Learning to Plan Like the Human Brain via Visuospatial Perception and Semantic-Episodic Synergistic Decision-Making
Authors: Tianyuan Jia
Ziyu Li
Qing Li
Xiuxing Li
Xiang Li
Chen Wei
Li Yao
Xia Wu
Venue: NeurIPS 2025 poster ()
Keywords: Brain-inspired learning; Motion planning; Graph neural networks;
Primary area: reinforcement_learning
TL;DR: A brain-inspired framework learns to construct safer graphs and enhance knowledge representation for enhancing motion planning.

Abstract: Motion planning in high-dimensional continuous spaces remains challenging due to complex environments and computational constraints. Although learning-based planners, especially graph neural network (GNN)-based, have significantly improved planning performance, they still struggle with inaccurate graph construction and limited structural reasoning, constraining search efficiency and path quality. The human brain exhibits efficient planning through a two-stage Perception-Decision model. First, egocentric spatial representations from visual and proprioceptive input are constructed, and then semantic–episodic synergy is leveraged to support decision-making in uncertainty scenarios. Inspired by this process, we propose NeuroMP, a brain-inspired planning framework that learns to plan like the human brain. NeuroMP integrates a Perceptive Segment Selector inspired by visuospatial perception to construct safer graphs, and a Global Alignment Heuristic guide search in weakly connected graphs by modeling semantic-episodic synergistic decision-making. Experimental results demonstrate that NeuroMP significantly outperforms existing planning methods in efficiency and quality while maintaining a high success rate.

Learning to Plan Like the Human Brain via Visuospatial Perception and Semantic-Episodic Synergistic Decision-Making
Tianyuan Jia Beijing Normal University Beijing Institute of Technology tianyj @ mail. www.ll.uuu......
Ziyu Li
Beijing Institute of Technology ziyuli @ bit. edu.cn
Qing Li'
Xiuxing Li
Xiang
Beijing Institute of Technology liqing bit.eddu.cn
Beijing Institute of Technology xxl@bit bit.edu.cn
Li Auto Inc.
iixian339lixxinn.com
Wei Chen
Li Yao
Xia Wu
Li Auto Inc. chenwei 1 lixiang.com
Beijing Normal University yaoli bnu.edu.cn
Beijing Institute of Technology
wuxia@bit.eduu
Abstract
Motion planning in nigh-dimensional continuous spaces remains challenging due complex environments and computational constraints. Although learning-based planners, especially graph neural network (GNN)-based, have significantly im- proved planning performance, they still struggle with inaccurate graph construction and limited structural reasoning, constraining search efficiency and path qual- ity. The human brain exhibits efficient planning through a two-stage Perception- Decision model. First, egocentric spatial representations from visual and propri- oceptive input are constructed, and then cemantic-episodii synergy is leveraged to support decision- propose NeuroMP, brain-inspired planning framework that learns to plan like the human brain. NeuroMP integrates Perceptive Segment Selector inspired by visuospatial perception to construct safer graphs, and a Global Alignment Heuristic guide search in weakly connected graphs by modeling semantic-episodic synergis- decision-making. Experimental results demonstrate that NeuroMP significantly outperforms existing planning methods in efficiency and quality while maintaining a high success rate.
in uncertainty scenarios. Inspired by this process, we
Introduction
Motion planning is fundamental to robotic systems, with broad applications in autonomous vehicles [. logistics [2], and so on. Its primary objective is to compute a high-quality, collision- free path in the configuration space that connects the start and goal (3). However, real-world configuration spaces often involve numerous continuous variables and complex high-dimensional properties, significantly increasing the difficulty of the planning problem. Classical motion planners are typically categorized as search- based or sampling-basse based. Search-based methods, such as A* [] and Dijkstra [4), formulate planning graph search. While sampling-bas based methods, such as RRT 5 and its variants (6] (7).
Corresponding Author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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construct paths by randomly sampling the configuration space. However, these methods suffer from a rapid increase in complexity in nigh-dimensional continuous spaces
To enhance planning efficiency and quality, researchers have proposed learning-based planners that integrate data-driven models with classical planning methods. By leveraging the learning and representation capabilities of deep neural networks, these methods can extract key patterns from the configuration space or learn the behavior of oracle planners, thereby optimizing critical steps in the planning process to enhance overall performance (9] Various neural-network-dree
motion planners
have been proposed, including convolutional neural networks (CNNs) [T0 recurrent neural networks (RNNs) [5), and graph neural networks |9 I7]. Among these, GNN-based methods demonstrate significant advantages in processing high- sigh-dimensional graph tasks. Specifically, CNN-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. They also predict node or edge priorities via graph pattern learning, reducing redundancy and improving path exploration quality.
GNN-based planners, such as GNN-Explorer y and GraphMP 18] demonstrate strong performance but still exhibit notable limitations. GNN-Explorer prioritizes edges without considering total path costs, limiting optimal path selection. GraphMP addresses this issue by incorporating a Neural Collision Checker to remove predicted collision edges and embedding GNN-based heuristics within an A search framework. However, GNN-based planners still face two key limitations: (i) Inaccurate graph construction. Neural Collision Checker may incorrectly retain collision edges or remove valid ones, disrupting heuristic estimation. (ii) Limited structural reasoning. Excessive edge removal weakens the structural cues essential for reasoning, degrading information propagation and repre- sentation. This issue stems from the reliance on local feature aggregation and neighborhood-beee based message passing, which are insufficient to capture global structural information, thereby limiting the representational capacity of models. Although Brainy [9] introduces subgraph structures to enhance representation, it remains limited by subgraph coverage and redundant computation.
In contrast, humans exhibit remarkable capabilities in planning tasks, especially in uncertain or incomplete scenarios. The cognitive process can be divided into two functional stages: perception and decision-making [20 21. The first stage is visuospatial perception, where the brain initially acquires external environmental information through the visual system. The visual cortex encodes and processes raw visual signals from the retina, identifying key features such as obstacles, boundaries, and feasible regions 121. Subsequently, the posterior parietal cortex (PPC) transforms visual and proprioceptive information into egocentric spatial representations useful for planning 122 23). The second stage is semantic-episodic synergistic decision-muking, where the brain engages the semantic-episodic synergy mechanism to support environmental reasoning under weak or ambiguous conditions 26). Specifically, episodic and semantic information is integrated through coordinated activity of the prefrontal cortex (PFC), anterior insula (AI), and default mode network (DMN), triggering shared cognitive control mechanism [24 271. The global semantic framework provides contextual support for episodic memory, aiding decision-making under uncertain cues. While episodic memory refines corrects the semantic framework with specific event details. Accordingly, model the brain's 's perception and decision-makingg processes, as illustrated in Fig. I. offering valuable insights for improving motion planning systems.
dim..
Detalled event information
Visual cortes
Episedic Memory
DAEN
PPC
siouel
pespeloceptiee
Phonstng epeciti infoptation
Gobel ootional PUSEE
PPC
Visual cortics
Semantic
motir entimatt
pol miliaae (ppll))
Memory
(casecntrc)
Glabal comandir Kommenakk
I: vissospatial perception
Stage 2: semantic epioodic synergy
Plaaning
Perception Decision
Perception-eciee Decision Model
Figure 1: The two-stage Diccptiion-Decisiin model. The cognitive process of planning consists of two functional stages. Stage 1: Visuospatial perception inspires the extraction of environmental features and their interrelations for subsequent planning. Stage 2: Semantic-episodic synergistic decision-making provides two key insights: (i) incorporating global topological constraints to enrich representations, and (ii) bidirectional complementarity between complete graphs and weak graphs. Inspired by the two-stage Perception model, we propose MeuroMP. a brain-inspired motion planning framework to address the limitations of existing GNN-based planners. In the first stage,

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mimicking the visuospatial perception process, the Perceptive Segment Selector efficiently identifies and reasons environmental patterss and their spatial relationships to construct safer graphs. In the second stage, motivated by semantic-episodic synergistic decision-making. the Global Alignment Heuristic is proposed to improve structural reasoning. Specifically, drawing on the contextual understanding of the global knowledge framework in semantic memory, the module incorporates spectral features to capture global topological constraints. Furthermore, inspired by the bidirectional interaction process, the Alignment Dual-Flow Learning strategy leverages the complete graph to guide heuristic estimation in weakly connected graphs via dual-channel collaborative learning. The proposed method is evaluated maze and robotic-arm manipulation tasks, with experimental results demonstrating improved planning efficiency and path quality while maintaining high reliability.
2 Related Work
Classical planning methods. Current classical motion planners are primarily divided into two popular categories: search-based and campling-basedd planners. Search-based planners typically perform iterative searches on RGGs to find optimal paths, such as BFS [28] and Dijkstra [4] These methods are widely used in low-dimensional discrete scenarios but become inefficient in high-dimensional environments due to high computational complexity [6] To overcome this limitation, informed search strategies have been proposed, such as A* (3] and its variants [1] which significantly reduces the search space and enhances efficiency through heuristic functions. Nevertheless, these methods are typically limited to discrete spaces, and their search efficiency still suffers from exponential complexity in ligh-dimensional environments.
In contrast to search- basee methods, sampling-based methods find solutions by randomly sampling nodes in configuration spaces, such as RRT* [6] and its variants (7]. These methods avoid explicit discretization and construction of entire spaces, alleviating computational complexity. However, they often struggle to identify critical regions and efficiently sample sparse states accurately. To address these issues, heuristic-enhanced sampling-ban bbsed methods have been proposed, such as BIT [32] and LazySP [33]. Despite these improvements, campling-based methods yield only near-optimal solutions and exhibit limited performance in high-dimensional complex environments [10].
Learning-based planning methods. By leveraging the powerful representation capabilities of neural networks, learning-baate based methods have revitalized traditional search- and sampling-bais baaedd planners, significantly improving planning efficiency. Learning-basee search methods employ neural networks to generate enhanced heuristic functions or directly learn planning policies. For example, VIN 34 and SPT [13] directly learn search paths, reducing search space and time. Neural A [18] reformulates A as differentiable for end-to-end training in 2D spaces. Additionally, imitation learning has also been integrated into heuristic strategies. For instance, SAIL (35) and TransPath (36) learn heuristics
from environment representations using deep neural networks. However, these methods often rely on handcrafted heuristics and are limited to 2D workspaces.
Learning-basee based sampling planners have substantially improved efficiency and transfcrability by optimizing sampling strategies or directly generating paths. Representative approaches include MPNet (77, Me [3), and NeuralMP (39] which learn informative samples from environment and configuration data to accelerate planning. OracleNet 44 leverages imitation learning to replicate oracle behaviors: CVAE (8] learns sampling distributions to generate samples along solution paths; and NEXT 10 embeds high-dimensional state spaces into lower-dimensional representations and employs CNNs to learn local sampling strategies. While MPT [4] employs a Transformer to model innguration-envirnneee
relations and directly produce feasible paths from historical data and scene context, NTFiclds [42) learns neural potential fields to generate trajectories, and P-NTFiclds adopts a probabilistic formulation to handle uncertainty. In addition, dictionary-laaring methods optimize sampling dictionaries to enhance efficiency and generalization. RDT-RRT [12] and
43
481
NIRRT [|| refine sampling using curvature-aware CNNs and point-Net. Despite these advances, two challenges persist: (i) limited sample quality and collision-avoidane reliability, which can cause redundant exploration low-quality solutions; and (ii) reliance dense workspace encoding and extensive perceptual features, which incur substantial computational and memory costs.
GNNs have demonstrated superior performance owing to their strong capability in learning graph patterns and adapting to high-dimensional spaces. For example, GNN-Explorer [16] enhances planning efficiency and robustness by prioritizing the exploration of promising edges. GraphMP [9]
3

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combines GNNs with a differentiable A module to identify optimal paths over RGGs. Inspired by spatial and relational memory mechanisms, BrainyMP [9 enriches representations with subgraph structures to improve planning performance. However, its ability to capture global information inherently constrained by the number and coverage of subgraphs, which still limits structural reasoning. Integrating brain-inspired mechanisms more directly into GNN architectures is promising direction for advancing motion planning.
3 Preliminaries
Task setting. A motion planning problem in a d-dimensional continuous configuration space C' S R., where the configuration space is divided into the obstacle space Cobs S C' and the free space Ofree =C Cobs- The planning problem is typically formulated as the search process on the g = EV.E), where the set of nodes V is sampled from Creee and weighted edges & are constructed using K-nearest neighbors (K-NN). The start and goal nodes are denoted as Us. Uy E V, respectively. The aim is to search a finite set of edges that connects the start and goal nodes within the graph, denoted as { = 6 (U:-1, (1) where e, E Up Us by = Ug.. and in E V for all i E [0, 7).
Differentiable * Differentiable A [18) redefines the traditional A algorithm [3]. enabling end-to- end differentiable training. Further details are provided in the Appendix A.I
4 Methodology
4.1
Overview
The overall framework of NeuroMP is illustrated in Fig. 2 During training, the binary cross-entropy (BCE) loss minimizes the difference between predicted values and ground truth, improving the accuracy of the Perceptive Segment Selector N's. The Global Alignment Heuristic N is trained jointly with a differentiable A module using the Alignment Dual-Flow Learning (A2FL) strategy to optimize heuristic estimation. During online planning. selective sampling is employed construct the RGG based on the bias probability 3, reducing redundant exploration. Then, .Vss predicts edge collision probabilities and filters unsafe edges to generate safe RGG'. To address weak connectivity, Ni incorporates spectral features to impose global topological constraints, enabling more accurate passed the A module for path search, followed
heuristic predictions. Finally, these heuristics by shortcut retrieval to remove detours and improve path quality. Details of the selective sampling and shortcut retrieval optimization steps provided in the Appendix A.2
Back Propegation
Back Propegatine
Exa
ROG
Perceptive Septecei Scleteer Callden Produillly
Orade RGG
Global Alignncal Hourisiic
Palk
Spuiia
BGGG
feiree
I: Frateins Perogstry Sepweer Sibester
Suyp Training Ghobrl Algemment Horroi
Plunning Prabiers
Salectivo
Raw RGG
Perceptiv Segraint Selemee
Sote BGG
Glabal Allpaeeee Hearkde
Search
Breawing
salfora
Sporal
Frequency
(b)
Sogg li Drogk Coosunriin
Dog Gonmettig seft
Prediciing
Pashing
Figure 2: Overview of NeuroMP. (a) The training process. The N and N are trained independently. (b) The online planning process. The learned Ns. NH, and A modules are integrated to perform graph search-based planning.
4.2 Perceptive Segment Selector
In the first stage, the proposed Perceptive Segment Selector module identifies and reasons about spatial patterns and structural relationships, enhancing collision prediction accuracy and facilitating the construction of safer graphs. The overall architecture of Ns is illustrated in Fig. g

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For the input RGG G = (V.E), its nodes and edges are first encoded into a latent space with I E IR Vixdn E Rl where d, is the encoding size. Specifically, the embedding for the i-th node V and the I-th edge eij are represented as x; fu(1)) and Vij f (Us, Bj 2s - U3 where fz
and fy are two separate two-layer MLPs.
Singe
Perception: Perceptive Segment Selector
K.O.V
Dual-branch Transformer Block
O
Encoder
bbsteck
Ensoder
K.OON
Allention
GL.U
Novaa
FFN
Norma
Cincaat
Attentisn
Addd
Add &
MLPS
RGG
Enceder
BOGA
Stage Decisies Global Aligament Heuristic
Spotial Durian
Multi-scale Messgge Pasaing
Enedder
Menage
ROG
Win
Sede Selection
Pylo
Win
Scorch
Path
W.
A
Black
Spattal-Spociral Festuure Eacoding
Figure 3: The model architecture. The upper part illustrates the Perceptive Segment Selector, while the lower part presents the Global Alignment Heuristic.
Obstacle Encoding. The obstacle information is encoded into the node and edge features. To simplify the notation, the feature embeddings of all nodes and edges are denoted as and y, respectively. The obstacle configuration is denoted O E [glo|x2n, where |o] represents the variable number of obstacles, n denotes the workspace dimension. In the f-th iteration of obstacle encoding, the interactions between the node, edge, and obstacle features are encoded follows,
a = (1)) + GLU (AU(S (t) (O), (x (0)))
(++1) LN + f(t) (a )), with (1)) LN(a!
( ( + GLU (Att( (1) (O),
1 (0)))
(++1) LN(( + f1)) )), with a (N(
where LN refers layer normalization, fk., fq.. fV.. Say, fK,, fq., fv,, fay represent different o oo
b.) の (W, + bx), W.. W,, are learnable weight matrices, ba by are bias vectors. Au(K, Q, V) denotes the weighted results of self-scores and nodes, the attention mechanism can be computed as follows,
MLPs layers. The Gated Linear Unit (GLU) is defined as GLU(A) =
through the gating mechanism. For the obstacle encoding of
AIl(K, Q, V) softmax LQnK2 Quk
+ [V,, V.)
Vdl.
where the denotes the element-wise product, (Qn, Kn, VoJ. lQ, K.: Vo) represent the keys, queries, and values for the nodes and obstacles, respectively. The obstacle encoding of edges follows a similar process.
Collision Probability Prediction. Subsequently, the information of the graph and obstacles is encoded into joint embedding vector Uy for the feature embedding of each edge eij. After
T iterations of obstacle encoding, Uj is represented as u,j (1 , ,. x (T) xx Mig The collision probability Pij for each edge eig is computed through a three-layer MI.P fp. i.e., Pij (u:))
(T)
(T)) (T))
Learning Procedure. Fach training instance (g. Cobs) ) (0) consists of graph G (V,E) sampled within the configuration space and set of obstacles Cots. where V represents all the sampled nodes,
5

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E represents the edges constructed based on K-NN, and v. U E V. To optimize the model .Vs for predicting the collision probability of each edge, BCE loss employed minimize the gap between the predicted probability vector and the ground-truth labels. The loss function is defined as:
LN3= (Pij log Pij) + (1 (log(1 (Py)))
where Pij is determined by the Dijkstra algorithm, which labels each edge as 1 if no collision occurs and ( if a collision is detected.
4.3 Global Alignment Heuristic
In the second stage, the Global Alignment Heuristic incorporates spectral features to capture global topological constraints, enriching node representations. Furthermore, we propose a dual-channel collaborative learning strategy, called Alignment Dual-Flow Learning (A2FL). This strategy allows the complete graph to provide shared semantic representations to the weakly connected graph, while the weakly connected graph offers structural feedback to refine representations in the complete graph, thus improving heuristic estimation in weakly connected graphs. The network architecture of NH is shown in Fig.
4.3.1 Spatial-Spectral Feature Encoding
Traditional node and edge feature embeddings rely on local features, limiting the ability to capture the global topological structure. To overcome this limitation, introduce spectral features derived from the graph Laplacian matrix to capture the global topological characteristics. These features are then integrated into the node embedding, enhancing the model's graph representation capability.
Spatial Feature Encoding. Given the safe RGG' g' = (V', E') and the goal Vy as input, the nodes and edges of the G' are similarly encoded into a latent space. Specifically, the feature embedding of the robot state v; is computed by incorporating the difference and the 1.2 distance to the goal state V'g-
i.e. = (2 Lg I2 Zgg ||;; 22 and the feature embedding of (-th edge Eij is defined as rij ff 21,, Vy x;), where S and f are two different two-layer MLPs.
Spectral Feature Encoding. To enhance the node feature representation, we extract spectral features using the Graph Fourier Transform (GFT) to obtain filters through the eigendecomposition of the Laplacian matrix. The Laplacian matrix is defined as î. -- À UAUT, where Å is the normalized adjacency matrix, I the identity matrix, U is the matrix of eigenvectors, and A is the diagonal matrix of eigenvalues. Subsequently, node features recursively propagate through the Laplacian matrix L. The spectral feature of each node is after K-order propagation is computed as follows,
K h1 Σ Pa(L)a,W()) SWW K=U
where (L( denotes the k-th order polynomial expansion of the Laplacian matrix, S represents another feature subspace generated by the principal components of the structure matrix, and learnable weights (Kk) and W, enable flexible re-weighting of each feature subspace.
4.3.2 Multi-scale Message Passing
The spectral feature is concatenated with the spatial feature into embedding vector 2, (qi, h:). The node and edge embeddings are then iteratively updated by aggregating the local information of each node from its neighbors A (w:) = (ugleig E").
1 = mmx sa , 19
(9 (1)
( 2, ; 1 eN(i))))
(1) 1
(1+) f=(=19
(1) (00 Vo, EV'
(6)
( max(r!)) (1) fr(2() 20 2, )))) Vey 3'
(1) 11
where far fz, and fr are three different two-layer MLPs. After L iterations, the heuristic value of node v is computed as H. (z( where fH is a three-layer MLP.

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4.3.3 Alignment Dual-Flow Learning
To enhance the heuristic estimation capability of NH. we introduce the Alignment Dual-Flow Learning (A2FL) strategy to train NH, as illustrated Fig. 4 The original channel provides global knowledge to iteratively refine heuristic learning in the weak channel, while sparse connections in the weak channel also influence updates in the original channel. Subsequently, Wu is jointly trained with the A module end-to-end optimize heuristic estimation.
Aliguncct
Sparial Dienlan
Black
path e'
Spectrrl Decaton
Bustere Excnding
Graph
Spatial Dventes
poth
Spectred Dicesion Staceding
Origiaal Grophe
Alignment
Figure The Alignment Dual-Flow Learning(A2FL) Process.
Given training problem instance {G, g', Eg U/. 2.. 2000, where G' is the collision-fre RGG processed by an oracle planner and the binary vector e represents nodes of the oracle path. The training loss for each channel is calculated the LI distance between the closed list vector obtained from the A and the oracle planner, denoted as follows:
Lw -illcll, /
Co =
where the binary vectors c and c' mark the nodes in the found path based on the original graph 9 and the weakly connected graph G', respectively. The loss penalizes excessively explored nodes, guiding the search toward the optimal path.
To ensure semantic consistency between the two channels, an alignment loss is introduced to align the latent embeddings Z = [n(=) and Z' = f''(z') derived from node features z, x' of the two channels, where fn and fú are two separate MLPs. The alignment loss LA constructed by using positive contrastive difference (the similarity of node features across the two channels) and negative contrastive difference (non-diagonal features within and between channels).
1 2
f(Z,, Zz)
log f(Z,, Z,)
CA
log
Ejœs f(z,, 41)
Ejes f(Z,, 2,)
where f(a, b) = exp(cos(a. b)), cos(a. (as(a, b) is the cosine similarity function. The final objective function is given by LNw Lw Lo + CA, y is used to adjust the magnitude of different losses.
Experiments
5.1
General Setting
Dataset. The effectiveness of the proposed method is validated across six types of motion planning tasks with the following environment settings: (i) Stick3: 3-degrec-of-freedde
(DoF) stick robot operating in 2D workspace [TO]. (ii) Link8: an 8-DoF link robot in 2D workspace, sharing the same maze environments as Stick3. (iii) Ur5: 6-DoF UR5 robot operating in 3D workspace, (iv) Kukal3: a 13-DoF Kuka robotic arm in 3D workspace. (v) Kuka2Arms: dual 7-DoF Kuka robotic arm system in 3D workspace. (vi) Kuka3 Arms: three 7-DoF Kuka robotic arms in 3D workspace. The Kura-Auss environment referenced from [6). Among these environments, Stick3 and Link8 are maze-planning tasks, while the others involve robotic arm manipulation. These two categories represent classic motion planning scenarios, effectively simulating real-wor real-world challenges such obstacle avoidance, path selection, and precise maneuvering.
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Experimental Setting. For each environment, training data set of 2000 different planning problems constructed to train the Perceptive Segment Selector Nss and the Global Alignment Heuristic NH separately. Specifically, each problem instance {G, Coba ((0) consists of the randomly generated RGG and obstacles for Ns.. For NNr, each problem instance (G, ,U,, Vg. c) consists of the start and goal Ux; Vgg. sampled G, collision-free G', and the optimal path computed using Dijkstra ( Additionally, 500 problem instances are used as a validation data set, where weights of the .N with the lowest path cost are retained. After training, an end-to-end evaluation is performed on 1,000 test problems. The proposed method is implemented using PyTorch and executed in an environment equipped with NVIDIA RTX 4070 GPUs. Following GraphMP's s parameter settings, the Agg iterates obstacle encoding three times, with an output dimension of 64. The NE employs message-passiae neural network (MPNN) with five iterations and an output dimension of 32. The Adam optimizer 45 is used for training, with 400 epochs, a learning rate of 0.001, and a batch size of 8.
Baselines. Seven high-performing baseline planners selected for comparison evaluate the performance of Me comprehensively. These include three classical planners: RRT* (8),
BIT* [32. and LazySP [33;; CNN-based planner: NEXT [TO]: two GNN-based planners: GNN- Explorer [16] and GraphMP [9]; and a brain-inspired GNN-based planner: BrainyMP [19], which
represents the current state of the art (SOTA). Additionally, GNN-Smoother [6] is employed as a post-processing module for path optimization.
Evaluation Matrices. To comprehensively assess the performance of different methods, we select the following evaluation metrics. Specifically, success rate (SR) represents the proportion of successfully planned collision-free paths, indicating the model's reliability. Collision check (CK) denotes the average number of collision checks across test problems, and planning time (PT) measures the total execution time for solving 1,000 test problems. These two metrics assess planning efficiency. Path cost (PC) represents the mean Fuclidean length of successfully planned paths, reflecting path quality. Path cost with penalty (PCP) introduces large penalty for failed cases ensure fair comparison across different methods, which is necessary as planners with low success rates typically succeed only in simple tasks with lower costs while failing in more complex tasks that require higher costs.
5.2 Overall Performance
Table I compares the performance of our method with the baselines across six datasets. Our method achieves the optimal or near-optimal success rate, demonstrating competitiveness with SOTA planners. NeuroMP significantly reduces collision checks compared to GraphMP and BrainyMP across all environments, requiring only 71%, 61%. 57%, 61,, 66%, and 68% of the collision checks performed by GraphMP. This reduction highlights the effectiveness of its edge selection and heuristic estimation. However, a commonly raised issue with learning-bas based planners is the time overhead associated with the frequent use of large neural network models when solving problems, such as NEXT. However, GNN-based planning methods substantially reduce planning time by searching on the sampled RGG. Compared the SOTA planners. NeuroMP achieves acceleration across different environments. Classical planners such as RRT*, due to their simplistic design, require minimal planning time but suffer from frequent failures. Another advantage of NeuroMP is its low path cost, which finds high-quality paths across different environments and achieves the lowest path cost in Kukal3 and Kuka2Arms. Although RRT and NEXT occasionally achieve lower path costs in some environments, their low success rates result in significant penalty costs due to frequent failures. In contrast, the superior success rate of NeuroMP results in very low failure penalties. comprehensive analysis of the five key evaluation metrics can be found in the Appendix B
Collision Prediction Performance. Table 2 compares the collision probability prediction of the N' in NeuroMP and the Neural Collision Checker in GraphMP in various environments, treated as a binary classification task. Evaluation metrics include accuracy, recall, Fl score, and confidence. Higher accuracy, recall, and F1 scores indicate improved collision detection capabilities, while confidence reflects the model's certainty in its predictions. Experimental results demonstrate that Ns outperforms Neural Collision Checker across all metrics, with particular improvements in high- dimensional environments. This suggests that NeuroMP achieves superior collision detection by effectively reducing false positives and negatives, thereby enhancing the safety and efficiency of motion planning. Moreover, its higher confidence scores indicate more reliable predictions, ensuring stable collision detection support for motion planning.
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Table 1: Comparison of the planning performance of all methods across all environments.
Methnas
StidkS
LinkS
Ur5
SIRT
PCP1]
PC39]
SR1
PCC
PCPL
RRT
0.62
10106.15 18
1.36
6.38
235.55
0:41
9852.75
7.05
26.56
1254,05
0.39
$141.19
4.36
20.39
206.58
1911"
0.97
11645
1.20
2.15
164.1 18
0.93
22992
14.09
15.98
1350.51
1
5080.00
11:30
11.35
291 24
Lazy5?
0.96
7719
2.07
891.92
0.58
10387 94
24.15
3147.23
0.99
12.06
12.58
482.93
NEXT
0.96
6380.69
1.22
1.77
596.63
0.41
13002.17
7.92
26.95
19494.85
0.37
6512.62
3.65
25.68
$232.09
CiNN-Fpplorz
0.98
5905 60
2.02
2,35
687-95
0.91
10834 59
19.55
21.79
1872.64
0.96
3164.29
12.51
12.96
585.67
GmpbMi
7485.33
1.25
1,76
0.59
13222.95
10.59
13.50
1599.05
0.96
2706.42
5.78
10.05
MP
0.98
6900.51
1.39
1,68
339.63
0.50
9857.97
9.58
12.30
964.85
0.59
1639.40
7.39
7.76
150.71
MexsoMP
0.96
5327.99
1.32
1.62
345.65
0.83
S040.13
9:45
11:34
518.73
0.99
1547.76
7.50
7.70
158.24
GNN Explare w/ Smoothr
0.98
10447.45
1.74
1,90
730.60
0.91
14957.09
18.73
19.70
2083.58
0.95
5563.40
5.94
9.23
789.72
GophhllP wi Smoother
097
8232 41
1.27
1.49
514. 19
0.59
14935
10:45
13.64
1623.25
0.96
3450.92
7.50
9:05
900.87
Brumy MP Smoother
0.98
7003
1.30
1,47
0.90
10806
94
9.20
11.18
0.59
1935.59
7.30
7.47
196.51
Smootthr
74
1.25
1.45
269.26
0.93
10.44
552.25
1961.49
7.06
7.40
Methads
Kukkl1
Kukaa.Am
KakaaAras
SR1
CK]
PCP]
P71
SR1
PCP]
PCL
PCP)
RRT
0.68
7061 800
9.15
10:47
199.91
0.50
1810.07
9.49
20:57
203.75
0.25
7986.57
11:38
40.23
656.
BIT*
100
2223 43
12:07
12.22
209.14
1.00
1559.95
12.05
12.05
105.99
0.57
7947.42
17.79
31,80
1056.73
LayySP
$76.25
157.06
NEXT
0.61
4808.52
10.38
48.5%
3830.19
0.566
4637.57
30.26
63.74
3719.14
0.38
2141.48
15.39
37.25
4,33.600
0.99
741.34
15.75
15.89
104.35
0.99
$74.50
36.60
16.94
110.91
0.57
2850.16
20.62
33.40
764.84
GmphMP
645.51
12.68
581.96
25.68
MP
1,00
406.77
9.40
9.49
74.88
0.99
405.82
11:43
11.09
02.94
0.64
1575.30
16.13
24.75
806.92
NeuSOMP
100
392.33
9.32
9.40
69.53
0.99
385.06
10.33
10.53
62.81
0.64
1266,89
16,04
24.56
314/64
GNN-Esplon
Umphhbl' wi Smoother
0.9
200:22
9:22
9.20
138.00
0.98
646.40
9.57
10000
99.35
0.60
1979.20
10.73
20.21
869.32
BPU w/ Smoother
100
451.60
8.60
8.68
85.77
0.99
472.40
9.50
9.79
71.35
0.64
1671.10
11.06
19.70
422.95
NeurobiP Smooother
79.31
1362,06
10.98
19,61
Table 2: Comparison of collision probability prediction between Neural Collision Checker and Perceptive Segment Selector in different environments.
Methouls
Accumxy? V7.47
Recalif
Stik3
Contidencef 97:71
Accunacyt 9% 20.40
Recall"
Link
Contidncof 95 V7
Acceracyt 96-77
Hecallt
025
F1C
Contidence
Netral Collision Checker
98:99
97.92
95 46
55 42
V4.00
V7. 19
Perceprive Negreent Sellesee
98.62
90.32
08.99
98.74
96.03
99.38
97.16
97.90
92.49
98.88
W..3
98.82
Methods
Assunayy
Rasilt
Kobal
Fl1
Confidenest
Assunary
Rocall
KakkeAAmm
Fir
Accaracy!
Recallt
Kaka
F11
Codiderent
Neural Colliton Checker
91.007
91.26
01.17
85.44
$1.77
14.02
03.22
$4.20
80,00
86.54
8808
20.31
Pereptive Semeei Selecaue
92.89
94.33
93.65
94.00
93.88
95.67
94.76
95.09
91.11
88.30
59.73
92.24
5.3 Ablation Studies
We further discuss the effectiveness of five key components in NeuroMP to validate design choices, with experimental results presented in Table
Table 3: Comparison of different components on NeuroMP performance.
Stick
Links
Urd
Methods
SRT
CK]
SR1
CK]
PCJ
PT
PCJ
PT
w/o Selective Sampling
0.96
5499.89
1.36
251.48
0.91
8874.08
11.01
863.53
0.97
1758.08
8.42
187.96
Wro Perceptive Segment Selector
0.97
$386.01
1.32
280.86
0.89
8642. 14
10.81
844.62
0.96
1636.90
7.35
188.03
w/o Spectral Heature
0.97
5537, 49
1.37
234.20
0.90
8943.50
11.04
810.24
0.96
1653.71
7.41
187.68
w/o AZFL
0.97
5420.61
1.37
558.58
0.91
8425.45
9.59
819.29
0.98
1652.60
7.74
172.14
Shortcur Retrieval
0.98
4571.21
233.70
0.93
7928.49
9.92
813.78
1475.69
7.61
155.10
NeuroMP
0.98
5327.99
248.68
0.93
8040.13
9.43
818.73
1847.76
7.57
158.24
Kukal3
Kuka2Ams
Kuka3Amas
Methods
SR1
[K]
PCL
PTL
SR1
CK]
PCJ
SRC
CK)
PCJ
PT.
w/o Nelective Sampling
0.98
419.92
10.90
94.55
0..88
588.11
10.96
75.84
0.63
1267.21
16.11
320.54
wio Percepsive Segment Selector
0.98
415.80
9.43
93.13
0.98
409.83
10.43
82.09
0.62
1267.89
16.49
324.66
w/o Spectral Featuure
0.98
412.64
83.77
0.98
389.99
10.74
71.23
1265.51
16.47
316.01
A2FI.
0.98
410.46
9.58
85.87
0.99
387.77
10.94
77.29
0.63
1272.37
16.58
316.36
w/o Shorteut Retrieval
1.00
374,77
9.85
68.07
0.99
366.70
11.05
61.65
0.66
1256.16
16.88
313.67
NeuroMP
1.00
392,33
9.32
69.53
0.99
385.06
10.33
62.81
0.64
1266.69
16.04
314.64
Selective Sampling. Traditional uniform sampling during RGG construction may introduce redundant nodes, increasing search complexity and reducing planning efficiency. Selective sampling addresses this by prioritizing samples in high-value regions, reducing unnecessary exploration. Experimental results show that removing selective sampling leads to substantial increases in collision checks and planning time, indicating slower convergence and higher search overhead. In addition, the observed increase the path cost further confirms its contribution to improving the path quality. Overall, selective sampling enhances planning efficiency and solution quality while maintaining fcasibility.

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Perceptive Segment Selector Ns. The module N's predicts edge-wise collision probabilities within the RGG and removes potentially dangerous edges to generate a safer RGG'. This process significantly reduces the search space, improving planning efficiency. Compared to the Neural Collision Checker in GraphMP, the Wss offers more accurate filtering, mitigating invalid path exploration and enhancing search efficiency. Ablation studies show that replacing Ns with Neural Collision Checker increases collision checks and planning time, suggesting that Neural Collision Checker retains many unsafe edges, thereby inflating computational overhead. In contrast, the Ns enables more reliable graph pruning, improving downstream search stability and performance.
Global Alignment Heuristic. We analyze the effect of this module by incrementally introducing its two core components.
(i) Introducing Spectral Features. Traditional GNNs rely on local neighborhood information, which compromise topologiaal consistency in weakly connected graphs, hindering global path coherence. The module Nu addresses this by incorporating spectral features to enforce global topological constraints and enhance structural representation. Ablation studies show that removing spectral features results in increased path costs, higher collision checks, and reduced success rates in several environments. These findings demonstrate the importance of spectral features in preserving path continuity, reducing search overhead, and improving planning reliability.
(ii) Alignment Dual-Flor Learning (A2FL). GNN-based methods often limited by sparse connec- tivity, making it challenging for some critical nodes to obtain effective heuristic values. To address this, A2FL incorporates a completed channel to assist the weak channel during training, enhancing information propagation in sparse graphs. Consequently, the NE can provide more accurate heuristic estimations in weakly connected graphs. Experimental results indicate that NeuroMP trained without A2FL exhibits increased collision checks, higher path curvature, and longer planning times across various environments. These findings demonstrate that A2FL improves the estimation capability of Nr. reducing redundant exploration and improving path quality.
Shorteut Retrieval. To reduce unnecessary detours, NeuroMP employs the Shorteut Retrieval step to remove redundant nodes from the searched path. Ablation experiments indicate that although this step slightly increases collision checks and planning time, it significantly reduces path redundancy and enhances path quality. The time complexity of this step is O(T2), where T represents the numher of nodes in the searched path. Since the A block typically generates short paths, this step effectively reduces path costs with minimal computational overhead.
5.4 Parameters Discussion
We empirically set the range of the maximum sample number, k-values, and the bias sampling probability 3 and collision probability threshold a to [200, 700], [20, 30), [0.2, 0.4., and [0. 0.1], respectively. A more detailed results and analysis of these parameter settings are in Appendix C
5.5 Further Performance Comparison of Weakly Connected Graphs
In weakly connected graphs with a collision threshold of 0.9, we present the retained edge ratio and planning performance of NeuroMP, BrainyMP and GraphMP. Results indicate that NeuroMP demonstrates enhanced stability in sparse graphs and improves planning performance. Detailed results and analyses are provided in the Appendix
6 Conclusion
Inspired by the two-stage Perception-Decisse model, this paper presents NeuroMP, a two-stage brain-inspired motion planning framework to enhance planning performance in high-dimensional spaces. Across various motion planning tasks, NeuroMP demonstrates superior planning efficiency and path quality, highlighting the potential of brain-inspired methods to improve robotic decision making. Future work will focus on extending the model to dynamic, large-scale, and real-world scenarios while further enhancing computational efficiency.
10

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Acknowledgments
This work supported by the State Key Program of National Natural Science of China (Grant No. 62236001), the Natural Science Foundation of Beijing, China (Grant No. L24701 1), the Major Research Plan of the National Natural Science Foundation of China (Grant No. 92470125), and Hebei Natural Science Foundation (Grant No. F2024105033). It is also supported by the MoE Key Laboratory of Brain-inspired Intelligent Perception and Cognition, University of Science and Technology of China (Grant No. 2421000 and Key Laboratory of Machine Intelligence and System Control, Ministry of Education (Grant No. MISC-202403).
References
[1] Bowen Wang, Xinle Gong, Peiyuan Lyu, and Sheng Liang. Iterative learning-based cooperative
motion planning and decision-making for connected and autonomous vehicles coordination at on-ramps. IEFF Transactions Intelligent Transportation Systems, 25(7):8 (177):8805-11220 20, 2024.
[2] Ahmed Zermane, Niels Dehio, and Abderrahmane Kheddar. Planning impact-driven logistic tasks. IEEE Robotics and Automation Letters, (93:2184-2191 2024.
[3] Peter E Hart, Nils J Nilsson, and Bertram Raphael. A formal basis for the heuristic determination of minimum cost paths. IEEE Transactions on Systems Science and Cybernetics, 4(2):100-107, 1968.
[4] Edsger W Dijkstra. The humble programmer. Communications of the ACM, 15(1))855-866 1972.
[5] Steven LaVale.. Rapidly-exploring random trees: A new tool for path planning. Research Report, 1998.
[6] Sertae Karaman and Emilio Frazzoli. Sampling based algorithms for optimal motion planning. The International Journal of Robotics Research, 30(7):846-894, 2011.
[7] Jonathan D Gammell, Siddhartha S Srinivasa, and Timothy D Barfoot. Informed rrt: Optimal sampling-basee path planning focused via direct sampling of admissible ellipsoidal heuristic. In 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 2997-3004 IEEE, 2014.
[8] Brian Ichter, James Harrison, and Marco Pavone. Learning sampling distributions for robot motion planning. In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages 7087-7094 IEEE, 2018
[9] Xiao Zang, Miao Yin, Jinqi Xiao, Saman Zonouz, and Bo Yuan. Graphmp: Graph neural network-based motion planning with efficient graph search. In Advances in Neural Information Processing Systems, volume 36, pages 3131-3142, 2023.
[10] Binghong Chen, Bo Dai, Qinjie Lin, Guo Ye, Han Liu, and Le Song. Learning to plan in high dimensions via neural exploration-exploitttion trees. In 8th International Conference Learning Representations, 2020.
[11] Zhe Huang, Hongyu Chen, John Pohovey, and Katherine Driggs-Camphell. Neural informed r Learning- based path planning with point cloud state representations under admissible ellipsoidal constraints. In 2024 IEEE International Conference on Robotics and Automation (ICRA), pages 8742-8748. IEEE, 2024.
[12] Jiaxing Yu, Ci Chen, Aliasghar Arab, Jingang Yi, Xiaofei Pei, and Xuexun Guo. Rdt-rrt: Real-time double-tree rapidly-exploring random tree path planning for autonomous vehicles. Expert Systems with Applications, 240: 2024.
[13] Xiao Zang, Miao Yin, Lingyi Huang, Jingjin Yu, Saman Zonouz, and Bo Yuan. Robot motion planning as video prediction: A spatio-temporal neural network-based motion planner. In 2022 JEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 12499. IEEE, 2022.

---

[14] Zhijun Zhang, Haotian He, and Xianzhi Deng. An ingaeemmleeeeeed antinoise fuzzy recurrent neural network for motion planning redundant robot manipulators. IEEE Transactions on Neural Networks and Learning Systems, 2023.
[15] Zhijun Zhang, Zhongwen Cao, and Xingru Li. Neural dynamic fault-tolerant scheme for collaborative motion planning of dual-redundant robot manipulators. IEEE Transactions on Neural Networks and Learning Systems, 2024.
[16] Chenning Yu and Sicun Gao. Reducing collision checking for sampling- saapingg-asedd motion planning using graph neural networks. In Advances in Neural Information Processing Systems, volume 34, pages 4274 4289, 2021.
[17] Smail Ait Bouhsain, Rachid Alami, and Thierry Simeon. Learning geometric reasoning networks for robot task and motion planning. In 13th International Conference on Learning Representations, 2025.
[18] Ryo Yonetani, Tatsunori Taniai, Mohammadamin Barekatain, Mai Nishimura, and Asako Kanezaki. Path planning using neural a search. In International Conference on Machine Learning, pages 12029-12039. PMLR, 2021.
[19] Tianyuan Jia, Ziyu Li, Qing Li, Xiuxing Li, and Xia Wu. Brainymp: Enhancing motion planning using graph neural network inspired by brain spatial relational memory. IEEE Transactions on Intelligent Transportation Systems, (((6):88808899 2025.
[20] Adrian Haith, Jina Pakpoor, and John Krakauer. Independence of movement preparation and movement initiation. Journal of Neuroscience, 531330000 2016.
[21] Melvyn A Goodale and A David Milner. Separate visual pathways for perception and action. Trends in neurosciences, 25(1):20-25, 1992.
[22] Richard A Andersen and He Cui. Intention, action planning, and decision making in parietal- frontal circuits. Neuron, (3(5):568-588) 2009.
[23] Lin Zhong, Yuan Zhang, Chunyu A Duan, Ji Deng, Jingwei Pan, and Ning-long Xu. Causal contributions of parictal cortex to perceptual decision making during stimulus categorization. Nature neuroscience, 22(6))963-973, 2019.
decision-making
[24] Deniz Vatansever, Jonathan Smallwood, and Elizabeth Jefferies. Varying demands for cognitive control reveals shared neural processes supporting semantic and episodic memory retrieval. Nature communications, 2:214,4,, 2021.
[25] Donna Gift Cabalo, Jordan DeKraker, Jessica Royer, Ke Xie, Shahin Tavakol, Raúl Rodríguez- Cruces, Andrea Bernasconi, Neda Bernasconi, Alexander Weil, Raluca Pana, et al. Differential reorganization of episodic and semantic memory systems in epilepsy-related mesiotemporal pathology. Brain, 147( 10:3118-393333 2024.
[26] Karalyn Patterson, Peter Nestor, and Timothy T Rogers. Where do you know what you know? the representation of semantic knowledge in the human brain. Nature Reviews Neuroscience, 8(12):976-98) 2007.
[27] Yitzhak Norman, Omri Raccah, Su Liu, Josef Parvizi, and Rafael Malach. Hippocampal ripples and their coordinated dialogue with the default mode network during recent and remote recollection. Neuron, 109((7):2767-2780 2021.
[28] Charles E Leiserson and Tao Schardl. A work-efficient parallel breadth-firs, first search algorithm (or how to cope with the nondeterminism of reducers). In Proceedings of the twenty-Second Annual ACM Symposium on Parallelism in Algorithms and Architectures, pages 303-314, 2010.
[29] Maxim Likhachev, Geoffrey Gordon, and Sebastian Thrun. Ara*: Anytime a* with provable bounds on sub-optimality. Advances in Neural Information Processing Systems, 16, 2003.
[30] Chao Liu, Lei Wu, Guangxin Li, Hao Zhang. Wensheng Xiao, Dengpan Xu, Jingjing Guo, and Wentao Li. Improved multi-search strategy a algorithm to solve three-dimensional pipe routing design. Expert Systems with Applications, 240: 122313, 2024.
12

---

[31] Dmitri Dolgov, Sebastian Thrun, Michael Montemerlo, and James Diebel. Practical search techniques in path planning for autonomous driving. Ann Arbor, 1001(48105):188800 80, 2008.
[32] Jonathan D Gammell, Siddhartha S Srinivasa, and Timothy D Barfoot. Batch informed trees (bit): Sampling-baser optimal planning via the heuristically guided search of implicit random geometric graphs. In 2015 IEEE International Conference on Robotics and Automation (ICRA), pages 3067-3074. IEEE, 2015.
[33] Nika Haghtalab, Simon Mackenzie, Ariel Procaccia, Oren Salzman, and Siddhartha Srinivasa. The provable virtue of laziness in motion planning. In Proceedings of the International Conference on Aulomated Planning and Scheduling, volume 28, pages 106-113, 2018.
[34] Aviv Tamar, Yi Wu, Garrett Thomas, Sergey Levine, and Picter Abbeel. Value iteration networks. Advances in Neural Information Processing Systems, 29, 2016.
[35] Mohak Bhardwaj, Sanjiban Choudhury, and Sebastian Scherer. Learning heuristic search via imitation. In Conference on Robot Learning, pages 271 271-222111 1-0. PMLR, 2017.
[36] Daniil Kirilenko, Anton Andreychuk, Aleksandr Panov, and Konstantin Yakovlev. Transpath: Learning heuristics for grid-based pathfinding via transformers. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 37, pages 11436-1244,, 2023.
[37] Ahmed Hussain Qureshi, Yinglong Miao, Anthony Simeonov, and Michael C Yip. Motion planning networks: Bridging the gap between learning- and classical motion planners. IEEE Transactions on Robolics, 37(1):48-66 2020.
[38] Adam Fishman, Adithyavairavan Murali, Clemens Eppner, Bryan Peele, Byron Boots, and Dieter Fox. Motion policy networks. conference on Robot Learning, pages 967-977. PMLR, 2023.
[39] Murtaza Dalal, Jiahui Yang. Russell Mendonca, Youssef Khaky, Russ Salakhutdinov, and Deepak Pathak. Neural mp: A generalist neural motion planner. 2nd CoRL Workshop on Learning Effective Abstractions for Planning.
[40] Mayur J Bency, Ahmed H Qureshi, and Michael C Yip. Neural path planning: Fixed time, opar-optimal path generation via oracle imitation. In 2019 JFFE/RSI International Conference on Intelligent Robots and Systems (IROS), pages 3965-3972. IEEE, 2019.
[41] Jacob J Johnson, Uday S Kalra, Ankit Bhatia, Linjun Li, Ahmed H Qureshi, and Michael C Yip. Motion planning transformers: A motion planning framework for mobile robots. arXiv preprint arXiv:2106.0279. 2021.
[42] Ruiqi Ni and Ahmed Qureshi. Ntfields: planning. In / 1tth International Conference on Learning Representations, 2023.
Neural time fields for physics-informed robot motion
physics-informed [43] Ruiqi Ni and Ahmed H Qureshi. Progressive learning for physics informed neural motion planning. In RSS 2023 Workshop on Symmetries in Robot Learning. 2023.
[44] Jacob J Johnson, Ahmed H Qureshi, and Michael C Yip. Learning sampling dictionaries for efficient and generalizable robot motion planning with transformers. IEEE Robotics and Automation Letters, 8(12):794679933, 2023.
[45] Diederik P Kingma. Adam: A method for stochastic optimization. arXiv:1412.6980 2014.
[46] Nathan R Sturtevant. Benchmarks for grid-based pathfinding. IEEE Transactions on Computa- tional Intelligence and Al Games, 4(2):144-444 2012.
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1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: Our abstract and introduction accurately reflect the scope and contributions of this work, namely we propose a brain-inspired motion planning framework to address limitations in existing GNN-based planners.
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A Methodology
A.1 Differentiable A
Differentiable A [8] redefines the traditional A algorithm 3 enabling end-to-end differentiable training. The open list and closed list are represented by binary vectors o E [0, 10.1j and с E [0, 1 respectively. The candidate node with the lowest path cost then selected based on the following calculations.
exp(- (G + H)/A) oo (exp( (G H)
Imax
(10) where G is the cumulative cost, H is the heuristic value estimated by the neural network, and is preset parameter. I is the function that returns a one-hot vector, and the element-wise product @ is used mask the nodes.
o o c=
During the node expansion process, the neighbors of candidate nodes can be computed as Vnbr Av* (1 - c). where Vubr is binary vector, with the entries corresponding neighboring nodes marked 1, A [0, 1][||*[И is the adjaceney matrix, and 1 is vector of all ones. Subsequently, G and are iteratively updated as the node expansion process progresses,
G' = G G Wv,
(11)
V = ((1 (1- +00 (G> G')) @ Vnbr G (1 1) + G' O
(12)
0 (1 V)Vnbr
(13)
where G'denote the accumulated cost of the nodes along the path, including the currently selected nodes, W e R [|V||V]| is the weighted adjacency matrix, and Wv computes the distance from v'to each of its neighboring vertices. The accumulated costs of the neighboring nodes are then updated according to Eq 12 Subsequently, Ois expanded by incorporating the newly explored neighbors.
A.2 Optimization in Online Planning
When NeuroMP performs online planning for a new problem, the trained modules Ns. Nu. and A are integrated to perform the graph search. To further improve path quality and efficiency, two optimization steps are incorporated during the inference procedure of online planning.
Selective Sampling. In traditional graph construction, uniform sampling methods often ignore the environmental structure, leading to purposeless sampling. To address this, we employ a selective sam- pling approach, where hyperparameter 3 E [0, 1] controls the balance between biased and uniform sampling, optimizing exploration efficiency while preserving probabilistic integrity. Specifically, the robot samples nodes from guiding region with probability B8 and uniformly samples from the entire configuration space with probability - B. The guiding region is the circular area with the start and goal as its diameter, reducing redundant sampling.
Shortcut Retrieval. Although the A algorithm completes the pathfinding, the resulting path may path quality. A check window is defined to identify collision-fre shorteut edges. The window length set If found, these two nodes are directly connected, and then redundant intermediate nodes are removed, eliminating unnecessary detours.
have detours. Shorteut retrieval [9] is applied to improve
B Detailed Overall Performance Analysis
Table Salleppreeentt a comparative result NeuroMP and other baselines across six environments. Across all environments, the maximum sampling number is limited to 1000 for all methods, except for RRT* and NEXT in the Link8 environment, where increased to 2000 due to their low success rates (approximately 0.2). By leveraging selective sampling, accurate collision prediction, and optimized A search, NeuroMP achieves a high success rate while significantly reducing collision checks and planning time, maintaining competitive path quality.
21

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Success Rate. NeuroMP consistently achieves optimal or near-optimal success rates across all environments, demonstrating strong competitiveness with state-of-the-art (SOTA) planners. In contrast, RRT* exhibits low success rates, reaching only 0.41 and 0.39 in the Link8 and Ur5 environments, highlighting the instability of classical planners in high-dimensional settings. BIT* and LazySP, benefiting from manually designed heuristics, achieve high success rates in most scenarios. While the CNN-based planner NEXT performs adequately in simpler 3D environments, its success rate drops sharply as dimensionality increases, attaining only 0.41 and 0.37 in Link8 and Ur5, respectively. By comparison, GNN-based planners exhibit consistently superior success rates across all environments.
Collision Check. The collision check is a critical factor influencing planning time and computational efficiency, with fewer checks indicating more optimized search spaces. NeuroMP achieves signifi- cantly fewer collision checks than SOTA methods across all environments. In addition, NeuroMP significantly reduces collision checks compared to GraphMP and GNN-Explorer in all environments, requiring only 71, 61%, 57%, 61%, 66%, and 68% of the collision checks performed by GraphMP. This reduction highlights the effectiveness of its precise edge selection and efficient heuristic search. While LazySP benefits from lazy collision check strategy, NeuroMP achieves further improvements, reducing collision checks to 69%. 77%. 57%, 90%, 67%, and 48% of those by LazySP. Even in the Kuka2Arms and Kuka3Arms environments, NeuroMP maintains low collision check counts of 385.06 and 1266.69, respectively, outperforming all baselines. Furthermore, although NEXT and RRT* show lower path costs, their extremely low success rates indicate poor reliability, as they can only solve relatively simple cases.
Planning Time. A common concern with seaning--asedd methods their high computational cost due to frequent neural network evaluations, such as in NEXT. However, GNN-based planning methods mitigate this issue by operating on sampled RGGs, substantially reducing planning time. Compared to SOTA planners, NeuroMP achieves competitive or faster planning across environments. Although classical planners like RRT exhibit lower planning time due to their simplicity, they suffer from low reliability. Compared to RRT*, NeuroMP achieves comparable planning time in Stick, while providing x, 0.31x, 2.88 x, 2.24x, and 1.12x x speedups in the Link8-Kuka3 Kuka3 environments.
Path cost and Path Cost with Penalty. NeuroMP w/ Smoother achieves the lowest path cost from the Kuka 13 to the Kuka3Arms environment. Although RRT* and NEXT occasionally achieve lower path costs in some environments, their low success rates result in significant penalty costs due to frequent failures. The path cost with penalty confirms that NeuroMP maintains superior path quality even under high-success-rate conditions. Furthermore, NeuroMP outperforms the SOTA planner in environments with high obstruction density (Stick3) and high-dimensional spaces (Kuka3Arms), highlighting its robustness in complex conditions.
C Parameters Discussion
C.1 Maximum Sampling Number
Fig. 5 illustrates the impact of varying maximum sampling numbers on NeuroMP's performance. In GNN based planners, the number of sampled nodes directly influences graph density, connectivity. and computational complexity. Specifically, increasing the number of sampled nodes results in denser graph, covering more feasible areas and reducing failures caused by insufficient sampling. However, once the sampling density reaches the coverage threshold, additional nodes contribute less to finding new paths, causing the success rate to plateau. Similarly, denser graphs may contain more optimal paths, leading slight reduction in path cost. However, collision checks and planning time increase significantly as more nodes and edges expand the search space, thereby increasing collision checks and computational costs.
C.2 l Value
We assume sufficient sample points are available, with the maximum number of samples set within the range [300, 700). Fig. iillustrates the impact varying k-values on NeuroMP's performance. As the l value increases, each node connects to more neighboring nodes, constructing denser edge structure that enhances overall graph connectivity, increasing the success rate. However, when the k-value exceeds the actual connectivity requirement for the current environment, the success rate improvement
22

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03
30
M21
1983
109
510
1000
100
1090
Makias Google
Maddo seqlecanke
Maai aude
Figure 5: Maximum sampling number. (a) Success rate, (b) Collision check, (c) Path cost, (d)
Planning time.
plateaus or slightly decreases. A denser edge structure also increases the likelihood of finding shorter paths, which reduces path cost but slightly increases collision checks. The planning time initially decreases, benefiting from improved heuristic search efficiency due higher graph connectivity, but excessive edges introduce redundancy, leading to longer computation times. Therefore, selecting an appropriate value based on environmental characteristics is essential. In our experimental setup, the optimal threshold range is set to 30).
158+
08
Ervakan
Figure 6: The ls value of K-NN. (a) Success rate, (b) Collision check, (c) Path cost, (d) Planning time.
C.3 The Bias Sampling Probability
Fig. 7 presents the performance of NeuroMP under different , values without applying shortcut retrieval. The success rate initially increases and then decreases as 3 grows, since a higher sampling density in the connection region between start and goal improves the likelihood of discovering feasible paths. However, excessive concentration this region reduces exploration diversity, making it harder to circumvent dense obstacles, thus increasing failure cases. Collision checks generally decline with increasing 3, as samples in the connection region are more likely to form coherent path segments, reducing redundant edge validation. Moreover, high-density sampling in this area expedites the discovery of near-straight-lin paths, potentially lowering path costs. Nonetheless, overly concentrated nodes can lead to local detours around obstacles, increasing overall path cost. Planning time also varies with environment characteristics: in low-obstacle settings (e.g., Kukal3), concentrated sampling reduces RGG size and accelerates planning: in high-obstacle settings (e.g., Stick3), it may trigger more frequent backtracking in the A search.
204
175+
3.4
800
305
Figure 7: Varying bias sampling probability B. (a) Success rate, (b) Collision check, (c) Path cost, (d) Planning time.
23

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C.4
Collision Probability Threshold
Fig. g iillustrates NeuroMP's performance under varying a values, with the maximum sampling number set within [300, 700] and shortcut retrieval disabled. As a increases, more high-risk edges are removed, reducing path interruptions during A search and improving success rates. However, when >>> 0.5, excessive filtering degrades graph connectivity, severing critical connections and increasing failure rates due to the inability to bypass dense obstacles. Without filtering, infeasible edges can obstruct viable paths; conversely, over-filtering reduces the likelihood of finding collision-free paths. Path cost rises with a as detours become more frequent, while planning time decreases due to reduced traversed edges. These results indicate that must balance safety (filtering risky edges) and connectivity (preserving feasible paths), with optimal performance observed in the range [0.2, 0.4].
18
8.5
800
8.4
Calaaan
600
92
04
60
02 01
04
05
60
04
85
01
Calliin puli
Colauee promeity
Colada prdk
Figure 8: Varying collision probability threshold a. (a) Success rate, (b) Collision check, (c) Path
cost, (d) Planning time.
D Further Performance Comparison of Weakly Connected Graphs
In weakly connected graphs with a collision threshold of 0.9, Table 4 presents the retained edge ratio and planning performance of NeuroMP, BrainyMP, and GraphMP. When a = 0.9, most high-risk edges are removed, allowing NeuroMP to surpass GraphMP in planning efficiency and path quality, demonstrating a significant advantage in success rates. When selector performance is comparable, MeuroMP produces more informative heuristics than BrainyMP, yielding significantly faster searches. In more complex settings (c.g., Kuka13 and Kuka2Arms), NeuroMP's selector more accurately removes risky edges and demonstrates significant advantage in success rates. In denser graphs (with more retained edges), NeuroMP achieves slightly higher efficiency while still producing low-cost paths. These results indicate that NeuroMP demonstrates enhanced stability in sparse graphs and improves planning performance.
Table 4: Performance comparison between NeuroMP and GraphMP, BrainyMP with a = 0.9.
Medasia
mil
.RR1
[XC
St6k3
PCC
PCTP]
P7T
rafo
SR1
[3K]
PTLL
PCP
[T]
mil
SR1
PC1
PCPL
PT.
1166
0.90
1100 64
1.40
1.37
354.03
0.41
11.72
10765 37
9-43
13.00
946.71
0.22
0.57
3530.55
3.56
14.97
205.2
BeangiM
0.59
0.96
750075
1.41
2.12
2/0085
0.41
0.77
9996 57
8,35
14.36
930.21
0.22
0.90
2639.14
805
11315
241.10
NewebtP
0.6
9275,00
15.36
262.14
Mobooca
1860
6RT
[K]
Kila15
PCL
PCP]
P7L
SR1
CK1
KatalArms
PCL
PCP
PT]
5R1
CK1
KataTArma
PCJ
PCPL
PT.
GrgesshiP
0.36
0.55
613.35
10:22
21.42
121.45
0.31
0.52
514.22
9:98
20000
91.49
0.22
0:44
1571.25
15.77
25.86
335.2
Bu
0.26
24.29
196.5
0.64
578.37
19.29
29.21
358.79
E Discussion on Map Size and Obstacle Density
E.1
Different Map Sizes
Under fixed robot shape (e.g., point robot) and obstacle density, we evaluate the performance of NeuroMP, BrainyMP, and GraphMP across various map sizes, as shown in Fig. 9 with the maximum number of samples limited to 1000. As the map size increases, all methods exhibit reduced path quality and planning efficiency, but the degradation is more gradual for NeuroMP. Specifically, while overall success rates decline, NeuroMP sustains a higher success rate on the 50 x 50 map, whereas GraphMP shows a marked drop, highlighting NeuroMP's superior robustness in large- scale environments. The increased map size introduces more nodes and edges, clevating collision
24

---

checks and computational costs, thereby reducing search efficiency. Nevertheless, compared to GraphMP and BrainyMP, NeuroMP performs more efficient path searches and substantially reduces unnecessary collision checks by approximately 60% and 40% on the 50 x 50 map. Although path costs increase due to longer step sizes, NeuroMP consistently generates lower-cost paths. While exhibits faster planning on smaller maps, planning time increases notably in larger maps. Future work will aim to further optimize computational efficiency in large-scale environments to enhance practical applicability.
0.5
12
1ap
Mdg 102
700g--00
Figure 9: Performance comparison of MeuroMP, BrainyMP and GraphMP under different map sizes environments. (a) Success rate, (b) Collision check, (c) Path cost, (d) Planning time.
Additionally, Table compares the collision prediction performance of Perceptive Segment Selector Ns in NeuroMP and Neural Collision Checker in GraphMP and BrainyMP across different map sizes. The module Ns consistently outperforms Neural Collision Checker, particularly on smaller maps (from 15 30), with significantly higher accuracy, recall, Fl score, and confidence. Although all methods experience decline in prediction quality on larger maps, NeuroMP maintains clear advantages. Moreover, NeuroMP achieves consistently higher confidence levels, indicating more stable and reliable predictions, thereby enabling more accurate collision detection across varying environmental scales.
Table 5: Comparison collision probability prediction between Neural Collision Checker and Perceptive Segment Selector in different map size environments.
Map Size
Methods
Accuracyt
Recall
F11
Confidence
Neural Collision Checker
99.23
99.37
99.30
97.72
15
Perceptive Segment Selector
99.43
99.71
99.57
99.45
Neural Collision Checker
97.29
97.96
97.63
97.28
20
Perceptive Segment Selector
99.32
99.48
99.40
99.36
Neural Collision Checker
93.45
91.01
92.22
94.09
30
Perceptive Segment Selector
94.33
92.85
93.58
94.73
Neural Collision Checker
85,90
73.00
78.93
86.88
40
Perceptive Segment Selector
86.69
74.99
80.42
87.72
Neural Collision Checker
85.33
61.33
71.37
85.90
50
Perceptive Segment Selector
85.46
62.53
72.22
85.95
E.2
Varying Obstacle Densities
We construct three obstacle density levels in 15 15 maze environment based on point robots. The obstacle densities for the easy, normal, and hard environments are set to 26%-36%, 36%-47%, and 47%-60% respectively. Fig. [0 illustrras the performance of NeuroMP, BrainyMP, and GraphMP under these varying densities, with the maximum number of samples limited to 1000. Although success rates slightly decline obstacle density increases. NeuroMP consistently achieves 100%. 99.9 99.95%, and 99. 99.90% success rates in the respective scenarios. As complexity increases, all methods require more collision checks and longer planning times. However, NeuroMP outperforms both GraphMP and BrainyMP across all settings, requiring only about one-third the number of collision checks compared to GraphMP. This improvement attributed to the more accurate filtering of high-risk edges by NeuroMP, which effectively reduces redundant checks. Moreover, while GraphMP exhibits notable increase in path cost under high-density conditions, NeuroMP maintains more stable and reliable path quality.
25

---

24
108
O1 Amilyy
Cheta In Braliyy
Olitoii draddy
Figure 10: Performance comparison of NeuroMP, BrainyMP and GraphMP under varying obstacle densities. (a) Success rate, (b) Collision check, (c) Path cost, (d) Planning time.
Furthermore, Table compares the module Ns and Neural Collision Checker in collision prediction across varying obstacle densities. The module Wys consistently outperforms Neural Collision Checker in accuracy and confidence across all difficulty levels, demonstrating more stable and reliable predictions that enhance collision checking in complex environments.
Table 6: Comparison collision probability prediction between Neural Collision Checker and Perceptive Segment Selector in environments with different obstacle densities.
Obstacle Density
Methods
Accuracyt
Recall
F1
Confidence?
Neural Collision Checker
99.37
99.59
99.48
99.22
Easy
Perceptive Segment Selector
99.74
99.87
99.80
99.77
Neural Collision Checker
99.05
99.19
99.12
97.13
Normal
Perceptive Segment Selector
99.30
99.61
99.46
99.38
Neural Collision Checker
99.02
98.20
99.21
99.20
Hard
Perceptive Segment Selector
99.57
99.73
99.65
99.60
Discussion of the U-shaped environment
The U-shaped environment is canonical challenge in motion planning, so U-shape tests were added to further validate our method. In a 15x15 2D workspace, U-shaped obstacles are generated to simulate passages between shelves. The starting point is positioned near the bottom inside the U-shaped obstacle, while the goal is placed outside the U-shaped obstacle. The tests are conducted with stick and link8 robots on 500 U-shaped map instances. The results for both robots in the U- shaped environment are shown in the Table 7 Our method shows significant ad advantages in reasoning efficiency, success rate, and path quality.
Table 7: Comparison of all methods in the U-shaped environment.
Stick3
Link8
Methods
SR
CK|
PCJ
PCPL
PT
SR
CK.
PCJ
PCP
PTІ
RRT
0.68
7290.000
1.44
6.81
84.34
0.68
6187.61
6.21
16.75
450.11
BIT
1.00
4704.71
1.62
1.62
60.04
0.95
13545.35
10.31
12.29
582.36
LazySP
0.99
1856.48
1.73
1.78
31.61
0.92
6829.40 40
11.36
13.36
927.80
NEXT
0.99
2051.83
1.42
1.68
115.14
0.63
9656.06
7.65
19.36
4838.95
GNN-Explorer
1.00
1419.12
2.19
33.77
0.93
7926.33
12.76
14.10
681.33
GraphMP
0.99
1791.17
1.68
1.77
40.08
0.93
8085.31
8.23
9.94
556.76
BrainyMP
0.99
1276.75
1.48
1.60
27.03
0.95
6923.27
8.03
9.49
367.59
NeuroMP
0.99
1132.01
1.46
24.72
0.95
5848.10
8.90
287.44
G Case Study in a Real- World Setting
Real-world scenarios or simulations that mimic real-world conditions can further validate the effec- tiveness of our method. We select the City/Strret Map (CSM) Dataset the real-world scenario
26

---

for validation. Sturtevant et al. 46 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 8: Comparison of the planning performance of all methods on the CSM dataset.
Methods
SKT
CKI
PCJ
PCP.
PT1
RRT
0.82
1609.79
0.97
2.61
112.99
BIT*
0.86
1262.28
0.94
2.24
363.39
LazySP
0.85
662.99
0.98
2.31
206.71
NEXT
0.79
6552.28
0.90
2.78
2590.84
GNN-Explorer
0.85
805.70
1.04
2.38
362.55
GraphMP
0.86
1045.66
0.90
2.06
151.27
BrainyMP
0.87
692.84
0.90
1.94
125.39
NeuroMP
0.88
526.42
0.88
102.78
GNN-Explorer w/ Smoother
0.85
951.39
0.95
2.00
373.34
GraphMP w/ Smoother
0.86
1064,91
0.89
1.91
153.96
BrainyMP w/ Smoother
0.87
714.79
0.89
1.80
127.77
NeuroMP Smoother
0.88
545.07
0.87
1.74
105.02
The results on the CSM dataset demonstrated in Table g 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.
H Limitations
Despite its strong performance, NeuroMP has the following limitations.
Sensitivity to Perception Quality. The Perceptive Segment Selector in NeuroMP relies identifying and reasoning about key features of the environment for accurate collision prediction. In scenarios with significant perception noise blurred obstacle boundaries, errors in perception may lead to inaccurate graph construction, thereby affecting the overall performance of path planning.
Lack of Asymptotical Optimality Guarantees. Searching the true optimal path, thereby limiting theoretical optimality, Although our selective sampling strategy mitigates this issue some degree, it cannot ensure optimal-path coverage. In the future. we strategies that leverage prior knowledge to guide sampling,
RGG cannot guarantee inclusion of
(i) design enhanced reduce randomness, and increase the probability that optimal-path structures represented; (ii) explore cuvironment-awart dynamic pruning, which can adaptively refine the RGG online to improve coverage of critical connections and ensure robust path representation.
Generalization Not Fully Evaluated. Current experiments focus on maze planning and robotic arm manipulation. Systematic evaluations across broader task domains are still lacking, especially in dynamic environments or real-world scenarios. In the future, the experimental scope can be expanded to include dynamic scenarios with moving obstacles and time-varying environmental parameters, enabling assessment under nonstationary conditions. In addition, studies will be conducted realistic settings (e.g., indoor navigation and autonomous driving), using real data to quantify performance. These extended evaluations are expected to inform architectural refinements and improve robustness and generalization in dynamic and woal-world environments.
27


Reviews:
[{"review_id": "48ZahQy6QU", "reviewer": "Reviewer_1SA8", "summary": "This paper presents NeuroMP, a brain-inspired motion planning framework that models human planning processes through a two-stage structure: visuospatial perception and semantic-episodic synergistic decision-making. The proposed method is validated on multiple high-dimensional robotic arm tasks, showing superiority over existing classical and learning-based baselines.", "questions": "1.\tPlease clarify whether all baseline methods use the same selective sampling strategy. If not, please provide additional comparisons.\n2.\tCan you explain the difference between NeuroMP and BrainyMP in more detail?", "limitations": "Yes, the authors have adequately addressed limitations in Appendix G.", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "Strengths:\n1.\tThis paper is well-motivated, the brain-inspired method is very interesting; Each module has a clear purpose and is validated via ablation studies.\n2.\tThe evaluation is comprehensive, covering multiple environments and comparing against a wide range of baselines. \n3.\tThe paper is well-organized with clear figures and comprehensive methodology descriptions.\nWeaknesses:\n1.\tThe selective sampling strategy proposed in the paper wasn’t used for the baseline methods, which might make NeuroMP look better than it actually is. A fair comparison would make the results more convincing.\n2.\tAlthough NeuroMP introduces new components, its overall architecture and motivation share notable overlap with BrainyMP, particularly in brain-inspired design and selective sampling strategy. The distinction in contributions could be more clearly articulated.\n3.\tThe main idea is built on existing GNN-based planning methods, and most of the improvements seem like incremental design. But the experimental results are solid and promising, so I recommend a borderline acceptance.", "was_revised": false, "final_justification": "", "rebuttal": "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.\n\n**Q1: Selective sampling**\n\nWe 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 :\n#### Table 1: Performance comparison on Stick3 on Link8\n|Method|SR|CK|PC|PCP|PT|SR|CK|PC|PCP|PT|\n|--|--|--|--|--|--|--|--|--|--|--|\n|GraphMP|0.97|7485.33|1.35|1.76|491.02|0.89|13222.98|10.59|13.80|1569.65|\n|**GraphMP w/**|0.97|7677.42|**1.33**|**1.67**|502.30|0.89|**12590.42**|**9.24**|**11.97**|**1520.51**|\n|GNN-Explorer|0.98|8805.60|2.02|2.23|687.95|0.91|10824.59|19.53|21.29|1872.64|\n|**GNN-Explorer w/**|0.98|9479.68|**1.93**|**2.14**|816.45|**0.93**|10152.95|**17.10**|**18.73**|**1767.66**|\n|NEXT|0.96|6380.69|1.22|1.77|586.63|0.41|13022.17|7.92|26.95|19494.83|\n|**NEXT w/**|0.96|6426.98|1.22|1.77|590.12|**0.42**|**12795.21**|7.97|**26.49**|**19146.13**|\n|RRT*|0.62|10106.18|1.36|6.38|235.55|0.41|9332.73|7.95|26.86|1254.93|\n|**RRT* w/**|**0.63**|10150.64|**1.33**|**6.22**|**224.17**|**0.47**|**8630.95**|**7.32**|**24.77**|**1167.35**|\n\n#### Table 2: Performance comparison on Ur5 and Kuka13\n|Method|SR|CK|PC|PCP|PT|SR|CK|PC|PCP|PT|\n|-----------|------|------|------|------|------|-----|------|------|------|------|\n|GraphMP|0.96|2706.42|8.78|10.05|266.55|0.99|645.51|11.42|12.68|124.71|\n|**GraphMP w/**|**0.98**|**2529.90**|**8.01**|**8.58**|**240.90**|0.99|**627.85**|**11.02**|**12.21**|**119.59**|\n|GNN-Explorer|0.98|3184.29|12.51|12.86|585.67|0.99|741.34|15.75|15.89|104.35|\n|**GNN-Explorer w/**|**0.99**|2844.05|**11.38**|**11.57**|478.06|**1.00**|681.97|**15.52**|**15.55**|108.35|\n|NEXT|0.37|6241.26|4.67|24.04|5014.84|0.61|4868.52|10.35|48.58|3830.19|\n|**NEXT w/**|0.37|**6172.81**|**4.63**|**23.83**|**4961.66**|**0.62**|4811.00|**10.24**|**45.89**|3956.78|\n|RRT*|0.39|3141.19|4.06|29.39|291.74|0.67|2981.80|9.15|30.47|269.91|\n|**RRT* w/**|**0.41**|3121.14|**4.03**|**28.86**|207.81|**0.69**|**2916.34**|**9.12**|**29.49**|**258.25**|\n\n#### Table 3: Performance comparison on Kuka2Arms and Kuka3Arms\n|Method|SR|CK|PC|PCP|PT|SR|CK|PC|PCP|PT|\n|-----------|-----|-----|----|----|------|---|-----|----|----|------|\n|GraphMP|0.98|581.96|11.19|11.77|88.94|0.61|1875.29|16.37|25.68|412.06|\n|**GraphMP w/**|0.98|**572.89**|**10.97**|**11.61**|**87.27**|**0.62**|**1855.84**|16.48|**25.44**|**406.63**|\n|GNN-Explorer|1.00|574.80|16.60|16.94|110.91|0.57|2880.16|20.62|33.40|764.84|\n|**GNN-Explorer w/**|1.00|597.39|**15.00**|**15.98**|161.26|0.57|**2865.41**|**20.21**|**33.01**|**745.60**|\n|NEXT|0.66|4637.57|10.26|48.74|3719.14|0.38|2141.68|15.39|37.25|4383.60|\n|**NEXT w/**|0.66|**4581.39**|**10.07**|**47.34**|3778.16|0.37|2188.96|**15.02**|37.45|**4316.56**|\n|RRT*|0.70|2810.07|9.69|29.87|203.75|0.25|2986.57|11.38|40.23|666.92|\n|**RRT* w/**|**0.72**|**2690.14**|**9.56**|**28.25**|**186.84**|0.25|3228.56|**10.76**|**39.94**|737.03|\n\nThese 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.\n\n**Q2. The difference between NeuroMP and BrainyMP**\n\nWe 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.\n\n1. Addressing BrainyMP's limitations by technical design\n\nBrainyMP 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: \n\n(i) Inaccurate graph construction. The selector may mistakenly retain collision-prone edges or eliminate valid ones, which adversely affects heuristic estimation. \n\n(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.\n\n(iii) Computational complexity and redundancy. The process of extracting subgraphs incurs a high computational cost, and different subgraphs may contain redundant information, reducing efficiency.\n\nTo address these limitations, we propose NeuroMP with the following key contributions: \n\n(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. \n\n(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.\n\n(iii) Spectral features help avoid incomplete coverage, and compared to the introduction of subgraphs, they reduce computational complexity.\n\n2. Distinct brain-inspired principles\n\nWhile both works draw inspiration from neuroscience, the level of abstraction and specific cognitive processes modeled differ significantly.\n\nBrainyMP 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.\n\nIn 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."}, {"review_id": "pLwzvCFqsH", "reviewer": "Reviewer_3DsE", "summary": "This paper proposes to revisit ML-based path planning by designing a new pipeline inspired from human cognitive mechanisms, implementing a two-stage Perception-Decision model. The perception stage constructs an RGG using Transformer blocks while the decision stage uses a dual spatial and spectral RGG encoding to inform an A*-variant search. Results are presented on a number of robotics path planning benchmarks, reporting progress over the SotA.", "questions": "Questions:\nWhy are spectral features used at the decision rather than the perception part of the pipeline? \nIn the ablation study, the contribution of spectral features appears to vary significantly with the benchmarks considered: could you elaborate on this?\nWhy have you not considered standard path planning benchmarks [Sturtevant, 2012]?\n\nSturtevant, N.R., 2012. Benchmarks for grid-based pathfinding. IEEE Transactions on Computational Intelligence and AI in Games, 4(2), pp.144-148.", "limitations": "Limitations:\nAlthough not specifically designated as a limitations section the discussion of subsections 5.4-5.6 addresses transparently and appropriately a number of limitations.\n\nHowever, one major limitation of the paper is the imbalance between the effort and complexity of the method and the restriction to static environments. It might also defeat the brain metaphor, as cognitive systems would be primarily intended for dynamic environments and aim at horizon-bound, suboptimal, dynamic path planning (more on the RTA* philosophy).", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\nThe paper reports compelling results from comprehensive tests, comparing it to other SotA path planners (both ML planners and classical planner), on a number of benchmarks.\nThe text is very rigorously organized and presented, which partly compensates for the complexity of the contents. Highlights include balance between various sections and the level of detail of results presentation and ablation studies. \n\nWeaknesses: \nIn my view the main weakness of this paper rests with the overall complexity of the approach, which may preclude its actual deployment on two levels: replicability and scalability. In that sense it would constitute more a ‘significance’ weakness than a ‘technical soundness’ weakness. Perhaps the overall architecture should be better justified rather than incrementally constructed (and somehow discussed later through the ablation study). \nOther aspects, like restriction to static environments may constitute more a limitation than an intrinsic weakness at this stage of the research development.", "was_revised": true, "final_justification": "The authors provided an extremely detailed rebuttal which answered my most important points. The results on the named additional benchmarks were particularly convincing at short notice. Answers on spectral aspects were equally satisfactory.\nThe concern over static environments remains, however the proposed paper reframing under \"limited resources\" should improve its significance and perception.\nHaving considered other reviews but most importantly the similar quality of responses to other reviewers I have decided to upgrade my rating for the paper.", "rebuttal": "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.\n\n## For weaknesses:\n**W1. Replicability and scalability**\n\nWe 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.\n\n1. Technical reproducibility\n\nTo 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.\n\n2. Model complexity\n\nAlthough 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.\n\n3. Scalability & Real-world generalization\n\nReal-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.\n\nCSM 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.\n#### Table 1 Comparison of all methods on the CSM dataset\n|Method|SR|CK|PC|PCP|PT|\n|-|-|-|-|-|--|\n|RRT*|0.82|1609.79|0.97|2.61|112.99|\n|BIT*|0.86|1262.28|0.94|2.24|363.39|\n|LasySP|0.85|662.99|0.98|2.31|206.71|\n|NEXT|0.79|6552.28|0.90|2.78|2590.84|\n|GNN-Explorer|0.85|805.70|1.04|2.38|362.55|\n|GraphMP|0.86|1045.66|0.90|2.06|151.27|\n|BrainyMP|0.87|692.84|0.90|1.94|125.39|\n|**NeuroMP**|**0.88**|**526.42**|0.88|1.86|**102.78**|\n|GNN-Explorer-S|0.85|951.39|0.95|2.00|373.34|\n|GraphMP-S|0.86|1064.91|0.89|1.91|153.96|\n|BrainyMP-S|0.87|714.79|0.89|1.80|127.77|\n|**NeuroMP-S**|**0.88**|545.07|**0.87**|**1.74**|105.02|\n\nThe 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.\n\nOur 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.\n\n**W2. Restriction to static environments**\n\nWe 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.\n\n## For questions:\n**Q1. Utilization stage of spectral features**\n\n1. Alignment between spectral features and the requirements of the decision stage\n\nThe 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.\n\n2. Computational efficiency and progressive information processing\n\nInspired 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.\n\n**Q2. The contribution of spectral features**\n\nThe 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.\n\n**Q3. Dataset selection**\n\nOur 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.\n\n## For limitations:\n\nWe 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:\n\n1. Imbalance between method complexity and static environment constraints\n\nOur 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.\n\n[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.\n\n2. Justification of the brain-inspired analogy\n\nWe 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."}, {"review_id": "kMWs9uz6oq", "reviewer": "Reviewer_d3Rn", "summary": "This paper presents NeuroMP, a two-stage brain-inspired motion planning framework designed to enhance planning performance in high-dimensional spaces. In the first stage, the method constructs a graph through selective sampling, removing edges that violate constraints through edge selection to create a safe graph. Finally, node heuristics are predicted for this safe graph to determine the path solution that connects the start and goal. Across various motion planning tasks, NeuroMP demonstrates superior planning efficiency and path quality, highlighting the potential of brain-inspired methods to improve robotic decision-making.", "questions": "How do these methods compare to algorithms like P-NTFields, which do not require expert demonstrations but exhibit high inference efficiency and success rates?\n\nIs the brain-inspired approach genuinely beneficial in this context? The computational times are relatively higher than those observed in many end-to-end learning-based methods like MPNet and NTFields. Is the brain-inspired approach helping or is it acting as a limiting factor? This needs to be evaluated.\n\nDoes the method recover from failure? What would be the pathway to address failure cases? Where did the method generally fail?\n\nLearning-based methods often struggle with convoluted U-shaped environments. For instance, consider a robot manipulator moving from one shelf to another, where the start and goal positions are deep inside those shelves. Have you tested your approach in those scenarios?\n\nThe overall performance gain is very marginal over brainyMP. What were the key components that contributed to the relatively improved performance?\n\nWhy did performance significantly drop in the Kuka 3 tests?\n\nThe performance variations between all ablative approaches are marginal. For instance, is shortcut retrieval really necessary?", "limitations": "Yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 1, "significance": 2, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n\nThe paper is technically sound. The approach is multistaged, making progress step by step towards finding solutions. Experiments demonstrate improvements in some metrics compared to prior methods.\n\n**Weaknesses:**\nThe idea presented in this paper shares similarities with many existing learning-based approaches for motion planning; however, these works are neither cited nor compared. These methods also plan in stages: For instance, \"Motion Planning Transformers\" and \"Learning Sampling Dictionaries for Efficient and Generalizable Robot Motion Planning with Transformers.\" The literature review is generally lacking and misses several key contributions in learning-based motion planning, such as MPNet, NeuralMP, NTFields, P-NTFields, and MPiNet.\n\nThe repeated analogy between the brain and the proposed algorithm is unnecessary and negatively impacts the flow for the reader. Although the method is straightforward, it is presented in a convoluted manner. The paper dedicates excessive space to discussing the relationship between brain function and the proposed approach. A simple, intuitive description would have sufficed, allowing for a more thorough literature review and better presentation of the results.\n\nAdditionally, there is no demonstration or illustration of task complexity, making it difficult to gauge the efficacy of the proposed method. The paper would benefit from including real-world experiments. \n\nFurthermore, there is no discussion on the training times or the time required to collect the dataset.", "was_revised": true, "final_justification": "Overall, the authors have addressed some of my concerns, so I will increase my score. However, I believe the paper requires major revisions, particularly in the areas of writing and the literature review.", "rebuttal": "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. \n\n**W1. Literature review and comparisons**\n\nWe 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).\n\n**W2. Simplifying presentation & brain analogy**\n\nWe appreciate your valuable suggestions on improving the readability and structure of the paper. In response to your concerns:\n\n1. 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.\n\n2. 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).\n\n**W3. Task complexity description**\n\nTo 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.\n#### Table 1 Datasets complexity\n|Environment|Obstacles|Map Size|Robot|Configuration Dimension|\n|-|-|-|-|-|\n|Stick3|>46%|15*15|A 3DoF robot|3D|\n|Link8|>46%|15*15|A 8DoF robot |8D|\n|Ur5|Two sets of boxes, poles, pads|15 * 15 * 15|A 6DoF UR5 robot|6D|\n|Kuka13|Some boxes|15 * 15 * 15|A13DoFKUKAarm|13D|\n|Kuka2Arms|Some boxes|15 * 15 * 15|Two 7DoF KUKA arms|14D|\n|Kuka3Arms|Some boxes|15 * 15 * 15|Three 7DoF KUKA arms|21D|\n\n**W4. Discussion on the training times and model complexity**\n\nThank 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.\n#### Table 2 Training times (mm:ss)\n||Stick3|link8|ur5|kuka13|kuka2arms|kuka3arms|\n|-|-|-|-|-|-|-|\n|Selector|00:44|01:32|03:30|02:37|03:46|04:02|\n|Heuristic|02:11|03:55|04:03|05:20|04:34|07:11|\n\nModel complexity. Detailed experimental results and analysis can be found in the response to Reviewer 7bRM \"Q2\". \n\n**Q1. Comparison with P-NTFields**\n\nThank 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.\n#### Table 3 Comparison with P-NTFields\n|Methods|Params|SR|CK|PC|PCP|PT|\n|-|-|-|-|-|-|-|\n|Our|0.0721M|0.99|1547.76|7.37|7.70|158.24|\n|P-NTField|0.5761M|0.54|1717.42|12.92|19.09|768.04|\n\n**Q2&Q5&Q7. Discussion on component performance improvement**\n\n1. Contributions of components and ablation differences\n\nThe 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. \n\nThe 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.\n\n2. Performance differences with BrainyMP\n\nIn 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.\n#### Table 4  BrainyMP and NeuroMP in Stick3\n|Method|Ratio|SR|CK|PC|PCP|PT|\n|-|-|-|-|-|-|-|\n|NeuroMP|0.63|0.97|6664.90|1.4|1.74|245.35|\n|BrainyMP|0.69|0.96|7300.75|1.41|2.12|270.86|\n#### Table 5 BrainyMP and NeuroMP in Kuka13\n|Method|Ratio|SR|CK|PC|PCP|PT|\n|-|-|-|-|-|-|-|\n|NeuroMP|0.46|0.91|624.66|10.02|12.75|117.50|\n|BrainyMP|0.26|0.52|543.24|10.29|24.29|106.85|\n\n**Q3. How to address failure cases**\n\nOur 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.\n\n**Q4. Discussion of the U-shaped environment**\n\nThe 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.\n\n|Method|SR|CK|PC|PCP|PT|\n|-|-|-|-|-|-|\n|RRT*|0.60|7290.00|1.44|6.81|84.34|\n|BIT*|1.00|4704.71|1.62|1.62|60.04|\n|LazySP|0.99|1856.48|1.73|1.78|31.61|\n|NEXT|0.99|2051.83|1.42|1.68|115.14|\n|GNN-Explorer|1.00|1419.12|2.19|1.78|33.77|\n|Graphmp|0.99|1791.17|1.68|1.77|40.08|\n|BrainyMP|0.99|1276.75|1.48|1.60|27.03|\n|NeuroMP|0.99|**1132.01**|**1.46**|**1.55**|**24.72**|\n\n**Q6. Performance decline in the Kuka3Arms**\n\nThe 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."}, {"review_id": "Ri2xDy9tHW", "reviewer": "Reviewer_7bRM", "summary": "This paper introduces NeuroMP, a novel brain - inspired motion planning framework for high - dimensional continuous spaces. Modeling the two - stage Perception - Decision process of the human brain, NeuroMP incorporates a Perceptive Segment Selector and a Global Alignment Heuristic. The former constructs safer graphs, and the latter guides search in weakly connected graphs. Experimental results demonstrate NeuroMP's superiority in planning efficiency and path quality over existing methods while maintaining a high success rate.", "questions": "1. The experiments are conducted in static settings. How will you adapt NeuroMP to dynamic or real - world environments with uncertainties in the future? What modifications or extensions are needed for the model to handle these challenges?\n\n2. Could you provide a more detailed analysis of NeuroMP's computational complexity and memory usage in different environmental settings? This would help assess its suitability for resource - constrained devices and guide further algorithmic optimization.\n\n3. Have you considered combining NeuroMP with other advanced planning algorithms or architectures to leverage their respective advantages? For instance, integrating it with reinforcement - learning - based methods could enhance its decision - making and adaptability in complex environments.", "limitations": "Yes", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### Strengths\n1. NeuroMP, simulating the brain's two - stage model, offers a new solution for high - dimensional motion planning.\n2. NeuroMP outperforms other advanced planners in success rate, collision checks, and planning time across various scenes, proving its better planning efficiency and path quality.\n3. The Perceptive Segment Selector accurately identifies environment patterns to build safer graphs. The Global Alignment Heuristic, with spectral features and A2FL, enhances structural reasoning and heuristic estimation.\n\n### Weaknesses\n1. As NeuroMP searches for paths on sampled random geometric graphs, it cannot ensure the existence of the optimal path within the constructed graph, limiting its application in optimal - path - critical scenarios.\n2. Experiments mainly focus on specific static environments like mazes and robotic - arm operation tasks. The model's generalization ability in dynamic or real - world settings remains unverified.", "was_revised": true, "final_justification": "Overall, the authors have addressed some of my concerns, so I will increase my score.", "rebuttal": "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. \n\n### For Weaknesses:\n\n**W1. Limitation of the optimal path**\n\nWe 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. \n\n**W2. Generalization are not fully evaluated**\n\nWe 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.\n\n1. Generalization of real-world environments\n\nReal-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.\n\nCSM. 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.\n#### Table 1 Comparison of all methods on the CSM dataset\n|Method|SR|CK|PC|PCP|PT|\n|-|-|-|-|-|--|\n|RRT*|0.82|1609.79|0.97|2.61|112.99|\n|BIT*|0.86|1262.28|0.94|2.24|363.39|\n|LasySP|0.85|662.99|0.98|2.31|206.71|\n|NEXT|0.79|6552.28|0.90|2.78|2590.84|\n|GNN-Explorer|0.85|805.70|1.04|2.38|362.55|\n|GraphMP|0.86|1045.66|0.90|2.06|151.27|\n|BrainyMP|0.87|692.84|0.90|1.94|125.39|\n|**NeuroMP**|**0.88**|**526.42**|0.88|1.86|**102.78**|\n|GNN-Explorer-S|0.85|951.39|0.95|2.00|373.34|\n|GraphMP-S|0.86|1064.91|0.89|1.91|153.96|\n|BrainyMP-S|0.87|714.79|0.89|1.80|127.77|\n|**NeuroMP-S**|**0.88**|545.07|**0.87**|**1.74**|105.02|\n\nThe 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.\n\n[1] N. R. Sturtevant, “Benchmarks for grid-based pathfinding,” IEEE Trans. Comput. Intell. AI Games, vol. 4, no. 2,pp. 144–148, 2012\n\n2. Generalization of dynamic environments\n\nOur 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.\n\nWe also recognize the need for broader validation on more complex real‑world datasets. We will therefore expand the experimental scope to comprehensively assess generalization. \n\n[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.\n\n### For Questions:\n**Q1. How will NeuroMP adapt to dynamic or real‑world environments**\n\nWe appreciate the insightful question. Adapting NeuroMP to uncertainty in dynamic and real‑world settings will be our future focus, with two main extensions:\n\n1. 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.\n\n2. 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.\n\nThese enhancements will be detailed in the revised manuscript’s Future Work section.\n\n**Q2. Model Complexity**\n\nWe 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.\n\n1. Parameters and FLOPs\n\nWe 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.\n#### Table 2 Parameters comparison\n|Method|Stick3|link8|ur5|kuka13|kuka2arms|kuka3arms|\n|-|-|-|-|--|-|-|\n|NEXT|0.1644M|0.1645M|0.3959M|0.3968M|0.3969M|0.3978M|\n|GNN-E|0.0911M|0.3580M|0.0925M|0.0952M|0.0956M|0.0982M|\n|GraphMP|0.0694M|0.0711M|0.0711M|0.0731M|0.0734M|0.0759M|\n|BrainyMP|0.0868M|0.0885M|0.0881M|0.0906M|0.0909M|0.0934M|\n|Our|0.0707M|0.0726M|0.0721M|0.0748M|0.0753M|0.0779M|\n\n#### Table 3 FLOPs comparison\n|Method|Stick3|link8|ur5|kuka13|kuka2arms|kuka3arms|\n|-|-|-|-|-|-|-|\n|NEXT|0.3775G|0.3375G|10.5719G|10.5719G|10.5719G|10.5719G|\n|GNN-E|0.0626G|0.2493G|0.0631G|0.0641G|0.0643G|0.0654G|\n|GraphMP|0.0538G|0.0546G|0.0543G|0.0555G|0.0557G|0.0568G|\n|BrainyMP|0.0622G|0.0538G|0.0664G|0.0704G|0.0706G|0.0718G|\n|Our|0.0609G|0.0622G|0.0615G|0.0627G|0.0629G|0.0642G|\n\n2. Optimization for resource-constrained devices\n\nAlthough 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.\n\n**Q3. Future integration of NeuroMP with other methods**\n\nWe 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."}, {"review_id": "Z5taEzSozL", "reviewer": "Reviewer_snn6", "summary": "In this paper, the authors proposed a new two-staged planning method, NeuroMP, motivated by the multi-level planning functionalities in the human brain: perception and decision-making. NeuroMP mimics these functionalities with a Perceptive Segment Selector and Global Alignment Heuristic. The Perceptive Segment Selector encodes local obstacle information to predict collision probabilities and filter unsafe edges, producing a safe Random Geometric Graph (RGG). In the second stage, the Global Alignment Heuristic incorporates both spatial features (e.g., distance to goal) and spectral features (e.g., global graph topology through eigendecomposition) to compute heuristic values $H$ for more efficient A* search. NeuroMP demonstrates on-par or better success rates than previous methods across diverse motion planning tasks, achieving lower path costs through improved graph construction while reducing planning time via better heuristic guidance.", "questions": "- Random Geometric Graphs (RGGs) are mentioned in line 36 before being properly introduced. Please define this upon first use to improve readability.\n- The Perceptive Segment Selector uses $T$ iterations of obstacle encoding. Did you conduct ablation studies on the number of iterations T?\n- While NeuroMP demonstrates clear efficiency gains (reduced collision checks, faster planning), the improvements in fundamental planning capabilities (success rate, path quality) appear marginal. Can you identify specific scenarios where the two-stage perception-decision architecture provides qualitative advantages beyond efficiency?\n- Can you update the results with the error bars to conduct the statistical significance tests?", "limitations": "yes.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "## Strengths\n\n**Neuroscience Inspired Architecture.** The primary strength of this work lies in its novel and principled approach to motion planning, drawing direct inspiration from the two-stage Perception-Decision model of the human brain. This cognitive science foundation provides a strong and elegant motivation for the architectural choices , particularly the separation of the Perceptive Segment Selector (mimicking visuospatial perception ) and the Global Alignment Heuristic (mimicking semantic-episodic synergy ). This is a commendable effort to bridge the gap between neuroscience and robotic planning.\n\n**High Clarity of Presentation.** The paper is well-written and presented. The methodology is explained with good clarity, and Figures 2 and 3, in particular, provide an intuitive and comprehensive overview of the proposed NeuroMP framework and its components. This high level of detail significantly aids in understanding the complex interactions within the model and contributes positively to the potential reproducibility of the work.\n\n**Thorough Empirical Evaluation.** The empirical evaluation is both thorough and convincing. The authors test their method across six challenging motion planning tasks, including high-DoF robotic arms , and use a comprehensive set of metrics (SR, CK, PC, PT, PCP) to provide a multi-faceted view of performance. Furthermore, the detailed ablation studies in Section 5.3 and Appendix C rigorously validate the contribution of each proposed component (e.g., Perceptive Segment Selector, Spectral Features, A2FL) and additional experimental results in Appendix E and F provide the evidences for enhanced stability and superior performances in large-scale environments. The separate analysis of collision prediction performance (Table 2) further strengthens the claims regarding the superiority of the Perceptive Segment Selector.\n\n## Weaknesses\n\n**Marginal Improvement in Success Rate and Path Cost on Saturated Benchmarks.** While the proposed method demonstrates clear improvements in planning efficiency (fewer collision checks, less plan time), its improvement in success rate (SR) and Path Cost (PC) over the SOTA baseline (BrainyMP) is marginal. This is likely because the SR on these benchmarks is already saturated near 100% for the best-performing methods, leaving little room for improvement. However, based on the provided results, the primary contribution of NeuroMP appears to be enhancing the efficiency, rather than fundamentally increasing the solvability of problems and the quality of the plans.\n\n**Lack of Statistical Significant Analysis.** The paper does not report error bars or conduct statistical significance tests for its main results in Table 1. For example, the reported improvements in Path Cost and Planning Time over BrainyMP are often small (e.g., in Ur5, PC is 7.37 vs 7.39; in Kuka2Arms, PT is 62.81s vs 62.94s). Without statistical validation (e.g., running experiments with multiple random seeds and reporting mean and standard deviation), it is difficult to conclude whether these small gains are statistically significant or simply due to random experimental variance. This makes it challenging to robustly assess the true margin of improvement.", "was_revised": true, "final_justification": "The authors have satisfactorily addressed my initial concerns, including those regarding the statistical analysis. More importantly, the critical issue I raised concerning the marginal performance improvement has been resolved through their additional discussion. Therefore, I have raised my score to recommend acceptance.", "rebuttal": "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.\n\n**W1. Marginal improvements in success rate and path cost on saturated benchmarks**\n\nWe 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: \n\n1. Generalization of real-world environments\n\nReal-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.\"\n\n2. Future work\n\nWe 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.\n\n**W2 & Q3. Lack of statistical significant analysis**\n\nWe 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.\n\nAdditionally, 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. \n\n#### Table 1: Comparison and significant differences in success rate under different environments\n|SR|stick3|link8|ur5|kuka13|kuka2Arms|kuka3Arms|\n|-|-|-|--|-|-|-|\n|RRT*|0.62±0.03(**)|0.41±0.06(**)|0.39±0.02(**)|0.67±0.09(**)|0.69±0.05(**)|0.25±0.07(**)|\n|BIT*|0.97±0.03(*)|0.93±0.03(-)|0.99±0.02(**)|1.00±0.00(**)|1.00±0.01(**)|0.57±0.00(**)|\n|LazySP|0.98±0.02(-)|0.88±0.03(**)|0.99±0.01(*)|1.00±0.02(**)|0.99±0.01(**)|0.56±0.00(**)|\n|NEXT|0.96±0.02(**)|0.41±0.04(**)|0.38±0.05(**)|0.61±0.02(**)|0.66±0.04(**)|0.37±0.13(**)|\n|GNN-Explorer|0.98±0.01(**)|0.92±0.03(**)|0.98±0.02(*)|1.00±0.02(-)|1.00±0.01(**)|0.57±0.00(**)|\n|GraphMP|0.97±0.05(**)|0.89±0.04(**)|0.96±0.02(**)|0.98±0.04(**)|0.98±0.02(**)|0.61±0.10(**)|\n|BrainyMP|0.97±0.03(*)|0.90±0.01(**)|0.99±0.02(**)|0.99±0.03(**)|0.99±0.01(**)|0.64±0.03(*)|\n|Our|0.98±0.01|0.93±0.02|0.99±0.02|1.00±0.01|0.99±0.02|0.64±0.02|\n\n#### Table 2 Comparison and significant differences in collision check under different environments\n|CK|stick3|link8|ur5|kuka13|kuka2Arms|kuka3Arms|\n|-|-|-|-|-|--|-|\n|RRT*|10150.45±61.71(**)|9351.92±71.21(**)|3142.53±6.79(**)|3001.12±21.74(**)|2818.19±38.72(**)|2996.24±25.08(**)|\n|BIT*|11357.34±341.89(**)|21419.08±937.17(**)|5418.59±490.37(**)|2060.64±974.84(**)|1787.27±176.63(**)|8127.88±117.93(**)|\n|LazySP|7707.78±127.51(**)|10410.65±106.11(**)|2775.13±97.89(**)|469.56±44.13(**)|567.75±28.30(**)|2699.10±92.57(**)|\n|NEXT|6241.26±115.26(**)|12979.51±45.84(**)|6406.80±99.50(**)|4908.82±33.22(**)|4577.05±51.34(**)|2226.26±70.56(**)|\n|GNN-Explorer|9022.12±268.86(**)|11242.59±335.63(**)|3014.54±193.82(**)|683.99±39.34(**)|605.37±36.39(**)|2913.49±31.52(**)|\n|GraphMP|7496.27±111.95(**)|13066.42±282.84(**)|2696.48±47.32(**)|627.05±11.14(**)|583.56±1.65(**)|1866.42±10.15(**)|\n|BrainyMP|6932.28±89.16(**)|9747.70±209.49(**)|1631.12±25.05(*)|401.06±5.04(*)|405.74±2.04(**)|1576.54±6.14(**)|\n|Our|5300.38±24.46|8029.68±178.82|1568.36±19.13|390.96±3.17|386.19±1.39|1256.47±12.24|\n\n#### Table 3:  Comparison and significant differences in path cost under different environments\n|PC|stick3|link8|ur5|kuka13|kuka2Arms|kuka3Arms|\n|-|-|-|-|-|-|-|\n|RRT*|1.37±0.01(**)|7.96±0.03(**)|4.11±0.03(**)|9.19±0.05(**)|9.69±0.03(**)|11.28±0.12(**)|\n|BIT*|1.73±0.02(**)|14.25±0.20(**)|11.45±0.15(**)|11.95±0.33(**)|12.05±0.06(**)|17.82±0.13(**)|\n|LazySP|1.84±0.01(**)|15.74±0.07(**)|11.95±0.16(**)|16.58±0.19(**)|16.12±0.11(**)|21.14±0.15(**)|\n|NEXT|1.23±0.01(**)|7.97±0.03(**)|4.85±0.11(**)|48.58±0.04(**)|10.10±0.09(**)|15.23±0.10(**)|\n|GNN-Explorer|2.02±0.01(**)|19.16±0.44(**)|12.70±0.20(**)|16.77±0.59(**)|16.71±0.14(**)|20.37±0.31(**)|\n|GraphMP|1.36±0.01(**)|10.62±0.04(**)|8.69±0.06(**)|11.15±0.17(**)|11.19±0.03(**)|16.70±0.34(**)|\n|BrainyMP|1.39±0.01(**)|9.77±0.16(**)|7.42±0.02(*)|9.31±0.07(-)|11.19±0.15(**)|16.64±0.31(-)|\n|Our|1.31±0.01|9.28±0.10|7.39±0.01|9.34±0.03|10.28±0.05|16.27±0.18|\n\n#### Table 4:  Comparison and significant differences in planning time under different environments\n|PT|stick3|link8|ur5|kuka13|kuka2Arms|kuka3Arms|\n|-|-|-|-|-|-|-|\n|RRT*|234.33±1.36(*)|1261.37±29.46(**)|295.52±2.44(**)|268.17±4.60(**)|195.42±6.99(**)|667.03±5.54(**)|\n|BIT*|355.06±10.87(**)|1418.83±43.52(**)|303.35±27.81(**)|211.94±38.90(**)|127.94±12.41(**)|1079.48±22.26(**)|\n|LazySP|894.47±36.23(**)|3160.85±42.49(**)|490.30±28.36(**)|118.93±23.53(**)|171.51±12.37(**)|855.14±10.64(**)|\n|NEXT|588.75±9.35(**)|19514.14±260.53(**)|5205.27±111.67(**)|3918.85±104.21(**)|3808.32±70.80(**)|4421.12±22.54(**)|\n|GNN-Explorer|692.75±26.34(**)|1936.34±39.33(**)|569.55±52.02(**)|122.85±11.97(**)|111.76±15.61(**)|769.18±6.06(**)|\n|GraphMP|501.94±13.28(**)|1621.73±40.14(**)|293.84±40.24(**)|133.99±6.65(**)|91.75±1.96(**)|410.42±2.87(**)|\n|BrainyMP|332.63±9.20(**)|961.48±43.42(**)|165.14±2.90(-)|76.49±1.30(**)|63.78±1.91(-)|403.44±8.42(**)|\n|Our|244.43±3.27|790.20±23.48|162.25±2.75|68.13±1.87|62.61±0.99|321.53±6.23|\n\n**Q1. Definition of random geometric graphs (RGGs)**\n\nThank 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.\"\n\n**Q2. Iterations of obstacle encoding T**\n\nThank 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."}]

Author rebuttal:

Meta-review: The paper proposes a path-planning mechanism for robotics. The perception module builds a graph that approximates the possible safe paths and transitions.The decision module assigns heuristic values to the graph, allowing an efficient A*-style search. The method does not depend on specific features in the perception stage for defining the search space. Instead, the authors employ a differentiable variant of A*, which assumes, among other things, that the nodes are vectors. The submission claims that the heuristic helps compensate for errors in the graph prediction, avoiding dangerous edges.

The reviewers find the work technically solid and the manuscript well written. There was some discussion of novelty. The consensus is that the work is novel and interesting, though gaps in the scholarship caused some hesitation. For one reviewer, it was important to clarify the differences with respect to BrainyMP.

The sampling mechanism was also discussed at length. Since the representation depends on the samples, questions arose regarding the quality of the resulting graph. The authors addressed the general issue of sampling for graph construction. The experiments in the submission, together with additional results posted during the discussion, persuaded the reviewers of the soundness of this aspect. A more detailed discussion of the complexity of the benchmarks also helped to convince the reviewers that the paper deserves acceptance.

The authors must improve the scholarship of the paper. They should clarify the differences with prior work, update the experimental results, and discuss the significance of the new experiments.
Decision: Accept (poster)