement that this is performing under an Uninformative Prior is misleading and not truly precise since the work highly leverages the existence of a pretrained diffusion model. I would appreciate this being addressed. It would be relevant to study how this truly affects the performance.

A2: When we referred to “uninformative prior,” our intention was to highlight the lack of domain-specific prior rather than the absence of any meaningful semantic information. As we stated in the motivation, our design was inspired by how the human brain handles novel tasks, where long-term memory always exists and contributes, but when facing an unfamiliar scenario, it often performs suboptimally and requires the assistance of a short-term memory module to adapt quickly. Similarly, in our framework, the permanent memory (pretrained diffusion model) provides a general prior, while the transient memory ($h$-transform module) rapidly adjusts to task-specific information. However, we fully agree that "Uninformative" is a general term, its precise meaning does vary based on the context. Thus, we will be very careful about the terminology usage.

We have a detailed discussion with supporting experimental results on the effects of using a weak permanent memory in A1. We appreciate your insightful question.

Q3: Equation (10) has text over it.

A3: Thank you for pointing this out. We will certainly fix this in our updated draft.

Q4: The authors did not address the limitations of this work, which I believe exist. They are described both under Weaknesses and Questions.

A4: Thank you for this question. We have observed that when the permanent memory component is extremely weak and lacks semantically meaningful information for certain active target discovery tasks, the performance of EM-PTDM may be impacted. We will include a thorough discussion of these scenarios in the Limitation section of the revised manuscript to provide valuable context and help inform future research directions.

Q5: A more detailed discussion of the total computational cost per sampling step (in terms of time or resources) would be beneficial for understanding its practical deployment feasibility.

A5: This is a great question. We completely agree! Following this suggestion, we have conducted a detailed evaluation of sampling time and computational requirements of EM-PTDM across various search space sizes. We present the results in the following table.

Our results show that EM-PTDM remains efficient even as the search space scales, with sampling time per observation step ranging from 0.83 to 1.87 seconds, which is well within practical limits for most downstream applications. This further reinforces EM-PTDM’s scalability and real-world applicability. We will include these additional details in our updated draft.

Q6: A rather simple approach to the exploration-exploitation phase, which could potentially be improved and more fine-tuned for this specific application.

A6: Thank you for this question. Our sole objective here is to provide a general framework for Exploration-Exploitation phase. Nevertheless, we agree that it can be fine-tuned further according to the requirements of downstream specific application.

Thank you for your thoughtful and encouraging feedback. We are glad to hear that the clarity of our writing and presentation of complex algorithms resonated well. We appreciate your recognition of the novel and insightful connection between neuroscience and statistical modeling, as well as your positive assessment of our well-motivated theoretical contributions and the rigorous support provided by our theorems. Next, we clarify all your concerns.

Q1: While the EM algorithm is known to be unstable, the authors propose heuristics—such as selectively updating the model rather than after every observation—that help mitigate this issue.

A1: Thank you for highlighting this important point. To address the instability, we introduced selective model update strategy, and provided both qualitative and quantitative evidence demonstrating its effectiveness. We appreciate your attention to this aspect and hope our results clearly illustrate how these strategies mitigate instability in practice.

Q2: How stable is the training scheme? I could not find any error bars reported in the results. Given that the EM algorithm is known to be potentially unstable, some quantitative measure of variance would help assess robustness.

A2:

• Thank you for raising this important question regarding the stability of our training scheme. We provide a detailed analysis of the training dynamics in Appendix Section M, where we track the L2 distance between the ground-truth and predicted posterior after each update of the $h$-model (transient memory). Our observations reveal that this distance decreases exponentially as the number of update steps increases, indicating rapid convergence of the $h$-model. We see a similar pattern when comparing the predicted and ground-truth targets, further reinforcing the model’s effective learning.

• To directly address concerns about stability, we followed your helpful suggestion and conducted additional experiments using 5 different random seeds. For each run, we recorded the training loss of the $h$-model—as defined in Equation 7—after every update step. The aggregated results, summarized in the table below, demonstrate that the variance in training loss across these independent trials is minimal. We will add a variance plot of training loss across different observation steps in the updated version of our paper. This consistency strongly suggests that our training procedure is stable and robust, exhibiting reliable convergence behavior regardless of initialization. We appreciate your insightful feedback, which helped us strengthen this aspect of our evaluation and provide a clearer understanding of the robustness of our approach.

Variance of Training Scheme:

Q3: I found it difficult to follow the details of the reward model and its necessity in the overall framework. What is the role of the reward model? Could you clarify why an explicit reward model is introduced?

A3: Thank you for your insightful question about the role and necessity of the reward model in our framework. The explicit reward model is crucial to guiding active target discovery within our approach. Our sampling strategy is based on a composite score that balances exploration and exploitation, as defined in Equation 11. The exploitation component (as defined in Equation 10), in particular, represents a reward-weighted expected log-likelihood, where the reward for each unobserved region is estimated using an incrementally trained reward model. This reward model is therefore essential for accurately evaluating and prioritizing candidate regions, enabling our method to efficiently target areas with higher potential for discovery. We provide a concise discussion of these mechanics in Lines 238–258 of the main text, with further implementation details available in the Appendix Section V. For a visual overview, Figure 20 in the Appendix illustrates how the reward model integrates into the overall EM-PTDM framework and enhances its effectiveness. We appreciate this opportunity to clarify the importance of the reward model, and we hope that these references help shed light on its central role in our proposed approach.

Q4: What is the difference between this work and Variational Search Distribution [1]? I found this work is quite similar.

A4: Thank you for bringing up the Variational Search Distribution (VSD) paper—it's a valuable and relevant comparison. While VSD and our work share some surface similarities in addressing efficient search strategies, there are several fundamental distinctions that set ATD apart:

• Data Assumptions: VSD operates under the assumption that supervised label data from the target domain is available, including examples from the target class. In contrast, ATD is specifically designed for scenarios where no supervised labels are accessible prior to deployment, making it suitable for real-world settings with severe data scarcity.
• Domain Priors: The VSD framework leverages explicit domain priors, whereas ATD is tailored for situations where such prior information may be sparse, incomplete, or entirely unavailable.
• Data Types and Problem Focus: VSD primarily focuses on discrete and semi-discrete design spaces. ATD, on the other hand, is devised to handle continuous, spatially structured, and partially observed environments—such as those found in medical imaging or ecological field discovery—which pose unique challenges not addressed by VSD.
• Search Setup: VSD conducts search over large-scale, fully accessible databases or pools of candidates. In contrast, ATD targets the discovery of target-rich regions within a single, partially observed instance—requiring strategic querying and reasoning about unobserved areas within a sample.

We will include the suggested reference in the related work section.

Q5: I could not find a dedicated limitations section in the paper, which is typically included in the conclusion. While the authors may have discussed some limitations elsewhere in the text, it would be helpful to clearly summarise them in the conclusion for the reader.

A5: Thank you for this suggestion. In response to your feedback, we will clearly summarize the limitation and ensure they are explicitly included in the conclusion section of the revised paper.

Q6: Since the method relies on the EM algorithm, it inherits well-known issues related to stability, slow convergence, and sensitivity to initialization. These concerns have been highlighted in prior work (e.g., [2]) and should be acknowledged.

A6: Thank you for pointing this out. We will certainly acknowledge the prior work as you suggested in the updated version of our paper.

Thank you for your positive and encouraging remarks. We appreciate your recognition of the well-motivated problem setting, the clarity of our writing and figures, the rigorous description of our method, and the clear performance improvements demonstrated across diverse problem settings compared to strong baselines. Below, we clarify all your concerns.

Q1: The paper currently only briefly describes the underlying DiffATD method. It would be helpful if the authors add a brief section describing that method to better ground the reader.

A1: Thank you very much for your valuable suggestion. We agree that including a brief section outlining the underlying DiffATD method will greatly help readers gain a clearer and more intuitive understanding of the concepts. Following your feedback, we will add a concise and accessible overview of DiffATD in the revised manuscript to better ground the reader and enhance the overall clarity of the paper.

Q2: It's unclear to me whether the two problem settings shown are representative (not a big weakness; but my confidence would be higher with more evaluation settings shown)

A2: Thank you for this question. The problem settings we chose are grounded in real-world applications where active target discovery is critical, such as remote sensing and species discovery. While these scenarios highlight the strengths of EM-PTDM, we believe EM-PTDM establishes a foundational framework for active target discovery and, given its generality, holds significant promise for broader applicability across diverse domains beyond those discussed in this work, including active drug discovery and novel disease detection. We are enthusiastic about exploring these other domains in our future work.

Q3: I'm still struggling a bit to understand the terminology of updating the "prior". Does this not violate Bayesian principles of encoding beliefs before seeing the data? Do you think it is possible that this approach risks overfitting to the presented observations?

A3: Thank you for raising this important question. We distinguish between two types of memory in our approach: the permanent memory, which acts as a true Bayesian prior, and the transient memory, which serves as an adaptive correction mechanism. The permanent memory remains fixed during the active target discovery process and is pre-trained on a dataset from a different domain, thereby encoding general, domain-agnostic knowledge before seeing any new observations from the domain of interest. This ensures adherence to Bayesian principles.

In contrast, the transient memory is updated periodically with newly observed data to capture task-specific context and align the model dynamically with the current environment. Importantly, this transient memory is re-initialized at the start of each new active target discovery task, preventing carryover of task-specific biases and mitigating the risk of overfitting to limited observations. By separating stable prior knowledge from adaptive task-specific updates, our approach balances principled Bayesian inference with the flexibility required for effective active discovery in dynamic, data-scarce settings. We hope this clarifies how our update strategy respects Bayesian principles while enhancing adaptability and robustness.

Q4: What is the standard deviation one should expect with the experiments shown for each method? Are the current experiments reporting single runs or repeats?

A4: This is a great question. We present the detailed standard deviation values across different settings in Appendix Section X, offering transparency regarding the variability of each method’s performance. We would like to emphasize that we report all the results in our paper as averages over 5 independent experimental trials to ensure the reliability of our findings. We hope this additional information helps clarify the robustness of our experiments.

Q5: To provide a better understanding of capability, it would have been useful if the authors showed scenarios in which their method does not, in fact, perform very well.

A5: Thank you for this insightful suggestion. In our experiments, we observed that when the permanent memory component is extremely weak and doesn't contain any semantically meaningful information for certain active target discovery tasks, the performance of EM-PTDM can be affected. We will include a detailed discussion of these scenarios in the Limitations section of the revised manuscript, which we believe will offer valuable context and guide future research directions. Thank you again for encouraging this important reflection.

Thank you for your thoughtful and encouraging feedback. We appreciate your recognition of our clear problem framing, the creative analogy to brain memory systems, the rigorous methodological development, the strong empirical results in low-data settings, and our commitment to reproducibility through code and public datasets. Next, we address all your concerns.

Q1: The paper is quite dense and could be hard to follow for readers without a strong ML background. Adding simpler diagrams or pseudocode could help.

A1: Thank you for your helpful suggestion. To address accessibility, we had included several explanations in the Appendix, including simpler diagrams (see Figure 20 in the Appendix Section W) and detailed pseudocode (see Algorithm 1 and 2 in the Appendix Section I). Following your feedback, we will move some of these explanations back into the main paper to help readers follow the content more easily.

Q2: The authors mention instability if the h-model is updated too often early on. It’d be helpful to see how sensitive the results are to different update frequencies.

A2: Thank you for this insightful observation. We agree that updating the $h$-model too frequently during the early discovery phase can lead to instability. To investigate this, we conducted a controlled experiment comparing posterior sample generation when updating the $h$-model after every observation versus after several observation steps. Our results show that frequent updates produce noisier posterior samples, and we provide a detailed discussion of this phenomenon in Section 3 (see lines 184–208, and Figure 2 for a visualization of this fact). Building on these findings, we further analyze the sensitivity of the results to different update frequencies in the Appendix Section R. Additionally, we propose an adaptive update strategy, described in Section H.1 of the Appendix, which dynamically adjusts the update schedule. Empirically, this adaptive approach outperforms fixed-interval update schedules, resulting in improved discovery performance (See Table 8). These results highlight the important role that update frequency plays in the stability and effectiveness of the $h$-model, which in turn impact the discovery performance.

Q3: It would be good to test simpler baselines too—for example, training on random samples and then re-ranking spots based on how similar they are to places where targets were found, without retraining the diffusion model.

A3: Thank you for your suggestion. Following your feedback, we compare the performance of EM-PTDM with the suggested approach. We report our findings in the following Table. The experimental outcomes further reinforce the impact of EM-PTDM, and further justify the importance of both Permanent and Transient Memory.

ATD Performance Comparison Using DOTA