Learning to Plan Like the Human Brain via Visuospatial Perception and Semantic-Episodic Synergistic Decision-Making

Thank you very much for your positive comment regarding our work as "High Clarity of Presentation" and "Thorough Empirical Evaluation". We also greatly appreciate your insightful comments pointing out the weaknesses in our work. Following your suggestions, we have provided detailed point-by-point responses below. We hope our replies will adequately address your concerns.

W1. Marginal improvements in success rate and path cost on saturated benchmarks

We appreciate your detailed analysis and comprehensive evaluation of our saturated benchmark results. NeuroMP’s improvements in success rate (SR) and path cost (PC) over BrainyMP are limited, with most benefits stemming from planning efficiency improvements. We fully agree that when success rates approach 100%, the margin for further improvement is inherently narrow. These benchmarks have been extensively studied, and existing advanced algorithms already exploit much of their planning potential, pushing performance toward theoretical limits. Nonetheless, we emphasize that reductions in planning time and collision checks remain highly valuable in practice. In real‑time applications (such as autonomous driving or emergency obstacle avoidance), faster planning directly enhances responsiveness and stability. Additionally, fewer collision checks decrease the computational load, making the method more suitable for resource-constrained platforms. Next, we discuss two key areas:

1. Generalization of real-world environments

Real-world scenarios or simulations that mimic real-world conditions can further validate the effectiveness of our method. Thus, we select the City/Street Map (CSM) Dataset as the real-world scenario for validation. Our approach achieves competitive success rates, requiring the fewest collision checks and the shortest planning times. Due to space limitations, detailed experimental results and analysis can be found in the response to Reviewer 7bRM under "W2. Generalizations are Not Fully Evaluated."

2. Future work

We recognize the need for further improvements in solvability and plan quality for NeuroMP. Our plans include: (i) Challenging Test Scenarios: Evaluating NeuroMP in dynamic and multi-objective conflict environments to enhance solvability and planning quality. (ii) Enhancing plan quality. Refining graph construction with advanced cost metrics, incorporating environmental risk and execution difficulty, and exploring reinforcement learning to optimize path-search strategies. (iii) Comprehensive comparisons. We will systematically compare NeuroMP and BrainyMP across a wider range of unsaturated benchmarks to more fully characterize each method’s strengths and areas for improvement.

W2 & Q3. Lack of statistical significant analysis

We fully agree that omitting error bars and significance tests can undermine confidence in the reported findings, especially when differences in metrics such as path cost and planning time are subtle. We computed the average and standard deviation of four metrics (SR, CK, PC, PT) for all methods using four different random seeds. The results are presented in Tables 1-4, where the results for GNN-based methods exclude the GNN-smoother step. In most environments, our method outperforms the comparison methods in success rate, while also exhibiting lower collision checks and planning times. This suggests that our method is more efficient in avoiding unnecessary collisions and demonstrates superior reasoning capabilities. While maintaining high planning efficiency, our method is also capable of finding high-quality paths. Moreover, from the standard deviation, it is evident that our method exhibits more robust performance across different environments.

Additionally, we further analyze the statistical significance of the differences between our method and the comparison methods for each metric (**:p<=0.01; *:p<=0.05; -:p>0.05). There are clear and significant differences between our method and the comparison methods across all four metrics in the vast majority of environments.

Table 1: Comparison and significant differences in success rate under different environments

Table 2 Comparison and significant differences in collision check under different environments

Table 3: Comparison and significant differences in path cost under different environments

Table 4: Comparison and significant differences in planning time under different environments

Q1. Definition of random geometric graphs (RGGs)

Thank you for this valuable suggestion. We agree that formally defining the random geometric graphs (RGGs) upon their first mention is essential for reader clarity. We have added the following definition at line 36. "Specifically, GNN-based methods enhance search efficiency by operating on random geometric graphs (RGGs) constructed from sampled configurations, avoiding full workspace encoding [16]. Here, RGGs denote the undirected k-nearest neighbor (k-NN) graph built on free configuration space."

Q2. Iterations of obstacle encoding T

Thank you for pointing out he need for an ablation study on the number of iterations T in the Selector. Our choice of T=3 was based on precedent in related work [GNN-Explorer, GraphMP, BrainyMP], all of which apply three iterations for obstacle encoding on the same public dataset and with similar modules. Consequently, we followed prior work in setting the iteration count T and did not perform a dedicated ablation study. We have updated the Experimental Setting (Section 5.1) to include a detailed description of the iteration in the Perceptive Segment Selectors. We apologize that we are currently unable to train the Selector at different T values due to time constraints. In future work, we will conduct experiments varying T∈{1,2,3,5,10} to evaluate its impact on planning performance and to establish a stronger empirical basis for choosing this parameter.

Thank you very much for your positive comment regarding our work as "novel brain-inspired framework". We also appreciate your valuable suggestions. Following your suggestions, we provide point‑by‑point responses below and hope they adequately address your concerns.

For Weaknesses:

W1. Limitation of the optimal path

We fully agree that searching on a sampled random geometric graph (RGG) cannot guarantee inclusion of the true optimal path, thereby limiting theoretical optimality. Although our selective sampling strategy mitigates this issue to some degree, it cannot ensure optimal‑path coverage. To address this, we will (i) design enhanced graph‑construction strategies that leverage prior knowledge to guide sampling, reduce randomness, and increase the probability that optimal‑path structures are represented; (ii) Exploring environment‑aware dynamic pruning, which can adaptively refine the RGG online to improve coverage of critical connections and ensure robust path representation.

W2. Generalization are not fully evaluated

We appreciate your comment on limitations of our experimental settings and the need to verify generalization in dynamic or real‑world scenarios. Our current evaluation focuses on static environments. Following your suggestion, we have added a focused discussion of the model’s generalization to dynamic and real‑world settings and clarified how these considerations inform our future extensions and evaluations.

1. Generalization of real-world environments

Real-world scenarios or simulations that mimic real-world conditions can further validate the effectiveness of our method. Following your suggestion, we select the City/Street Map (CSM) Dataset as the real-world scenario for validation. We have included a description of the dataset, experimental results, and analysis.

CSM. Sturtevant et al.[1] used drones to collect 30 real city maps with marked obstacles represented as binary images. Based on this, we randomly generate 2000 training maps and 1000 test instances from the 30 maps. For each map, the start and goal are randomly generated in the free space. These maps present significantly higher complexity than synthetic environments: irregular obstacle shapes, narrow alleyways, and dense urban structures that challenge traditional planners.

Table 1 Comparison of all methods on the CSM dataset

The results on the CSM dataset are demonstrated in Table 1. In real-world environments with fine-grained and densely distributed obstacles, robots typically require more collision checks and longer planning times. NeuroMP achieves the highest success rate (0.88) while requiring 67% fewer collision checks than RRT* and 87% faster planning than BIT*. Due to encoding the entire workspace, NEXT incurs substantially higher computational overhead compared to other methods. In contrast, our method not only achieves competitive success rates but also the fewest collision checks and the shortest planning time across all baselines. These results demonstrate superior real-world generalization of GNN-based approaches, particularly ours, offering excellent stability in complex urban environments.

[1] N. R. Sturtevant, “Benchmarks for grid-based pathfinding,” IEEE Trans. Comput. Intell. AI Games, vol. 4, no. 2,pp. 144–148, 2012

2. Generalization of dynamic environments

Our study uses strict static environments to validate the method. However, multi-arm manipulation scenarios (e.g., Kuka2Arms, Kuka3Arms) are considered dynamic environments by the work [2] due to the interactions between manipulators. Coordinating multiple manipulators to avoid collisions with each other and with static obstacles poses significant challenges. This both highlights our framework’s partial applicability to dynamic settings and underscores the need to handle moving obstacles. In future work, we will (i) design dynamic pruning strategies for RGGs to adapt to real-time changes in the environment, and (ii) encode temporal information into the graph and heuristic to model time‑varying constraints and interactions.

We also recognize the need for broader validation on more complex real‑world datasets. We will therefore expand the experimental scope to comprehensively assess generalization.

[2] Zhang R., Y et. al. Learning-based motion planning in dynamic environments using gnns and temporal encoding. Advances in Neural Information Processing Systems, 2022, 35, 30003-30015.

For Questions:

Q1. How will NeuroMP adapt to dynamic or real‑world environments

We appreciate the insightful question. Adapting NeuroMP to uncertainty in dynamic and real‑world settings will be our future focus, with two main extensions:

1. Dynamic environments: (i) Architecture. Integrate a temporal perception module that learns and predicts scene changes, updating the random geometric graph (RGG) online. (ii) Adaptive Replanning. Trigger replanning when significant dynamics occur, using RGG pruning and path‑rewiring guided by historical decisions to maintain feasibility in real time.

2. Real‑world environments: (i) Dataset Expansion. Assemble a diverse, disturbance‑rich dynamic dataset (e.g., moving obstacles, sensor noise) with augmentation to improve generalization. (ii) RL Integration. Employ reinforcement learning to refine planning strategies via reward‑driven interaction, enabling online adjustment based on observed performance.

These enhancements will be detailed in the revised manuscript’s Future Work section.

Q2. Model Complexity

We sincerely appreciate your insightful question. Computational complexity and memory consumption are indeed critical factors in evaluating the applicability of a model on resource-constrained devices. Your suggestion provides valuable guidance for improving our analysis.

1. Parameters and FLOPs

We computed the number of model parameters (Params) and floating-point operations (FLOPs) for NeuroMP and learning-based baselines across different environments in Table 2. For NEXT, FLOPs increase dramatically with workspace dimensionality, and Params grow modestly with configuration-space dimension. For GNN-based planners, Params and FLOPs scale with the size of the processed RGG and the configuration-space dimension. To further assess scalability, we will compare these metrics across varying RGG sizes in future work. Overall, NeuroMP is more efficient than NEXT and GNN-Explorer, and competitive with GraphMP/BrainyMP, while delivering superior performance. This demonstrates that our model maintains a good balance between model capacity and computational cost, making it well-suited for deployment in resource-constrained scenarios.

Table 2 Parameters comparison

Table 3 FLOPs comparison

2. Optimization for resource-constrained devices

Although our framework comprises multiple stages, each module is individually lightweight and simple. Nonetheless, several optimization directions can be considered for deployment on resource-limited platforms: (i) incorporating sparse graph construction strategies to reduce overall complexity; (ii) employing quantized search algorithms (e.g., integer-based A* variants) to reduce floating-point computation; (iii) applying low-rank decomposition to compress node feature representations and reduce memory footprint; and (iv) dynamically releasing unused historical memory during local updates to improve memory efficiency.

Q3. Future integration of NeuroMP with other methods

We appreciate your suggestion and agree that integrating NeuroMP with other planning paradigms is a fruitful avenue. In particular, coupling with reinforcement learning (RL) could address NeuroMP’s limitations under dynamic uncertainty and multi‑objective trade‑offs. Specifically, we plan to explore: (i) Policy Optimization. RL can be used to train robots that adaptively adjust graph sampling density or node feature weighting based on environmental characteristics (e.g., obstacle distribution or dynamic frequency), enabling the constructed graph to better match real-time planning demands and improve efficiency and quality. (ii) Hybrid Decision Framework. Deploy NeuroMP for detailed local search while an RL agent oversees global strategy, selecting pivotal nodes, resolving competing objectives, or redirecting the search in rapidly evolving scenes. (iii) Experience‑Driven Adaptation. Store NeuroMP-generated paths as experience buffers and train an RL module to recall and reuse them when facing similar scenarios, reducing redundant exploration and speeding up replanning.

We sincerely appreciate the constructive comments and positive assessment. We will update the manuscript following your suggestions.

Thank you very much for your valuable feedback and for pointing out the weaknesses in our work. We apologize for the unclear statement that may have caused some misunderstanding. To clarify, the planning time refers to the total time taken to complete 1000 tasks, rather than the average time for a planning problem. Following your suggestions, we have provided detailed point-by-point responses below.

W1. Literature review and comparisons

We apologize for the incomplete overview of learning-based motion planning methods due to space limitations. As a result, we focused primarily on the most relevant work related to high-dimensional continuous motion planning. We agree that a more detailed discussion of the related work would indeed provide readers with a better understanding of the field's progress. Following your suggestion, we plan to incorporate the seven works you mentioned into the related work section under learning-based sampling methods. Additionally, we have already included direct comparison results and analysis with P-NTFields (Q1).

W2. Simplifying presentation & brain analogy

We appreciate your valuable suggestions on improving the readability and structure of the paper. In response to your concerns:

1. Simplification of the brain analogy. In the revised manuscript, we have implemented the following changes: (i) We briefly mention the perception-decision inspiration in the introduction and removed neural mechanism analogies that are less relevant to the core method to avoid unnecessary complexity. (ii) In the method section, we focus on the design motivation and modules, without reiterating the brain analogy.

2. Expansion of literature review and experimental analysis. We have included additional results and analyses, such as comparisons in real-world environments (detailed results and analysis can be found in the response to Reviewer 7bRM under "W2"), the U-shape environment (Q4), and with comparison methods (Q1).

W3. Task complexity description

To clarify the performance of our method across tasks of varying difficulty, we quantify the complexity of the datasets in Table 1. Except for Kuka3Arms, all datasets are publicly available, with Stick3 derived from NEXT and the others sourced from GNN-Explorer. By using publicly available datasets, we avoid the time-consuming process of data collection and annotation, ensuring a more efficient and fair comparison with similar methods. Detailed descriptions of each dataset have been added to the Appendix.

Table 1 Datasets complexity

W4. Discussion on the training times and model complexity

Thank you for your valuable feedback. Training time is an important factor when evaluating the practicality and reproducibility of methods. We computed the average time required to train two models (the Selector and Heuristic) for one epoch in Table 2, the training time is mainly proportional to the complexity of the environment. The time cost for training our models is relatively modest.

Table 2 Training times (mm:ss)

Model complexity. Detailed experimental results and analysis can be found in the response to Reviewer 7bRM "Q2".

Q1. Comparison with P-NTFields

Thank you for providing the new method. The advantage of P-NTFields is that it avoids the computation-heavy training process by not requiring expert demonstrations. In the P-NTFields's Ur5 environment, a cabinet with narrow passages was chosen. Its path planning mainly involves obstacle avoidance in a 2D plane. In contrast, our UR5 environment involves a 6-DOF robotic arm that not only needs to handle obstacles in 3D space but also considers the fixed base and movement limitations of the robot's joints. The configuration space includes the 3D workspace and the DoF of the robot arm. Therefore, our UR5 environment is more complex. This difference is further validated by the results of RRT*:RRT* achieves a 0.39 success rate in our UR5 environment, compared to a 0.67 success rate in the P-NTFields's UR5 environment. The results for P-NTFields in our UR5 environment are shown in Table 3, where PT refers to the total time taken to complete 1000 tasks. The success rate and inference efficiency of P-NTFields show a noticeable decline. Additionally, the number of parameters in our model is approximately 15% of that required by P-NTFields. Although our method is multi-stage, it is lightweight, simple, and effective.

Table 3 Comparison with P-NTFields

Q2&Q5&Q7. Discussion on component performance improvement

1. Contributions of components and ablation differences

The contributions of the components are as follows: (i) Selective Sampling initially optimizes graph construction, bringing it closer to the optimal solution space. (ii) The Selector effectively removes collision-risk edges from the original graph, providing a safe graph for subsequent searches and simplifying computations. (iii) The Heuristic provides reliable heuristic values to A*, optimizing search efficiency and path quality. (iv) Shortcut Retrieval can refine the searched path, resulting in further optimization of path cost in a minimal amount of time.

The performance improvement of the method does not rely on a single breakthrough from one component but rather on the synergistic optimization of different components, which enables better robustness and efficiency in complex high-dimensional scenarios. This gain might manifest as small differences in simpler scenarios but becomes significantly amplified in extreme cases. For instance, in extremely weak graph structures, our method shows a marked improvement in success rates compared to GraphMP, further optimizing planning efficiency and path quality.

2. Performance differences with BrainyMP

In saturated benchmark tests, further improvements in success rate and path cost are limited, with the main contribution of NeuroMP being in efficiency. Enhancing planning efficiency is crucial for practical applications, especially in real-time domains, where reduced planning time and collision checks improve system responsiveness and stability. We compared BrainyMP and NeuroMP in weak graph structures. Tables 4 and 5 show the retained edge ratio and planning performance for both methods. In the Stick3 environment, both selectors perform similarly. However, NeuroMP generates more accurate heuristics, significantly improving planning efficiency. In the more complex Kuka13 environment, NeuroMP’s selector better identifies dangerous edges, slightly increasing planning efficiency while finding higher-quality paths.

Table 4 BrainyMP and NeuroMP in Stick3

Table 5 BrainyMP and NeuroMP in Kuka13

Q3. How to address failure cases

Our method checks for collisions during the planning process by evaluating point and edge collisions. If a collision occurs, points are resampled or alternative edges are selected. If the goal region is not reached within the specified number of samples, the planning is considered a failure, and no post-processing is applied to failed paths. Future work will focus on: (i) Retrieving and trimming collision path segments, such as resampling near obstacles; (ii) Designing improved graph construction strategies that incorporate prior knowledge to reduce risky edge generation; (iii) Exploring dynamic pruning strategies for RGGs based on environmental features. Failure Causes: (i) Maze: Large map sizes, high obstacle densities, and high-DoF in robots may cause path failures. (ii) Robotic Arm: the number of robotic arms, their DoF, and obstacle placements affect path planning success.

Q4. Discussion of the U-shaped environment

The U-shaped environment, a common challenge in motion planning, has been added to the revised manuscript. In a 15×15 2D workspace, U-shaped obstacles simulate narrow passages between shelves, with the start point near the bottom inside the U-shaped obstacle and the goal outside. Tests are conducted with stick robots across 500 U-shaped map instances. Our method shows significant advantages in reasoning efficiency, success rate, and path quality. Due to time constraints, we are unable to test more complex robots, but we will explore the U-shaped environment further in future work.

Q6. Performance decline in the Kuka3Arms

The performance degradation in the Kuka3Arms environment may be due to: (i) Increased Configuration Space Dimensions(14D->21D). (ii)Coordinating three robotic arms increases the planning difficulty, especially since each arm needs to avoid collisions with both other arms and obstacles. (iii) The new arm makes collision avoidance more challenging.

Thank you very much for your positive comment regarding our work as "compelling results" and "rigorously organized and presented". We also greatly appreciate your insightful comments pointing out the weaknesses in our work. Following your suggestions, we have provided detailed point-by-point responses below. We hope our replies will adequately address your concerns.

For weaknesses:

W1. Replicability and scalability

We sincerely thank you for pointing out this concern. Our method adopts a multi-stage framework, which is indeed more complex compared to single-stage approaches. We discuss replicability and scalability from four aspects: technical reproducibility, model complexity, scalability, and real-world deployment.

1. Technical reproducibility

To ensure reproducibility, we have released the full source code, environmental configurations, and datasets. Additionally, Section 5.1 of the paper provides detailed descriptions of parameter settings, which collectively guarantee the feasibility of reproducing our results.

2. Model complexity

Although our framework consists of multiple stages, each module is individually simple and lightweight. We evaluated parameters (Params) and floating-point operations (FLOPs) for NeuroMP and learning-based baselines. Detailed experimental results and analysis can be found in the response to Reviewer 7bRM "Q2". NeuroMP is more efficient than NEXT and GNN-Explorer, and competitive with GraphMP and BrainyMP, while delivering superior performance. This balance is suitable for resource-constrained deployment.

3. Scalability & Real-world generalization

Real-world scenarios or simulations that mimic real-world conditions can further validate the effectiveness of our method. Following your suggestion, we select the City/Street Map (CSM) Dataset as the real-world scenario for validation.

CSM dataset. Sturtevant et al. used drones to collect 30 real city maps with marked obstacles represented as binary images. Based on this, we randomly generate 2000 training maps and 1000 test instances from the 30 maps. For each map, the start and goal are randomly generated in the free space. These maps present significantly higher complexity than synthetic environments: irregular obstacle shapes, narrow alleyways, and dense urban structures that challenge traditional planners.

Table 1 Comparison of all methods on the CSM dataset

The results on the CSM dataset are demonstrated in Table 1. In real-world environments with fine-grained and densely distributed obstacles, robots typically require more collision checks and longer planning times. NeuroMP achieves the highest success rate (0.88) while requiring 67% fewer collision checks than RRT* and 87% faster planning than BIT*. Due to encoding the entire workspace, NEXT incurs substantially higher computational overhead compared to other methods. In contrast, our method not only achieves competitive success rates but also the fewest collision checks and the shortest planning time across all baselines. These results demonstrate superior real-world generalization of GNN-based approaches, particularly ours, offering excellent stability in complex urban environments.

Our method requires further validation in real-world deployment scenarios, such as robotic arm manipulation in physical environments. For future work, we plan to evaluate our approach under more realistic settings, including robotic arm manipulation, mobile robot operations, and spatial navigation tasks.

W2. Restriction to static environments

We agree that the static environment focus constitutes a conscious limitation at this research stage rather than an inherent framework flaw. This scope is justified by its critical value in applications like robot-assisted surgery and spatial navigation, where our method establishes essential baselines for high-dimensional manipulation tasks. The demonstrated performance gains validate its effectiveness within this domain. In the revised Introduction, we have strengthened this context as you noted. Our method establishes reproducible benchmark conditions for real-world navigation and high-dimensional robotic manipulation tasks, and the observed performance improvements demonstrate its effectiveness.

For questions:

Q1. Utilization stage of spectral features

1. Alignment between spectral features and the requirements of the decision stage

The perception stage aims to capture local features, such as node position and local neighborhood structures. Introducing spectral features at this stage may introduce global information prematurely, potentially blurring local details and impairing the accurate recognition of specific environmental elements. In contrast, the decision-making stage requires reasoning from a global perspective, such as evaluating the overall cost of different paths or assessing the long-term effectiveness of strategies. Spectral features are well-suited to support decisions by compensating for the limitations of local features in capturing long-range dependencies and topological relationships.

2. Computational efficiency and progressive information processing

Inspired by the brain's two-stage Perception–Decision model, our framework adopts a progressive design that transitions from local perception to global decision-making: (i)During the perception stage, only local information is processed, resulting in low computational complexity and enabling a rapid initial understanding of the environment; (ii) In the decision stage, since redundant information has already been filtered during the perception stage, the computational burden associated with spectral feature extraction is significantly reduced. If spectral features are introduced directly during the perception stage, their high spatial dimensionality would result in substantial computational overhead, thereby compromising the practical efficiency of the method.

Q2. The contribution of spectral features

The significance of spectral features is in capturing global structural patterns, which is boost performance most in complex environments. In relatively simple environments (such as Kuka13 and Kuka3Arms), where obstacle density is low and planning goals are clear, local features (spatial features) are generally sufficient for effective decision-making. In such cases, the complementary effect of spectral features is limited, resulting in lower impact. However, in more complex environments like Link8, which exhibit high obstacle density and increased degrees of freedom, local features are prone to falling into "local optima." Spectral features significantly enhance global reasoning by encoding global topological properties through spectral distributions, thereby offering greater contributions under such challenging conditions.

Q3. Dataset selection

Our work focuses on high-dimensional continuous environments. Therefore, we adopt a publicly available dataset specifically designed for such settings, which has been widely adopted benchmarks used by NEXT, GNN-Explorer, GraphMP, and BrainyMP. This ensures a fair and consistent benchmark for performance comparison. On the other hand, the environments in [Sturtevant, 2012] are predominantly 2D discrete spaces, which differ significantly in structure and complexity from the problem settings we aim to address. As such, they may not be well-suited for evaluating motion planning methods in high-dimensional continuous spaces.

For limitations:

We sincerely thank you for pointing out this limitation. As discussed in Appendix G, we acknowledge the concern regarding the potential mismatch between the method’s complexity and its current application in static environments. We address this issue from two perspectives:

1. Imbalance between method complexity and static environment constraints

Our study uses strict static environments to validate the method. However, multi-arm manipulation scenarios (e.g., Kuka2Arms, Kuka3Arms) are considered dynamic environments by some works [1] due to the interactions between manipulators. Coordinating manipulators to avoid collisions with each other and static obstacles partially demonstrates the framework’s applicability to dynamic environments. In future work, we plan to extend our approach to dynamic settings (including moving obstacles) by (i) implementing dynamic pruning strategies for RGGs and (ii) using limited-horizon planning techniques like RTA* to improve decision-making efficiency.

[1] Zhang R., Y et. al. Learning-based motion planning in dynamic environments using gnns and temporal encoding. Advances in Neural Information Processing Systems, 2022, 35, 30003-30015.

2. Justification of the brain-inspired analogy

We agree with your observation on suboptimal, horizon-limited planning under dynamic conditions. The brain's two-stage Perception–Decision model excels in making efficient suboptimal decisions under incomplete information, which aligns with methods like RTA* that prioritize real-time responsiveness. We have revised the paper to focus on decision-making under limited computational resources rather than framing the method as a structural emulation of brain regions in static settings.

We sincerely thank you for your positive assessment of our work, describing it as "well-motivated", "comprehensive", and "well-organized". We also appreciate your valuable comments and for pointing out the limitations in our work. Following your suggestions, we have provided detailed point-by-point replies below. We hope our revisions and clarifications adequately address your concerns.

Q1: Selective sampling

We sincerely appreciate your valuable comments. We agree that a fair comparison is crucial and thank you for raising this point regarding the selective sampling. The selective sampling strategy enables the robot to sample nodes from a guiding region with probability $\beta$, and uniformly from the entire configuration space with probability $1 - \beta$. The guiding region is defined as the circular area whose diameter is the line segment between the start and goal. This strategy helps optimize the solution space to some extent, thereby improving planning efficiency and path quality. Among the baselines, BrainyMP inherently employs a similar selective sampling strategy. Additionally, BIT* and LazySP utilize informed sampling strategies that also concentrate sampling within heuristic regions connecting the start and goal. To ensure a comprehensive and fair comparison specifically for the selective sampling component you highlighted, we have now integrated our selective sampling strategy into the core sampling procedures of RRT*, NEXT, GNN-Explorer, and GraphMP. The augmented results across six environments are summarized below :

Table 1: Performance comparison on Stick3 on Link8

Table 2: Performance comparison on Ur5 and Kuka13

Table 3: Performance comparison on Kuka2Arms and Kuka3Arms

These results demonstrate that while selective sampling generally improves path quality and often efficiency, its impact varies with environmental complexity. In the Link8 to Kuka2Arms environments, collision checks and planning time are reduced. However, in the Stick3 environment, both increase slightly due to the high obstacle density, which introduces additional computational overhead in the heuristic region. Similarly, in the Kuka3Arms environment, planning efficiency decreases with the selective sampling strategy. This is likely due to the dense configuration of the three fixed-base manipulators, where sampling within the heuristic region often causes inter-arm collisions, increasing planning difficulty. Importantly, NeuroMP's superior performance reported in the original submission holds even when competing methods are augmented with this strategy, as evidenced by the comparative metrics.

Q2. The difference between NeuroMP and BrainyMP

We sincerely thank you for your valuable suggestions, which helped us improve the quality of our manuscript. Following your comments, we have clarified the differences between NeuroMP and BrainyMP in terms of motivation, technical design, and brain-inspired mechanisms. In addition, we have revised the introduction and related work sections to include a more detailed review of BrainyMP's core ideas and technical contributions.

1. Addressing BrainyMP's limitations by technical design

BrainyMP addresses this limitation by integrating subgraph structures with node positional relationships to enhance the model’s ability to capture local graph representation patterns, explicitly encoding local structural information. However, BrainyMP still faces several limitations: 

(i) Inaccurate graph construction. The selector may mistakenly retain collision-prone edges or eliminate valid ones, which adversely affects heuristic estimation. 

(ii) Limited structural reasoning. Under weakly connected graph structures, although subgraphs can partially enhance local–global relationships, their ability to capture global information is constrained by the number and coverage of subgraphs, limiting the overall structural reasoning capability.

(iii) Computational complexity and redundancy. The process of extracting subgraphs incurs a high computational cost, and different subgraphs may contain redundant information, reducing efficiency.

To address these limitations, we propose NeuroMP with the following key contributions:

(i) To improve collision probability prediction, the Perceptive Segment Selector adopts a gated dual-branch transformer architecture that efficiently identifies and reasons about environmental patterns and their interrelations.

(ii) To enhance heuristic estimation in weakly connected graphs, the Global Alignment Heuristic incorporates spectral features to impose global topological constraints. Additionally, a dual-channel collaborative learning strategy (A2FL) is introduced to leverage the complete graph to assist in training on weakly connected graphs.

(iii) Spectral features help avoid incomplete coverage, and compared to the introduction of subgraphs, they reduce computational complexity.

2. Distinct brain-inspired principles

While both works draw inspiration from neuroscience, the level of abstraction and specific cognitive processes modeled differ significantly.

BrainyMP draws inspiration from cognitive neuroscience, specifically the Tolman–Eichenbaum Model (TEM) of spatial relational memory, which emphasizes how the brain integrates sensory observations with relational structures to perform sensory inference. Based on this concept, BrainyMP enhances its model structure by incorporating subgraph-based representations to encode local relational patterns.

In contrast, NeuroMP is grounded in a higher-level cognitive framework, namely the two-stage Perception–Decision model observed in human planning and reasoning. The first stage, mimicking the visuospatial perception process, informs the design of the Perceptive Segment Selector, which captures environmental features and spatial relations to guide graph construction. The second stage, motivated by semantic–episodic synergistic decision-making, guides the design of both the heuristic model architecture and the learning strategy, enabling more effective structural reasoning and improved generalization in weakly connected graphs. Overall, compared to BrainyMP, NeuroMP leverages a higher-level cognitive framework to address the challenges of inaccurate graph construction and weak graph reasoning.