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GraRe: Grasp Candidate Re-Ranking for Frozen 6-DoF Grasp Detectors

Jibao Yuan, Yuhui Zhao, Yinzhen Lv, Chao Xu, Shun Li, Chenxi Deng, Shaofei Chen

Year: 2026Venue: arXiv preprintArea: cs.ROType: PreprintEmbeddings: 96

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Abstract

Abstract:Existing 6-DoF grasp detectors typically rank grasp candidates by detector confidence. However, our analysis on GraspNet-1Billion shows that detector confidence is often poorly aligned with grasp quality, causing successful grasp candidates to be ranked too low during execution. Motivated by this observation, we formulate grasp candidate re-ranking as a separate task for frozen detectors, aiming to improve candidate ordering without changing the detector or its grasp candidates. We propose GraRe, which estimates grasp quality from candidate attributes, shell-stratified local geometry, and object context. Candidate attributes condition the local geometric and object-context representations, and a Transformer fuses all three feature types. The predicted quality is combined with detector confidence to produce the final ranking. Experiments on GraspNet-1Billion with three frozen detectors show consistent improvements, with gains of up to 13.60 points in Average AP. Real-robot experiments further demonstrate robust grasping in cluttered scenes. These results show that improving candidate ranking provides a practical way to enhance frozen 6-DoF grasp detectors.

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GraRe: Grasp Candidate Re-Ranking for Frozen 6-DoF Grasp Detectors Jibao Yuan1, Yuhui Zhao1, Yinzhen Lv2, Chao Xu1, Shun Li1, Chenxi Deng1, Shaofei Chen1 Abstract Existing 6-DoF grasp detectors typically rank grasp candidates by detector confidence. However, our analysis on GraspNet-1Billion shows that detector confidence is often poorly aligned with grasp quality, causing successful grasp candidates to be ranked too low during execution. Motivated by this observation, we formulate grasp candidate re-ranking as a separate task for frozen detectors, aiming to improve candidate ordering without changing the detector or its grasp candidates. We propose GraRe, which estimates grasp quality from candidate attributes, shell-stratified local geometry, and object context. Candidate attributes condition the local geometric and object-context representations, and a Transformer fuses all three feature types. The predicted quality is combined with detector confidence to produce the final ranking. Experiments on GraspNet-1Billion with three frozen detectors show consistent improvements, with gains of up to 13.60 points in Average AP. Real-robot experiments further demonstrate robust grasping in cluttered scenes. These results show that improving candidate ranking provides a practical way to enhance frozen 6-DoF grasp detectors. 1 Introduction Grasping in cluttered scenes is fundamental to robotic manipulation in real-world environments. This capability supports applications such as industrial bin picking, warehouse automation, and household object manipulation [9, 8]. However, in such scenes, occlusion reduces object visibility, while nearby objects increase the risk of gripper collisions [16, 35]. Under these conditions, traditional grasp detection methods that rely on predefined 3D object models are difficult to apply [2]. With advances in depth sensing and deep learning, data-driven methods for 6-DoF grasp detection have shown strong performance in cluttered scenes [30, 3]. In general, data-driven 6-DoF grasp detection methods generate a set of grasp candidates from an RGB-D frame or point cloud. Each candidate contains a 6-DoF grasp pose, a gripper width, and an associated detector confidence. During execution, the robot attempts grasp candidates in descending order of detector confidence [10, 19, 36]. Therefore, grasping performance depends not only on the quality of candidate generation but also on the accuracy of candidate ranking. Figure 1: The left examples compare detector and oracle rankings of the same grasp candidates. The right plots compare the two rankings across multiple ranking metrics on GraspNet-1Billion. Grasping failures may arise for two reasons: a detector may fail to generate successful grasp candidates, or it may assign low confidence to candidates that would succeed. To distinguish these cases, we compare the confidence ranking with an oracle ranking that reorders the same grasp candidates using ground-truth labels (Fig. 1). Across multiple ranking metrics on GraspNet-1Billion [12], the oracle substantially outperforms the confidence ranking, showing that successful grasp candidates are often generated but not prioritized. This finding raises a key question: Can grasp candidates be ranked more accurately without modifying candidate generation? Motivated by this observation, we formulate grasp candidate re-ranking as a separate task. Given the grasp candidates produced by a frozen detector, the task keeps all candidates unchanged and predicts a new ordering. Based on this formulation, we propose GraRe. Its key idea is to evaluate each candidate using three complementary types of information: candidate attributes, shell-stratified local geometry, and object context. The shell-stratified representation preserves geometry across different distances from the gripper, while object context describes the candidate relative to the visible object. Candidate attributes condition both geometric representations before a Transformer fuses all three to predict grasp quality. GraRe combines the predicted quality with detector confidence for final ranking. Experiments on GraspNet-1Billion with three frozen detectors show consistent improvements, with gains of up to 13.60 points in Average AP. Ranking analysis shows that GraRe promotes successful grasp candidates, while real-robot experiments demonstrate robust grasping in cluttered scenes. The main contributions of this work are summarized as follows: • We identify the misalignment between detector confidence and grasp quality and formulate grasp candidate re-ranking as a separate task for frozen 6-DoF grasp detectors. The task aims to improve candidate ordering while keeping the detector and its grasp candidates unchanged. • We propose GraRe, which uses candidate attributes to condition shell-stratified local geometry and object context. A Transformer fuses the three representations to predict grasp quality. The predicted quality is combined with detector confidence for final ranking. • We evaluate GraRe with three frozen detectors on GraspNet-1Billion and conduct real-robot experiments. The results show Average AP gains of up to 13.60 points, improved ranking of successful grasp candidates, and robust grasping in cluttered scenes. 2 Related Work 6-DoF grasp detection has evolved from analytical and model-based methods to data-driven methods that predict grasps from RGB-D frames or point clouds [1, 22]. GPD samples grasp candidates and evaluates them using local geometry, while PointNetGPD uses a point-set network for grasp quality estimation [31, 18]. 6-DoF GraspNet generates grasps through variational sampling, while S4G predicts grasps directly from point clouds [21, 27]. The GraspNet-1Billion benchmark provided dense grasp annotations and a standardized evaluation protocol, while subsequent methods improved 6-DoF grasp detection with region-based grasp networks, graspness, and scale-balanced learning [12, 41, 33, 19]. HGGD uses heatmap guidance, FlexLoG predicts grasps from local regions, and Region-Centric Grasp Detection provides a data-efficient solution for cluttered scenes [6, 37, 5]. Beyond grasp generation, candidate ranking relies on grasp quality, which analytical methods evaluate using force closure and grasp wrench space metrics [13, 29]. GtG 2.0 instead estimates grasp quality from a graph of points inside and around the gripper [20]. End-to-end detectors such as AnyGrasp, RNGNet, and EconomicGrasp predict confidence for each grasp candidate and rank the candidates accordingly [11, 7, 36]. Existing methods generally integrate grasp quality estimation or confidence prediction into specific detection pipelines, while grasp candidate ranking has received less attention as a separate task. GraRe addresses this gap by combining predicted grasp quality with detector confidence to re-rank grasp candidates from a frozen detector. Local geometry around the gripper describes possible finger contacts and free space for gripper motion, while object context describes a grasp candidate relative to the visible object. Recent grasp detectors model geometry in point clouds using graph structures or serialization attention [39, 28, 14]. These representations are developed for grasp detection rather than for re-ranking candidates from frozen detectors. GraRe instead combines candidate attributes, shell-stratified local geometry, and object context to estimate grasp quality for grasp candidate re-ranking. 3 Problem Formulation Let S be a scene point cloud and I its aligned RGB image. A frozen 6-DoF grasp detector D for a parallel-jaw gripper takes S as input and produces K grasp candidates, denoted by =cii=1KC=\c_i\_i=1^K. Each candidate is represented as ci=(pi,wi,bi)c_i=(p_i,w_i,b_i). The 6-DoF grasp pose is pi=(i,ti)∈SE(3)p_i=(R_i,t_i) (3). The rotation i∈SO(3)R_i (3) and translation ti∈ℝ3t_i ^3 specify the gripper pose in the camera coordinate system. The scalar wi∈ℝ+w_i ^+ is the gripper width, and bi∈ℝb_i is the detector confidence. The detector ranks the candidates by bib_i. We denote this original order by π∈ΠKπ^D∈ _K. Grasp candidate re-ranking keeps C unchanged and predicts a new ordering of its elements. Let ΠK _K denote the set of all permutations of the K candidates. For any π∈ΠKπ∈ _K, ℰ(,π)E(C,π) measures the quality of the resulting ranking. On GraspNet-1Billion, ℰE is Average Precision (AP) under the official evaluation protocol, which uses multiple friction coefficients [12]. The best possible ranking for C is π⋆=arg⁡maxπ∈ΠK⁡ℰ(,π)π = _π∈ _KE(C,π). A learned re-ranker predicts πRπ^R. Its goal is to improve over the detector order, so that ℰ(,πR)≥ℰ(,π)E(C,π^R) (C,π^D). The detector and all grasp candidates remain unchanged. GraRe does not predict πRπ^R directly. Let θT_θ denote GraRe with learnable parameters θ. For each candidate, it predicts a grasp quality g^i=θ(ci,,I) g_i=T_θ(c_i,S,I) from the candidate, scene point cloud, and aligned RGB image. We combine g^i g_i with the detector confidence bib_i to obtain the final ranking score sis_i. Sorting the candidates by sis_i in descending order gives the re-ranked order πRπ^R. 4 Method GraRe re-ranks grasp candidates using candidate attributes, local geometry, and object context. It combines the predicted quality with detector confidence, and Figure 2 shows the overall architecture. Figure 2: Overview of GraRe. (a) A frozen 6-DoF detector produces confidence-ranked grasp candidates. (b) GraRe encodes each candidate from its attributes, shell-stratified local geometry, and object context, then fuses the three representations to predict grasp quality. (c) The normalized predicted quality and detector confidence are combined to re-rank the unchanged grasp candidates. Dashed output heads are used only during training. 4.1 Feature Extraction Given a grasp candidate ci=(pi,wi,bi)c_i=(p_i,w_i,b_i), the scene point cloud S, and its aligned RGB image I, GraRe extracts candidate, local geometric, and object-context features. These features are fused to predict g^i=θ(ci,,I) g_i=T_θ(c_i,S,I). Candidate Features. Candidate attributes provide information not contained in the geometric features. We encode the grasp pose pip_i, gripper width wiw_i, and detector confidence bib_i with an MLP: hicandidate=fcandidate([pi,wi,bi])h_i^candidate=f_candidate ([p_i,w_i,b_i] ) (1) The output hicandidateh_i^candidate conditions the local geometric and object-context features and is later fused with them. Local Geometric Features. Local geometry describes possible finger contacts and free space for gripper motion. Applying farthest point sampling (FPS) [26] to the full neighborhood may undersample some distance ranges. We therefore transform scene points into the gripper coordinate system and partition them into radial shells with boundaries r0<r1<⋯<rJr_0<r_1<·s<r_J: i,j=i⊤(x−ti)∣x∈,∥x−ti∥2∈[rj−1,rj)Y_i,j= \R_i (x-t_i) x ,\ x-t_i _2∈ [r_j-1,r_j ) \ (2) We apply FPS separately to each shell: i,jlocal=FPSκj(i,j)X_i,j^local= FPS_ _j (Y_i,j ) (3) Here, κj _j is the sampling budget. The local point set is: ilocal=⋃j=1Ji,jlocalX_i^local= _j=1^JX_i,j^local (4) Each shell is encoded by a shared MLP ϕlocal _local and max pooling [25]. Let mi,jm_i,j indicate whether shell j is nonempty: ηi,j=maxy∈i,jlocal⁡ϕlocal(y),mi,j=1 _i,j= _y _i,j^local _local(y), m_i,j=1 (5) Empty shells are excluded by the attention mask ℳiM_i. We add a learned embedding αj _j to retain the radial position of each shell: η~i=[ηi,j+αj]j=1J η_i= [ _i,j+ _j ]_j=1^J (6) A pre-normalized Transformer models interactions among the shell features [32, 38]: η¯i=η~i+MHA(LN(η~i);ℳi)Gilocal=η¯i+FFN(LN(η¯i)) \ array[]l η_i= η_i+MHA (LN( η_i);M_i )\\ G_i^local= η_i+FFN (LN( η_i) ) array . (7) Here, MHAMHA is multi-head self-attention and FFNFFN is a two-layer feed-forward network with GELU activation. We average the valid Transformer outputs and compute global max and mean features: zishell=∑j=1Jmi,jGi,jlocal∑j=1Jmi,jzimax=maxy∈ilocal⁡ϕlocal(y)zimean=1|ilocal|∑y∈ilocalϕlocal(y) \ array[]lz_i^shell= _j=1^Jm_i,jG_i,j^local _j=1^Jm_i,j\\ z_i^max= _y _i^local _local(y)\\ z_i^mean= 1|X_i^local| _y _i^local _local(y) array . (8) The three features are concatenated and projected to a local descriptor: uilocal=flocal([zishell,zimax,zimean])u_i^local=f_local ([z_i^shell,z_i^max,z_i^mean] ) (9) Because local geometry must be interpreted with the candidate attributes, feature-wise linear modulation (FiLM) [24] conditions the descriptor on hicandidateh_i^candidate: hilocal=FiLMlocal(uilocal,hicandidate)h_i^local=FiLM_local (u_i^local,h_i^candidate ) (10) Object-Context Features. Local features cover only the gripper neighborhood, so we use the visible shape of the associated object as context. We project the grasp center tit_i into the aligned RGB image and use the pixel as a prompt for MobileSAM [40]. The predicted mask selects 3D points from S, which are sampled by FPS to form iobjectX_i^object. The RGB image is used only for mask generation. Clutter and occlusion make iobjectX_i^object incomplete. We therefore encode it with Point-MAE, whose masked-patch pretraining supports incomplete shape modeling [23]. Before encoding, we normalize the points to the unit sphere and group them into patches using FPS and k-nearest neighbors (kNN): Giobject=PointMAE(ν(iobject))G_i^object=PointMAE (ν(X_i^object) ) (11) Here, ν denotes normalization and patch grouping. We freeze the Point-MAE backbone and map its mean- and max-pooled patch features through a trainable adapter: uiobject=fobject(Poolmean,max(Giobject))u_i^object=f_object (Pool_mean,max (G_i^object ) ) (12) Because one object can support grasps of different quality, FiLM conditions the object descriptor on hicandidateh_i^candidate: hiobject=FiLMobject(uiobject,hicandidate)h_i^object=FiLM_object (u_i^object,h_i^candidate ) (13) 4.2 Feature Fusion Local geometry is interpreted with grasp pose and gripper width. We fuse candidate, local geometric, and object-context features. Let ℛ=candidate,local,objectR=\candidate,local,object\ denote the three feature types. We add a learned type embedding ere^r and use a pre-normalized Transformer: Zi=[hir+er]r∈ℛHifusion=TFfusion(Zi)hifusion=ffusion(1|ℛ|∑r∈ℛHi,rfusion)g^i=fquality(hifusion) \ array[]lZ_i= [h_i^r+e^r ]_r \\ H_i^fusion=TF_fusion (Z_i )\\ h_i^fusion=f_fusion ( 1|R| _r H_i,r^fusion )\\ g_i=f_quality (h_i^fusion ) array . (14) 4.3 Training Objective During training, the GraspNet evaluator uses annotated scene geometry to obtain the minimum friction coefficient μi _i required for force closure [12]. It also provides the collision and empty-grasp labels yicolly_i^coll and yiemptyy_i^empty. We define the analytical grasp-quality target as: gi=τ−μ¯ig_i=τ- μ_i (15) Here, τ is the success threshold. We set μ¯i=μworst μ_i= _worst for non-finite μi _i and μ¯i=μi μ_i= _i otherwise. Lower friction produces a higher target, preserving differences discarded by binary labels. Because gig_i does not identify the failure type, we add collision and empty-grasp classifiers. An object-classification head regularizes the object-context feature. The total loss is: ℒ=ℒquality+ωcollℒcoll+ωemptyℒempty+ωobjℒobjL=L_quality+ _collL_coll+ _emptyL_empty+ _objL_obj (16) The quality loss is Smooth-ℓ1 _1, the binary heads use binary cross-entropy, and the object head uses cross-entropy. The coefficients ωcoll _coll, ωempty _empty, and ωobj _obj weight the auxiliary losses. These losses are used only during training. 4.4 Score Fusion The detector confidence bib_i and predicted quality g^i g_i have different scales. We apply z-score normalization within each candidate set to obtain b~i b_i and g~i g_i, then compute: si=(1−λ)b~i+λg~is_i=(1-λ) b_i+λ g_i (17) where λ∈[0,1]λ∈[0,1] controls the contribution of predicted quality. Sorting sis_i in descending order gives the final ranking. 5 Experiments 5.1 Benchmark, Baselines, and Metrics Benchmark. The GraspNet-1Billion benchmark [12] contains 97,280 RGB-D images of 88 objects in 190 cluttered scenes, captured with RealSense and Kinect cameras. It provides annotations for more than one billion 6-DoF grasp poses. We use the official split of 100 training scenes and 90 test scenes. The test set is divided into Seen, Similar, and Novel splits, each containing 30 scenes. Baselines. The three frozen 6-DoF grasp detector baselines are GraspNet-Baseline [10], Scale-Balanced Grasp [19], and EconomicGrasp [36]. They cover different architectures and performance levels. For each detector and camera, GraRe re-ranks the detector’s original grasp candidates. The detector parameters and grasp poses remain unchanged. Unless otherwise stated, all experiments use a single λ=1λ=1 for every detector and camera. Metric. We follow the official GraspNet evaluation protocol [12]. For each grasp, μi _i is the smallest coefficient in 0.2,0.4,0.6,0.8,1.0,1.2\0.2,0.4,0.6,0.8,1.0,1.2\ that satisfies force closure, with μi≤0 _i≤ 0 indicating an invalid grasp. For each frame and threshold μ, precision is evaluated at k=1,…,50k=1,…,50, counting a grasp as correct when 0<μi≤μ0< _i≤μ. AP averages precision over k, thresholds, frames, and scenes. We report AP for the Seen, Similar, and Novel splits and their mean, denoted as Average AP. The supplementary material provides complete experimental settings and hyperparameters. 5.2 Comparison with Existing Methods Table 1 compares GraRe with GPD [31], PointNetGPD [18], S4G [27], GraNet [34], GSNet [33], HGGD [6], GtG 2.0 [20], FlexLoG [37], and RNGNet [7] on GraspNet-1Billion. We abbreviate GraspNet-Baseline [10], Scale-Balanced Grasp [19], and EconomicGrasp [36] as GN, SBG, and EG, and their GraRe variants as GraReGNGraRe_GN, GraReSBGGraRe_SBG, and GraReEGGraRe_EG. We report only published results without collision detection. Method Seen Similar Novel Average GPD 22.87/24.38 21.33/23.18 8.24/9.58 17.48/19.05 PNetGPD 25.96/27.59 22.68/24.38 9.23/10.66 19.29/20.88 S4G 25.71/- 18.45/- 9.04/- 17.73/- GraNet 43.33/41.48 39.98/35.29 14.90/11.57 32.73/29.44 GSNet 65.70/61.19 53.75/47.39 23.98/19.01 47.81/42.53 HGGD 64.45/61.17 53.59/47.02 24.59/19.37 47.54/42.52 GtG 2.0 68.79/62.61 61.71/53.93 29.75/24.45 53.42/47.00 FlexLoG 72.81/69.44 65.21/59.01 30.04/23.67 56.02/50.67 RNGNet 75.20/72.23 66.62/58.43 32.38/26.05 58.06/52.24 GN 47.83/41.97 42.79/37.56 16.94/12.24 35.85/30.59 GraReGNGraRe_GN 64.48/53.94 58.78/46.39 25.10/16.04 49.45/38.79 SBG 62.27/- 56.92/- 23.80/- 47.66/- GraReSBGGraRe_SBG 68.76/- 62.64/- 27.51/- 52.97/- EG 69.30/63.75 61.50/52.43 25.28/19.61 52.02/45.26 GraReEGGraRe_EG 75.12/69.90 64.39/58.00 28.34/22.04 55.95/49.98 Table 1: Comparison on GraspNet-1Billion. Each entry reports AP (%) as RealSense/Kinect. “-” denotes an unavailable result. GraRe improves AP in every reported setting. It raises Average AP by 13.60/8.20 points for GN on RealSense/Kinect, 5.31 points for SBG on RealSense, and 3.93/4.72 points for EG on RealSense/Kinect. With EG, GraRe achieves an Average AP of 55.95/49.98 on RealSense/Kinect, 0.07/0.69 points below FlexLoG. Across seeds 7, 11, and 13, the sample standard deviation of Average AP is at most 0.26 points, and the best-seed results in Table 1 exceed the corresponding means by at most 0.28 points. All five seed-7 paired scene-bootstrap 95% confidence intervals exclude zero, with positive gains in 92.2–100% of scenes (Fig. 3). Figure 3: Paired scene-bootstrap results for the seed-7 models. Points show mean Average AP gains, intervals show 95% confidence intervals from 10,000 resamples, and the right column reports the percentage of scenes with positive gains. RS and K denote RealSense and Kinect. Table 2 evaluates parameter sharing across the three known detectors by jointly training one model on the RealSense candidate sets produced by GN, SBG, and EG. Variant GN SBG EG Detector-specific 48.77± 0.06 52.60± 0.21 55.64± 0.06 Joint 48.42± 0.11 52.75± 0.07 55.86± 0.12 Joint w/o Identifier 48.20± 0.16 52.60± 0.17 54.47± 0.29 Joint w/o Confidence 47.62± 0.44 51.40± 0.31 52.32± 0.70 Table 2: Joint training on RealSense. Values are mean Average AP (%) ± sample SD over seeds 7/11/13. All variants use candidate features and local geometric features without object-context features, and Joint includes a learned detector identifier. Joint training differs from the matched detector-specific models by at most 0.35 points in Average AP. The detector identifier improves EG by 1.39 points, and removing detector confidence lowers Average AP for all three detectors, with the largest decrease of 3.55 points on EG. Seed-level joint-training results and cross-detector transfer diagnostics are provided in the supplementary material. 5.3 Ablation Studies Table 3 reports the ablation results on the RealSense test set. Variant GN SBG EG Detector 35.85/↓ 13.60 47.66/↓ 5.31 52.02/↓ 3.93 Full GraRe 49.45/– 52.97/– 55.95/– Concat Fusion 48.63/↓ 0.82 52.71/↓ 0.26 55.83/↓ 0.12 w/o Candidate 47.66/↓ 1.79 50.81/↓ 2.16 50.49/↓ 5.46 w/o Local 45.03/↓ 4.42 50.54/↓ 2.43 54.22/↓ 1.73 w/o Object 48.71/↓ 0.74 52.54/↓ 0.43 55.63/↓ 0.32 w/o Shell-wise FPS 48.27/↓ 1.19 52.54/↓ 0.43 55.41/↓ 0.54 w/o Aux. Losses 49.03/↓ 0.43 52.19/↓ 0.78 55.26/↓ 0.69 Binary Loss 48.94/↓ 0.51 52.33/↓ 0.64 55.08/↓ 0.87 Random Labels 37.05/↓ 12.41 40.85/↓ 12.12 39.76/↓ 16.19 Table 3: Ablation results on the RealSense test set. Each cell reports Average AP (%) and its decrease from full GraRe. Concat Fusion is a capacity-matched variant that uses candidate and local geometric features and replaces FiLM and the feature fusion Transformer with concatenation and an MLP. Auxiliary losses include collision, empty-grasp, and object-classification losses. Binary Loss replaces the continuous quality target with binary success supervision at τ=0.6τ=0.6, and Random Labels permutes the continuous targets. Candidate features contribute most to EG, whereas local features contribute most to GN and SBG. The capacity-matched Concat Fusion variant reduces Average AP across all three detectors, and the remaining components provide further consistent gains. Replacing the continuous target with binary supervision reduces Average AP by 0.51–0.87 points, while randomizing the targets reduces it by 12.12–16.19 points. The supplementary material reports expanded feature, alignment, and target-supervision controls. Figure 4 shows detector-specific sensitivity to λ. GN improves as λ increases while remaining positive on all 90 scenes, whereas EG peaks at λ=0.75λ=0.75 with a 4.14-point mean gain and 89 positive scenes, indicating that retaining detector confidence benefits EG. Figure 4: Score-fusion sensitivity for the seed-7 RealSense models. Each cell reports mean Δ (top) and the number of scenes with positive gains out of 90 (bottom). Darker shading within each row indicates a larger gain, and the outlined cell marks the largest mean gain for that detector. 5.4 Candidate Ranking Analysis We analyze whether failures arise because a candidate set contains no successful grasp or because a successful grasp is ranked too low. A grasp is successful if it is collision-free, nonempty, and satisfies force closure at μi≤0.4 _i≤ 0.4. Discounted Success@K (DS@K) measures the rank-discounted percentage of successful grasps among the top K candidates. Following discounted cumulative gain (DCG) [15], a candidate at rank r is weighted by 1/log2⁡(r+1)1/ _2(r+1). The top-K frame success rate measures the percentage of frames containing at least one successful grasp among the top K candidates. At K=1K=1, we also count changes from failure to success and from success to failure after re-ranking. We construct an oracle ranking without changing the grasp candidates or their poses. It places successful grasps first and orders them by increasing finite μi _i, with ties resolved by detector confidence and the original candidate order. Because the oracle uses ground-truth test labels, it is not deployable. Its AP represents the upper bound attainable by re-ranking the existing grasp candidates. Figure 5: Candidate ranking analysis using the same grasp candidates from the GraspNet-1Billion RealSense test set. Panels show (a) Discounted Success@K, (b) top-K frame success rate, (c) Average AP, and (d) top-1 outcome changes. Curves in panels (a) and (b) are macro-averaged over three detectors and all 23,040 test frames per detector. Figure 6: Qualitative ranking examples for GN and GraRe using the same candidate sets. Panels (a)–(d) show failure-to-success changes, and panels (e)–(f) show success-to-failure changes. Insets mark the top-ranked grasps, and colors show scores normalized within each panel. Figure 5 shows that GraRe improves candidate ranking without changing the candidate sets. It exceeds the confidence ranking in DS@K at every evaluated K and raises DS@K at K=1K=1 from 49.35% to 59.97%, while the oracle reaches 98.95%. This oracle gap shows that successful candidates are often available but ranked too low, and the larger frame-success gains at small K indicate that re-ranking primarily improves the top of the ranking. Across GN, SBG, and EG, GraRe closes 36.97%, 19.09%, and 10.73% of the oracle AP gaps and yields net top-1 gains of 20.23, 5.82, and 5.82 points, demonstrating consistent gains across all three detectors. Figure 6 shows how re-ranking changes the top-ranked grasp while keeping the candidate set unchanged. In panels (a)–(d), GraRe replaces GN’s colliding top choices with successful candidates from the same set, showing that re-ranking can recover successful candidates overlooked by detector confidence. In panels (e)–(f), GraRe instead promotes candidates with μi=0.8 _i=0.8 and μi=0.6 _i=0.6 above GN’s successful choices. Both harmful cases are from the Novel split, indicating that unfamiliar geometry remains difficult to rank. 5.5 Real-Robot Experiments Setup and Objects. We evaluate grasp candidate re-ranking on a UR3 robot equipped with a RealSense D435 camera and a Robotiq 2F-85 gripper. The workspace contains separate grasping and placement regions. Figure 7 shows the complete object collection, including objects from YCB or GraspNet-1Billion [4, 12] and objects outside these datasets. Figure 7: Real-robot setup and test objects. Panel (a) shows the robot and workspace, and panel (b) shows the complete object collection. Protocol, Metrics, and Results. We construct ten cluttered scenes by mixing objects from the collection in Fig. 7. Based on object count, occlusion, and stacking, we group Scenes 1–2 as easy, Scenes 3–7 as medium, and Scenes 8–10 as hard. Each scene is evaluated with GN, SBG, and EG using both the detector order π^D and the corresponding GraRe order πRπ^R. Within each comparison, the hardware, detector, collision filtering, RRT* motion planning [17], and stopping condition remain unchanged, and only the candidate order changes. Grasp outcomes are manually verified from the recorded execution frames. Table 4 reports grasp success rate (GSR), completion rate (CR), maximum consecutive failures (MCF), and online inference latency (LAT). Detector GSR CR MCF LAT GN 73.4/88.9 10/100 4/2 1.06/1.45 SBG 70.4/87.2 30/90 6/2 0.95/1.21 EG 68.2/88.5 70/100 4/2 0.76/0.97 Table 4: Real-robot results over ten mixed-object cluttered scenes. Each entry reports π^D/πRπ^R. GSR and CR are percentages, MCF is the maximum number of consecutive failed grasp attempts in a scene, and LAT is the mean online inference latency per selected execution in seconds. GraRe raises GSR by 15.5, 16.8, and 20.3 points and CR by 90, 60, and 30 points for GN, SBG, and EG, respectively, while reducing MCF to two attempts for all detectors. The gains transfer to closed-loop execution at the cost of 0.21–0.39 seconds in mean online inference latency. Across the 30 evaluations, π^D clears 11 scenes, compared with 29 for πRπ^R. In medium and hard scenes, πRπ^R clears 23 of 24 evaluations, compared with 8 of 24 for π^D, showing that the gains are not confined to easy scenes. Re-ranking converts 18 incomplete evaluations to complete, leaves one incomplete, causes no regressions, and reduces unsuccessful physical attempts from 73 to 28 (61.6%). Figure 8: Real-robot evidence of re-ranking. Panel (a) compares the rank of each executed grasp under π^D (horizontal) and πRπ^R (vertical), with points below the diagonal promoted by re-ranking. Panels (b)–(c) show the same executed grasp (green) moving from rank 20 to rank 2 within the unchanged EG candidate set. Panel (d) shows the observation after successful removal. Of the 237 grasps executed under πRπ^R, 160 (67.5%) rank higher than under π^D, reducing the mean rank from 11.56 to 5.30 (Fig. 8(a)). Of the 37 grasps promoted from outside the top nine into the top three, 34 succeed, showing that GraRe improves physical execution by promoting successful grasp candidates ranked too low by detector confidence. In EG Scene 10, the successful grasp in Fig. 8(b)–(d) moves from rank 20 to rank 2. The resulting order clears the scene in nine attempts, whereas π^D succeeds in five of 12 attempts and leaves two objects. 6 Limitations GraRe does not improve every test scene. Across the five detector and camera settings in Fig. 3, each evaluated on 90 scenes, it improves scene-level AP in 435 of 450 comparisons (96.7%), while 12 of the 15 decreases occur with EG. One limitation is that GraRe estimates the grasp quality of each candidate independently, although ranking depends on their relative quality. Consequently, it can promote an unsuccessful grasp above a successful one, as shown in Fig. 6(e)–(f). 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In 2021 IEEE International Conference on Robotics and Automation (ICRA), 13474–13480. Supplement Material Appendix A Supplementary Roadmap The main paper reports the central benchmark and real-robot results. This supplement serves as an evidence map: it documents the shared protocol, expands the quantitative analyses, and connects changes in candidate order to closed-loop execution. It addresses four questions: • Q1: Do the reported AP gains persist across friction thresholds, random seeds, cameras, and scenes? We provide complete AP@μ profiles, seed-level results, paired bootstrap intervals, and scene-level scope statistics. • Q2: Which modeling and operating choices account for the gains? Feature, loss, and capacity-matched controls are complemented by sensitivity analyses for the candidate budget and score-fusion weight. • Q3: How does GraRe change the original candidate order, and how much oracle headroom remains? We analyze oracle ranking, top-K frame success, top-1 transitions, and re-ranking magnitude. • Q4: What practical trade-offs arise in parameter sharing, training cost, closed-loop execution, and failure cases? We report joint training on known detectors, model size and training cost, real-robot execution traces and latency, and qualitative failure cases. The Experimental Setup, Hyperparameter Settings, and Evaluation Protocol sections document reproducibility. In every comparison, GraRe changes only the order of the detector’s original grasp candidates; their identities, poses, and widths remain unchanged. Appendix B Experimental Setup Offline training and benchmark experiments are conducted on a Linux workstation equipped with eight NVIDIA GeForce RTX 5090 GPUs and two Intel Xeon Gold 6459C processors. Each processor has 32 physical cores and supports two hardware threads per core, providing 64 physical cores and 128 logical CPUs in total. The workstation has 754 GiB of system memory. The software environment consists of Python 3.12.3, PyTorch 2.12.1, CUDA 13.0, and cuDNN 9.2. The real-robot experiments use a UR3 robot, an Intel RealSense D435 RGB-D camera, and a Robotiq 2F-85 parallel-jaw gripper. Online candidate generation, GraRe inference, and grasp candidate re-ranking are performed on a deployment computer equipped with an NVIDIA GeForce RTX 2060 GPU, while the robot controller handles motion execution and device communication. Appendix C Hyperparameter Settings Unless stated otherwise, the same configuration is used for GN, SBG, and EG on both cameras. Configurations for each detector use its corresponding grasp candidates but do not change the GraRe architecture. Following the main paper, a frozen detector D produces the candidate set =cii=1KC=\c_i\_i=1^K, and GraRe keeps C unchanged during training and evaluation. Multi-seed experiments use seeds 7, 11, and 13; controlled single-seed experiments use seed 7. The notation below follows that of the main paper. Setting Value Optimizer AdamW Learning rate 2×10−42× 10^-4 Weight decay 1×10−41× 10^-4 Batch size 2,048 Gradient clipping 1.0 Validation split 10%, scene-level Validation split seed 7 Epoch range 20–40 Early-stopping patience 10 epochs Selection metric Validation ℒqualityL_quality LR schedule Reduce on plateau LR patience / factor 4 epochs / 0.7 Minimum learning rate 1×10−51× 10^-5 Mixed precision Automatic Initialization seeds 7, 11, 13 Table 5: Optimization and model-selection hyperparameters used by the default RealSense protocol and EG Kinect experiments. Test AP is not used for checkpoint selection. Setting Default GN Kinect Maximum epochs 40 80 Early-stop patience 10 15 Minimum optimizer steps 0 50,000 Minimum checkpoint steps 0 20,000 Checkpoint interval Disabled 5,000 Scheduler patience 4 8 Scheduler warm-up 0 30,000 Minimum learning rate 10−510^-5 10−610^-6 Local-health batches 0 4 Minimum local RMS 0 0.05 Minimum shuffle ratio 0 0.05 Table 6: Training-schedule overrides for the GN Kinect local-aligned model. All other hyperparameters retain their default values. Appendix D Evaluation Protocol We use the official GraspNet-1Billion split: 100 scenes for training and 90 scenes for testing. The test set contains 30 Seen, 30 Similar, and 30 Novel scenes, with 256 RGB-D frames per scene. GN, SBG, and EG denote GraspNet-Baseline, Scale-Balanced Grasp, and EconomicGrasp, respectively. For every comparison, the detector and GraRe use the same candidate identities, poses, and widths; only their order changes. Setting Value Retained candidates M M=KM=K (all candidates in C) Outer shell boundary rJr_J 40 m Voxel size 8 m Shell edges (r0,…,rJ)(r_0,…,r_J) (0,5,15,25,40)(0,5,15,25,40) m Shell budgets (κ1,…,κJ)( _1,…, _J) (64,128,128,192)(64,128,128,192) Local point budget 512 Object point budget 512 Prompt cluster radius 30 m Minimum mask area 200 pixels Maximum mask area 40% of image Object patch groups / size 32 / 32 points Table 7: Candidate and feature-construction hyperparameters. Setting Value Candidate-feature input dimension 14 Feature dimension dim(hir) (h_i^r) 128 Shell Transformer layers / heads 1 / 4 Shell Transformer FFN expansion 2× TFfusionTF_fusion layers / heads 1 / 4 TFfusionTF_fusion FFN expansion 2× Quality-head hidden dimension 0 Trainable Point-MAE blocks 0 Dropout 0.1 Success threshold τ 0.4 Collision weight ωcoll _coll 0.10 Empty-grasp weight ωempty _empty 0.05 Object weight ωobj _obj 0.05 Score-fusion weight λ 1.0 Table 8: Network, objective, and re-ranking hyperparameters. A zero quality-head hidden dimension denotes a linear fqualityf_quality; the Point-MAE adapter remains trainable. The official friction thresholds are 0.2, 0.4, 0.6, 0.8, 1.0, and 1.2. For each frame and threshold μ, the evaluator computes precision at k for k=1,…,50k=1,…,50, where a grasp is correct if 0<μi≤μ0< _i≤μ. AP for each split is the mean precision over all values of k, friction thresholds, frames, and scenes. We report AP for the Seen, Similar, and Novel splits and their mean, denoted as Average AP. AP@μ fixes the indicated friction threshold before averaging over ranks, frames, scenes, and splits. Main and controlled single-detector checkpoints are selected using held-out scene-level validation loss. The joint multi-detector models reported below instead use detector-balanced validation NDCG@50, as stated in their subsection. Test AP is never used to choose an epoch or an optimization hyperparameter. GN and EG are evaluated with both cameras. SBG is evaluated only with RealSense because a supported SBG Kinect detector checkpoint and its corresponding candidate set are unavailable. Appendix E Complete Benchmark Results (Q1) The main paper reports AP averaged over all six friction thresholds. Figure 9 expands this comparison by visualizing Average AP@μ at every official threshold and summarizing the corresponding Average AP gains. Figure 9: Complete Average AP@μ profiles. Panels (a)–(e) show the five detector–camera settings, and panel (f) summarizes their Average AP gains. Each profile averages the Seen, Similar, and Novel splits. Solid blue lines denote the re-ranked order πRπ^R, dashed gray lines denote the detector order π^D, and blue shading denotes the per-threshold gain. Curves use the reported checkpoints; seed variation is reported in Figure 10. Across all five detector–camera settings, the re-ranked order remains above the detector order at every official friction threshold. The gain varies with detector strength but does not arise from a single threshold, supporting the Average AP improvements reported in the main paper. Appendix F Training-Seed Stability (Q1) Figure 10 tests whether the main gains depend on initialization by reporting all completed main-model seeds. The main comparison uses the reported best-seed checkpoint for each detector–camera pair, while the figure shows all three runs and their dispersion. Figure 10: Training-seed stability. Points show seeds 7/11/13 centered by each detector–camera three-seed mean; pale segments span the observed range. Filled blue markers identify the checkpoints used in the main comparison, and right-hand labels report mean± SD over n=3n=3 runs. Across settings, sample SD is at most 0.26 AP and the minimum–maximum range is at most 0.51 AP, so the gains do not depend on an unstable initialization. Best-seed selection raises reported AP above the three-seed mean by only 0.14, 0.28, 0.17, 0.06, and 0.26 AP for RealSense GN/SBG/EG and Kinect GN/EG, respectively. Appendix G Additional Ablation Studies (Q2) G.1 Feature Sufficiency Figure 11(a) expands the main ablation to both cameras and includes single-feature sufficiency tests. All comparisons use seed 7, keep C unchanged, and set λ=1λ=1. “Candidate only” retains only hicandidateh_i^candidate, while “Local only” retains only local geometric features. Figure 11: Additional ablation studies. (a) Feature-sufficiency controls. (b) Auxiliary-loss controls. Cells report the change in Average AP from the matched full GraRe model; panel (a) headers also report full-model Average AP. The panels use independent color scales. C/E denotes collision and empty-grasp supervision. The dominant feature depends on the detector. Removing local geometric features has the largest effect for GN, while removing candidate features has the largest effect for EG. Object-context effects are smaller; in the matched seed-7 RealSense SBG comparison, removing object context changes Average AP by only 0.08 points. Candidate-only and local-only variants remain below full GraRe in every completed camera setting, indicating that candidate attributes and local geometry provide complementary evidence. G.2 Auxiliary Losses Figure 11(b) isolates the full auxiliary objective and its collision/empty-grasp and object-classification components. Removing all auxiliary losses lowers Average AP by 0.27–0.81 across the five settings. The individual loss groups are less consistent: removing collision/empty supervision slightly improves RealSense SBG and EG by 0.07–0.08 AP, while the corresponding Kinect changes are negative. For Kinect, the 95% intervals for removing collision/empty supervision are [−0.15,0.23][-0.15,0.23] AP for GN and [−0.12,0.51][-0.12,0.51] for EG; the intervals for removing object-classification supervision are [−0.15,0.31][-0.15,0.31] and [−0.22,0.36][-0.22,0.36], respectively. The aggregate auxiliary objective provides a modest benefit, but the individual components do not show reliable effects in isolation. G.3 Capacity-Matched Controls To test whether the gains can be explained by trainable parameter count, we compare three candidate-plus-local models over three seeds. PointNet+concat has 401,499 trainable parameters, ShellAttn+concat has 406,171, and GraRe-PL has 414,875; GraRe-PL is GraRe without object context. Camera Det. PointNet ShellAttn GraRe-PL RealSense GN 45.80± 4.21 48.83± 0.19 48.77± 0.06 RealSense SBG 52.40± 0.16 52.54± 0.18 52.60± 0.21 RealSense EG 55.45± 0.19 55.85± 0.20 55.64± 0.06 Kinect GN 38.00± 0.11 38.01± 0.10 38.04± 0.12 Kinect EG 49.37± 0.23 49.72± 0.33 49.66± 0.23 Table 9: Capacity-matched Average AP (%), reported as mean± SD over seeds 7/11/13. With comparable trainable parameter counts, ShellAttn+concat and GraRe-PL achieve closely matched AP across the five settings, differing by at most 0.21 points. This control shows that the gains cannot be attributed to parameter count alone. It characterizes two alternative shell-aware local-fusion implementations in the object-free setting; the full GraRe model additionally incorporates object context and joint three-feature fusion. G.4 Ranking Baselines To compare GraRe with alternative ranking objectives, we first evaluate ranking baselines under a capacity-matched protocol. Each run uses a matched budget of 144 candidates per frame, three initialization seeds, and the same official evaluator. The table reports Average AP as mean± SD over seeds 7/11/13. Method GN SBG EG PointNetGPD-style 45.88± 0.40 35.69± 1.35 44.84± 0.77 Set score-only 35.89± 0.04 47.61± 0.03 45.45± 1.28 RankNet PointNet-PL 48.18± 0.10 52.66± 0.29 47.94± 0.11 ListMLE PointNet-PL 47.75± 0.27 52.41± 0.09 48.03± 0.14 PointNet-PL 47.92± 0.21 52.34± 0.18 47.54± 0.28 GraRe-PL 48.13± 0.13 52.32± 0.06 47.81± 0.04 Score-only 35.85± 0.00 47.65± 0.00 46.30± 0.02 Pose-score 42.60± 0.15 49.57± 0.04 47.29± 0.11 Table 10: Capacity-matched ranking baselines, Average AP (%), under a 144-candidate budget. Bold marks the largest mean within each detector column; these comparisons use retained candidate subsets rather than all original candidates used in the main protocol. Under the 144-candidate budget, the largest mean depends on the detector: RankNet reaches 48.18 AP for GN and 52.66 AP for SBG, while ListMLE reaches 48.03 AP for EG. GraRe-PL remains close at 48.13, 52.32, and 47.81 AP, whereas the PointNetGPD-style, score-only, and pose-score controls are lower. Thus, within this restricted-budget control, the ranking objective does not determine a consistent ordering across detectors. This setting is distinct from the all-candidate protocol used for the main results. We further evaluate EG at its native candidate scale: RankNet and ListMLE with both PointNet-PL and GraRe-PL train and evaluate on all K=1,024K=1,024 original candidates in C. Each triplet is AP/AP@0.80.8/AP@0.40.4. Method AP/AP@0.80.8/AP@0.40.4 Δ vs. π^D Detector order π^D 52.02/61.91/44.25 — GraRe 55.95/65.83/48.08 +3.93 RankNet PointNet-PL 55.83/65.00/48.91 +3.81 ListMLE PointNet-PL 55.94/65.48/48.54 +3.92 RankNet GraRe-PL 55.70/64.81/48.88 +3.67 ListMLE GraRe-PL 55.58/65.16/48.05 +3.56 Table 11: EG native-candidate ranking controls. All learned models train and evaluate on the original K=1,024K=1,024 candidates in C, using seed 7. GraRe-PL denotes GraRe without object context. The evaluator uses the official top-50 protocol. At the native EG scale, the PointNet-PL RankNet and ListMLE controls improve the detector order by 3.81 and 3.92 AP, respectively, reaching 55.83 and 55.94 AP. The corresponding GraRe-PL rank-loss controls reach 55.70 and 55.58 AP, or +3.67 and +3.56 AP over the detector order. Full GraRe gives the largest AP (55.95), while ListMLE PointNet-PL is within 0.01 AP and RankNet PointNet-PL attains the highest AP@0.40.4. Together with the restricted-budget comparison, these results show that the candidate-scale-consistent protocol supports several competitive ranking objectives; full GraRe combines object context with joint candidate, local, and object-feature fusion. G.5 Local-Alignment Controls The shuffled-local control preserves the local encoder but deterministically assigns each candidate another candidate’s local point cloud. It therefore tests whether aligned candidate–geometry correspondence matters. Figure 12: Local-alignment controls. The horizontal axis reports the Average AP gain over the detector order π^D, whose Average AP appears in parentheses. The w/o Local and shuffled-local controls nearly coincide, whereas aligned full GraRe provides a further 1.76–4.33 AP. Shuffling local point sets closely matches removing them: the absolute difference is at most 0.20 AP. The aligned model exceeds the shuffled control by 1.76–4.33 AP across all five settings, indicating that local geometry is useful primarily when it remains associated with the correct grasp candidate. Appendix H Sensitivity and Robustness (Q2) Figure 13 summarizes score fusion, candidate budget, and supervision controls under the matched seed-7 protocol. Figure 13: Sensitivity and robustness. (a) Average AP gain over the detector order π^D as λ varies; the star marks the RealSense EG maximum. (b) Average AP under a strict top-M budget relative to all K original candidates; hollow red markers fall below the detector order. (c) Average AP change under the detector order, randomized targets, and binary-success targets. Figure 14: Original candidate-set size and retained candidate budget. (a) Mean candidates per frame in C, averaged over 90 test scenes. (b) Average AP under a strict top-M budget relative to all K original candidates. Solid lines denote RealSense and dashed lines denote Kinect; only evaluated budgets are connected. H.1 Score-Fusion Weight Figure 13(a) varies the score-fusion weight in si=(1−λ)b~i+λg~is_i=(1-λ) b_i+λ g_i without retraining. The unified setting is λ=1λ=1 for all detectors and cameras. GN and SBG RealSense and both Kinect settings improve monotonically over the evaluated grid. RealSense EG peaks at λ=0.75λ=0.75, 0.21 AP above λ=1λ=1. Unless otherwise stated, we use the detector-independent setting λ=1λ=1 for every detector and camera. Figure 15 gives λ a direct behavioral interpretation. At λ=0λ=0, the score reduces to normalized detector confidence and exactly reproduces the detector order. Increasing λ changes more top-ranked candidates and raises both failure-to-success and success-to-failure transitions. At λ=1λ=1, the top-ranked candidate changes on 96.71%, 89.67%, and 98.49% of GN, SBG, and EG frames, respectively. Figure 15: Signed RealSense top-1 transition matrix over 23,040 frames per detector. Blue positive cells show failure-to-success transitions, while red negative cells show success-to-failure transitions; the negative sign is used only to distinguish direction. Color intensity and cell labels report transition magnitude. The λ=0λ=0 detector order has zero transitions and is omitted. For GN, the net top-1 improvement increases monotonically with λ. For SBG, λ=0.75λ=0.75 gives a slightly larger net improvement than λ=1λ=1 (6.25 versus 5.82 points), while their Average AP differs by only 0.09. For EG, λ=0.75λ=0.75 gives the highest Average AP, whereas λ=1λ=1 gives the largest top-1 net improvement. Moving from λ=0.75λ=0.75 to 11 increases success-to-failure transitions by 3.43, 5.92, and 4.01 points for GN, SBG, and EG; their paired 10,000-resample scene-bootstrap 95% confidence intervals are [2.73, 4.16], [5.04, 6.80], and [2.95, 5.11], respectively. Thus, λ controls how conservatively GraRe departs from the detector order. The scene-level support follows the same tradeoff. Across the 270 RealSense detector–scene pairs, λ=0.25λ=0.25, 0.500.50, 0.750.75, and 1.001.00 improve Average AP on 270, 269, 269, and 262 pairs, respectively. Figure 16 shows that GN retains positive gains on all 90 scenes as its mean gain rises. For EG, λ=0.75λ=0.75 gives a 4.14-AP mean gain with 89/90 positive scenes, whereas λ=1λ=1 gives a 3.93-AP gain with 83/90 positive scenes. Thus, increasing λ can widen the negative scene-level tail depending on the detector. Figure 16: Score-fusion gain–coverage trajectories on RealSense. Each line connects λ=0.25λ=0.25, 0.500.50, 0.750.75, and 1.001.00 over 90 scenes; arrows point toward λ=1λ=1. GN retains complete coverage, whereas EG moves left and downward from λ=0.75λ=0.75 to 11. H.2 Candidate Budget For a strict top-M evaluation with M≤KM≤ K, candidates outside the detector’s original top M are removed before re-ranking and official evaluation. Figure 13(b) reports 100×AP(M)/AP(K)100×AP(M)/AP(K), where K is the number of original candidates in C produced by the frozen detector. Figure 14 additionally relates this retention curve to the number of original candidates. RealSense GN and SBG produce roughly 165 and 144 candidates per frame, whereas EG produces 1,024 candidates per frame with either camera; the latter therefore requires a substantially larger M to preserve the Average AP obtained using all original candidates. For GN and SBG, M=200M=200 is within 0.02 AP of the RealSense result using all original candidates; Kinect GN is equivalent at the displayed precision. EG requires a substantially larger budget: M=200M=200 is below the Average AP under the detector order on both cameras, while M=800M=800 is within 0.02 AP on RealSense and 0.09 AP on Kinect. Thus, the same retained candidate budget preserves different fractions of the detector’s original candidates across detectors. H.3 Target and Label Controls The score-only control uses only bib_i and reproduces each detector’s ordering exactly. We additionally permute the analytical training targets while preserving their marginal distribution, and replace the continuous target with binary success labels at two thresholds. Figure 13(c) shows that random labels lower AP by 12.41–16.19 points relative to the full model. GN remains 1.20 AP above its detector baseline, whereas SBG and EG fall below their baselines. Binary targets remain competitive but do not exceed the continuous-margin target in any detector setting. These controls show that the gain depends on meaningful continuous grasp-quality supervision; changing τ inside gi=τ−μ¯ig_i=τ- μ_i only adds a constant. Appendix I Statistical Analysis (Q1) To test whether the aggregate gains persist across scenes, we perform 10,000 paired scene-level bootstrap resamples between detector and GraRe AP. Each detector–camera comparison uses all 90 test scenes and all 256 frames per scene, giving 23,040 frame evaluations without frame subsampling. Across the five detector–camera settings, this gives 115,200 detector–camera–frame evaluations, corresponding to 46,080 distinct camera frames because the same RealSense or Kinect frames are evaluated by multiple detectors. Each scene-level AP value averages all 256 frames, ranks k=1,…,50k=1,…,50, and the six official friction thresholds. The RealSense rows use seed 7 so that they match the controlled ablation protocol; the Kinect rows use their corresponding seed-7 models. These confidence intervals measure variation across test scenes and are distinct from the training-seed variation in Figure 10. Figure 17: RealSense scene-level Average AP gains over the detector order π^D. Each point is one scene; boxes show the interquartile range and median. Labels report median gains, including negative values on some SBG and EG Similar scenes. Figure 17 complements the bootstrap intervals with the underlying scene distribution. GN has the largest and most consistent per-scene gains, while the stronger EG detector has a smaller and more heterogeneous gain, especially on Similar scenes. The plotted points include all 30 scenes in each split, for 90 scenes per detector. Tables 12 and 13 provide the complete split-level Average AP analysis. Each row compares the same scenes under the detector order π^D and re-ranked order πRπ^R; “Positive” is the fraction of scenes whose paired AP difference is greater than zero. Det. Split Δ 95% CI Positive GN Average 13.60 [12.39, 14.81] 100.0% Seen 16.65 [15.23, 18.13] 100.0% Similar 16.00 [14.43, 17.72] 100.0% Novel 8.16 [ 6.65, 10.04] 100.0% SBG Average 4.80 [ 4.23, 5.39] 98.9% Seen 5.99 [ 5.20, 6.75] 100.0% Similar 5.30 [ 4.18, 6.59] 96.7% Novel 3.10 [ 2.44, 3.86] 100.0% EG Average 3.93 [ 3.24, 4.57] 92.2% Seen 5.83 [ 4.88, 6.86] 100.0% Similar 2.89 [ 1.51, 4.15] 80.0% Novel 3.07 [ 2.29, 3.88] 96.7% Table 12: Complete RealSense scene-bootstrap results for the seed-7 models, Average AP. Det. Split Δ 95% CI Positive GN Average 8.12 [ 7.05, 9.14] 97.8% Seen 12.14 [10.83, 13.40] 100.0% Similar 8.52 [ 7.01, 10.08] 100.0% Novel 3.70 [ 2.56, 5.01] 93.3% EG Average 4.72 [ 3.96, 5.49] 94.4% Seen 6.16 [ 4.74, 7.62] 96.7% Similar 5.58 [ 4.33, 6.91] 93.3% Novel 2.43 [ 1.73, 3.18] 93.3% Table 13: Complete Kinect scene-bootstrap results for the seed-7 models, Average AP. All split-level confidence intervals exclude zero. The positive-scene fraction decreases as the detector becomes stronger, reaching 80.0% for RealSense EG Similar. Thus, the smaller EG gain is more scene-dependent than the GN gain, but it remains positive at the aggregate split level on both cameras. I.1 Scene-Level Scope Table 14 summarizes the sign and lower tail of all 450 detector–camera–scene comparisons. A scene is improved or degraded according to the paired difference AP(πR)−AP(π)AP(π^R)-AP(π^D) computed from its complete 256-frame evaluation. Setting Imp. Deg. ≤−0.5≤-0.5 Min. Δ RealSense GN 90 0 0 +2.78+2.78 RealSense SBG 89 1 1 −0.57-0.57 RealSense EG 83 7 6 −9.03-9.03 Kinect GN 88 2 1 −1.20-1.20 Kinect EG 85 5 4 −1.46-1.46 All 435 15 12 −9.03-9.03 Table 14: Scene-level applicability over the complete test set. Imp./Deg. count improved/degraded scenes; “≤−0.5≤-0.5” counts decreases of at least 0.5 AP. Each setting contains 90 scenes and 23,040 frames. Overall, 435/450 detector–camera–scene pairs (96.7%) improve, and 248 improve by at least 5 AP. Of the 15 degraded pairs, 12 decrease by at least 0.5 AP, six decrease by more than 1 AP, and one decreases by more than 5 AP. The Seen, Similar, and Novel splits contain 1/150, 9/150, and 5/150 degraded pairs, with mean gains of 9.35, 7.66, and 4.09 AP, respectively. Similar scenes therefore have the largest negative tail, concentrated in RealSense EG, whereas Novel scenes have the smallest mean benefit. EG accounts for 12 of the 15 degraded pairs. Only one scene is degraded for EG on both cameras; the remaining cases are specific to a detector–camera combination. Figure 18 visualizes both the scene-level distribution and its rank-wise origin. Panel (a) shows all 90 scenes in every detector–camera setting rather than only their aggregate mean. Panel (b) localizes the change within the official top-50 protocol. Positive scenes improve most strongly at the beginning of the re-ranked order and retain a positive gain through rank 50. For degraded scenes, the mean precision change is −7.96-7.96 points at rank 1 and −1.43-1.43 points at rank 20, approaches zero near rank 30, and reaches +1.02+1.02 points at rank 50. Their AP decrease is therefore concentrated near the head of the ranking. Figure 18: Scene-level applicability using the complete 23,040-frame evaluation for each setting. (a) Each point is one scene and colors identify the Seen, Similar, and Novel splits. Short black lines mark medians, the dashed line marks zero gain, and right-hand labels give the fraction of scenes with positive Δ . (b) Change in precision at rank k under πRπ^R relative to π^D. Lines show the mean over improved or degraded scenes, and shading shows the interquartile range across scenes; every scene value averages all frames and friction thresholds. The scene-level AP sign agrees with the top-1 Net sign in 14 of the 15 degraded pairs. However, 85 of the 435 improved pairs have a negative top-1 Net, because Average AP also measures deeper ranks and all six friction thresholds. The single degraded RealSense SBG scene illustrates the converse: its top-1 Net is +8.59+8.59 points, but its precision changes at ranks 5 and 10 are −3.35-3.35 and −3.91-3.91 points, producing a −0.57-0.57 AP change. The negative cases also reveal two applicability limits. For the seven degraded RealSense EG scenes, the detector produces 1,024 candidates and the oracle top-1 success rate is 100%, but failure-to-success and success-to-failure transitions average 14.12% and 26.90%, respectively. The five degraded Kinect EG scenes show the same ranking pattern, with 12.89% failure-to-success and 21.33% success-to-failure. In contrast, the two degraded Kinect GN Novel scenes average only 61.7 candidates and 84.8% oracle top-1 success, compared with 101.2 candidates and 97.3% for its positive scenes. EG degradation therefore primarily reflects errors near the head of the re-ranked order, whereas the Kinect GN Novel cases also reflect limited coverage of the detector’s original candidates. Appendix J Candidate Ranking Analysis (Q3) J.1 Oracle Ranking Following the main paper, the oracle ranking keeps the candidate set C and grasp poses unchanged. It places successful grasps first and orders them by increasing finite μi _i; ties are resolved by detector confidence and the original candidate order. The oracle uses analytical test labels and is not deployable. Its AP is the upper bound attainable by re-ranking the detector’s original candidates. The fraction of the gap closed by GraRe is (APGraRe−APdet)/(APoracle−APdet)(AP_GraRe-AP_det)/(AP_oracle-AP_det). Camera Det. Detector GraRe Oracle Gap closed RealSense GN 35.85 49.45 72.64 36.97% RealSense SBG 47.66 52.97 75.48 19.09% RealSense EG 52.02 55.95 88.62 10.73% Kinect GN 30.59 38.79 58.70 29.17% Kinect EG 45.26 49.98 85.32 11.79% Table 15: Oracle-ranking analysis using the unchanged grasp candidate sets, Average AP (%). GraRe closes 10.73–36.97% of the detector-to-oracle gap on RealSense and 11.79–29.17% on Kinect. The remaining gap is 32.67 AP for RealSense EG and 35.34 AP for Kinect EG, showing that substantial ranking headroom remains even for the stronger detector order. Det. M Detector GraRe Oracle GN 50 32.28 40.21 51.25 100 35.47 47.34 65.47 144 35.81 49.05 70.74 200 35.85 49.43 72.50 All candidates 35.85 49.45 72.64 SBG 50 40.80 43.78 55.40 100 46.79 51.19 70.51 144 47.57 52.33 74.65 All candidates 47.66 52.46 75.48 EG 50 29.40 30.62 37.39 100 37.32 39.10 49.88 144 41.51 43.70 57.25 200 45.01 47.59 64.13 All candidates 52.02 55.95 88.62 Table 16: Controlled seed-7 candidate-budget analysis for the RealSense oracle ranking, Average AP (%). “All candidates” denotes the detector’s original candidate set. Table 16 applies the same official evaluator after restricting the detector’s original candidate set to its top M. GraRe and the oracle ranking operate on exactly the same retained candidates as the corresponding detector order. GraRe improves the detector order at every evaluated budget. The oracle AP rises sharply as more candidates are retained, especially for EG, confirming that the larger EG original candidate set contains substantial ranking headroom rather than merely redundant proposals. J.2 Top-K Frame Success Rate The top-K frame success rate is the percentage of frames with at least one successful grasp among the first K candidates. As in the main paper, a grasp is successful if it is collision-free, nonempty, and satisfies force closure at μi≤0.4 _i≤ 0.4. The oracle top-1 frame success rate equals the fraction of frames whose original candidate set contains at least one such grasp. Top-1 success rate Top-50 success rate Camera Det. Det. GraRe Oracle Det. GraRe Oracle RealSense GN 38.32 58.55 98.58 95.36 97.37 98.58 RealSense SBG 54.29 60.11 98.80 96.96 97.60 98.80 RealSense EG 55.43 61.26 99.48 93.65 95.01 99.48 Kinect GN 36.56 48.79 96.99 94.77 95.95 96.99 Kinect EG 51.35 56.57 99.93 92.01 94.57 99.93 Table 17: Top-K frame success rate (%) at μi≤0.4 _i≤ 0.4, averaged over the Seen, Similar, and Novel splits. The oracle top-1 frame success rate of 96.99–99.93% shows that almost every frame already contains at least one successful grasp candidate. GraRe provides its largest improvement at rank 1; the improvement narrows by rank 50 because the detector order has more opportunities to include a successful candidate. J.3 Top-1 Transitions We count frame-level changes in the top-ranked outcome under the default λ=1λ=1 RealSense protocol. Failure-to-success and success-to-failure denote changes in the binary success criterion defined above. Det. Frames Failure→ Success→ Net GN 23,040 28.78% 8.55% +20.23 SBG 23,040 17.01% 11.19% +5.82 EG 23,040 17.40% 11.58% +5.82 Table 18: Complete RealSense top-1 transition statistics. The positive net transition is consistent with the Average AP and top-1 frame success-rate gains. GraRe replaces a successful detector top-ranked grasp with a failed grasp in 8.55–11.58% of frames. At λ=1λ=1, the success-to-failure rate is highest on Similar scenes for all three detectors: 10.72% for GN, 12.66% for SBG, and 16.05% for EG. J.4 Re-Ranking Magnitude Table 19 reports how often GraRe changes the detector’s top-ranked candidate and how much detector confidence is sacrificed by the selected replacement. Every comparison keeps the detector’s original candidate set unchanged. Det. Split Candidates Top-1 changed Δbi b_i GN Seen 167.13 96.05% -0.635 Similar 178.08 97.06% -0.625 Novel 151.12 97.01% -0.519 SBG Seen 150.12 91.43% -0.410 Similar 152.70 91.50% -0.377 Novel 129.24 86.07% -0.248 EG Seen 1024.00 99.34% -5.766 Similar 1024.00 99.09% -5.035 Novel 1024.00 97.06% -3.571 Table 19: Complete RealSense re-ranking statistics. Candidates is the mean number of candidates produced per frame, and Δbi b_i is the change in detector confidence from the top-ranked candidate under the detector order π^D to that under the re-ranked order πRπ^R. GraRe changes the top-ranked candidate in 86.07–99.34% of frames and consistently promotes candidates with lower original detector confidence. It therefore acts as a substantive re-ranker rather than a small perturbation of detector confidence. Because detector-confidence scales are model-specific, Δbi b_i is compared only within each detector. Appendix K Joint Training on Known Detectors (Q4) We train one model on the original candidate sets produced by GN, SBG, and EG. Detector-balanced sampling contributes two frames from each detector per optimization step. Checkpoints are selected by the mean held-out scene-level NDCG@50 across the three detectors; the test set is not used for model selection. “ID” adds a learned detector identifier, while “no conf.” removes detector confidence bib_i from the candidate representation. Joint model Det. Seeds 7/11/13 Mean± PointNet-PL/no ID GN 48.26/48.49/48.41 48.39± 0.12 SBG 52.54/52.63/52.48 52.55± 0.08 EG 54.65/54.78/54.84 54.76± 0.10 GraRe-PL/no ID GN 48.39/48.14/48.09 48.20± 0.16 SBG 52.78/52.44/52.58 52.60± 0.17 EG 54.79/54.36/54.25 54.47± 0.29 GraRe-PL/ID GN 48.35/48.37/48.54 48.42± 0.11 SBG 52.82/52.73/52.69 52.75± 0.07 EG 55.94/55.73/55.92 55.86± 0.12 GraRe-PL/no conf. GN 47.30/48.12/47.44 47.62± 0.44 SBG 51.13/51.74/51.32 51.40± 0.31 EG 51.63/53.03/52.30 52.32± 0.70 Table 20: Complete joint-training results on RealSense using the detector’s original candidate sets, Average AP (%). Each row reports all three official evaluations and their sample mean and SD. With detector identifiers, the joint model reaches 48.42, 52.75, and 55.86 AP on GN, SBG, and EG. These values differ from the matched detector-specific GraRe-PL three-seed means by at most 0.35 AP, and the SBG/EG values are slightly higher. Removing detector confidence lowers the joint ID model by 0.80, 1.35, and 3.55 AP, respectively, showing that bib_i remains particularly informative for EG. Joint training therefore supports parameter sharing across the known detectors when their identity is available. Appendix L Training Cost and Model Size (Q4) L.1 Parameter Counts We separate trainable parameters from the frozen Point-MAE backbone to identify the source of the model-size overhead. Variant Trainable parameters Total parameters Full GraRe 0.547 M 22.372 M w/o Candidate 0.455 M 22.279 M w/o Local 0.306 M 22.130 M w/o Object 0.415 M 0.415 M Table 21: Model size. Total parameters include the frozen Point-MAE backbone when object context is active. The object-context branch dominates total parameter count through its frozen backbone, but its trainable adapter is small. Removing object context reduces total size by more than 98%, while the Average AP changes in Figure 11(a) remain between +0.08+0.08 and −0.77-0.77 across the controlled settings. L.2 Training Resources and Checkpoints Table 22 reports the validation-selected checkpoint, dataset size, and recorded training resources for the principal RealSense seed-7 runs. Best epoch is selected using held-out validation score loss; the final test AP is reported for reference. Det. Variant Ep. h Data (GB) VRAM (GB) AP GN Full GraRe 39 0.962 38.59 9.736 49.45 GN w/o Cand. 35 0.954 32.58 9.722 47.66 GN w/o Local 37 0.707 32.58 0.502 45.03 GN w/o Obj. 32 0.954 26.54 9.642 48.71 SBG Full GraRe 39 0.797 31.79 9.736 52.46 SBG w/o Cand. 34 0.778 26.82 9.720 50.81 SBG w/o Local 36 0.244 26.82 0.501 50.54 SBG w/o Obj. 35 0.781 21.84 9.642 52.54 EG Full GraRe 36 5.546 202.25 19.321 55.95 EG w/o Cand. 38 5.516 202.25 19.290 50.49 EG w/o Local 37 1.510 202.25 0.855 54.22 EG w/o Obj. 38 5.512 164.75 19.215 55.63 Table 22: Training cost and validation-selected checkpoints for seed 7. Hours exclude official evaluation; VRAM is peak allocated GPU memory. EG requires substantially more training time and memory because of its larger candidate set. Removing local geometric features reduces resource use but also lowers Average AP, while removing object context changes Average AP only modestly in the matched seed-7 runs. Together with Table 21, these results show that the frozen object-context backbone dominates total model size, whereas local feature construction contributes more directly to the accuracy–resource tradeoff. Appendix M Real-Robot Experiments (Q4) We execute the protocol described in the main paper on ten mixed-object scenes using GN, SBG, and EG. Each detector is evaluated under its detector order π^D and GraRe order πRπ^R, yielding 60 detector–order–scene evaluations. Within each pair, the hardware, detector, collision filtering, the same motion-planning pipeline as in the main paper, and stopping condition remain unchanged. GraRe changes only the candidate order for each observation. Grasp outcomes and scene completion are manually verified from the recorded before-grasp, gripper-closed, and returned-to-view frames. Det. Order GSR CR MCF LAT GN π^D 73.4 (58/79) 10 (1/10) 4 1.06 GN πRπ^R 88.9 (72/81) 100 (10/10) 2 1.45 SBG π^D 70.4 (57/81) 30 (3/10) 6 0.95 SBG πRπ^R 87.2 (68/78) 90 (9/10) 2 1.21 EG π^D 68.2 (60/88) 70 (7/10) 4 0.76 EG πRπ^R 88.5 (69/78) 100 (10/10) 2 0.97 Table 23: Aggregate real-robot results. GSR and CR are percentages, with successful grasps/attempts and cleared scenes/ten in parentheses. MCF is the maximum number of consecutive failed grasp attempts in a scene. LAT is mean online inference latency per selected execution in seconds on an RTX 2060. GraRe raises GSR by 15.5, 16.8, and 20.3 percentage points for GN, SBG, and EG, respectively. CR rises by 90, 60, and 30 points, and MCF decreases to two attempts for every detector. The mean online inference overhead is 0.39, 0.26, and 0.21 s per selected execution. These aggregate results show improved closed-loop reliability across all three detector pipelines at a modest inference cost. Using the scene groups defined in the main paper—Scenes 1–2 as easy, Scenes 3–7 as medium, and Scenes 8–10 as hard—the detector order clears 3/6, 7/15, and 1/9 evaluations, respectively. The corresponding GraRe order clears 6/6, 14/15, and 9/9 evaluations. Across the medium and hard scenes, completion increases from 8/24 to 23/24, showing that the aggregate gains are not driven only by easy scenes. Figure 19: Scene-level completion outcomes for all 60 real-robot evaluations. Rows are detectors and columns use the paper scene numbering; vertical separators mark the easy, medium, and hard groups. Blue cells marked C denote cleared scenes, while pale cells denote incomplete runs. GraRe clears 29/30 detector–scene evaluations compared with 11/30 under the detector order. Det. Exec. Promoted Same Demoted Mean rank /RD/R GN 81 61 (75.3%) 4 16 16.59/7.38 SBG 78 54 (69.2%) 12 12 10.36/4.42 EG 78 45 (57.7%) 19 14 7.54/4.01 All 237 160 (67.5%) 35 42 11.56/5.30 Table 24: Detector-wise rank shifts for grasps executed under πRπ^R. Each row compares the same executed candidate under the detector and GraRe orders. “Promoted” and “demoted” indicate lower and higher numerical ranks under πRπ^R, respectively. GraRe promotes most executed grasps for every detector: 61/81 for GN, 54/78 for SBG, and 45/78 for EG. The detector-wise mean rank decreases from 16.59 to 7.38 for GN, from 10.36 to 4.42 for SBG, and from 7.54 to 4.01 for EG. The physical rank promotion is therefore consistent across all three detector pipelines. Before Gripper closed Returned view GN, Scene 9 SBG, Scene 8 Figure 20: Additional successful real-robot rank-promotion cases. In GN Scene 9 cycle 2, the executed grasp moves from rank 60 under π^D to rank 9 under πRπ^R; in SBG Scene 8 cycle 3, it moves from rank 12 to rank 1. Columns show the observation before execution, the closed gripper carrying the object, and the returned view after removal. The GraRe runs clear both scenes, whereas the corresponding detector-order runs leave one and two objects, respectively. M.1 Hard-Scene Progressions Figure 21 samples the complete logs for one detector on each hard scene. In SBG Scene 8, the detector order succeeds in 6/12 attempts and leaves two objects, whereas GraRe succeeds in 7/9 attempts and clears the scene. In GN Scene 9, the corresponding outcomes are 7/12 with one object remaining and 8/8 with the scene cleared. The largest contrast occurs in EG Scene 10: the detector order succeeds in 5/12 attempts and leaves two objects, while GraRe clears the scene with 9/9 successful attempts. These progressions show that re-ranking reduces repeated failures and residual objects throughout the run, rather than producing only isolated successful rank changes. Figure 21: Closed-loop progressions on the three hard scenes using the paper scene numbering. Each group shows GraRe above the detector order for separate executions of the same scene specification. Five logged observations are sampled from the initial state to the terminal observation; column labels give the corresponding GraRe (R) and detector-order (D) cycle indices. GraRe clears all three scenes, while the detector-order terminal observations retain one or two objects. M.2 Execution Trace We additionally instrument GN Scene 4, an eight-object medium scene under the paper scene numbering, to examine how the two orders interact with downstream execution. For each RGB-D observation, the frozen GN detector produces the candidate set C. GraRe replaces the detector order π^D with the re-ranked order πRπ^R before collision filtering and execution by the same motion-planning pipeline as in the main paper. The candidates themselves remain unchanged. A run terminates after at most 30 cycles or after two consecutive observations contain no segmented objects. Figures 22 and 23 follow the selected execution pose and candidate-score distribution through the logged cycles. 1 2 3 4 5 6 7 8 GraRe GN Figure 22: Selected execution poses for GN Scene 4. Columns are cycles 1–8, with the GraRe order above the detector order. Green grippers show the poses selected after collision checking and planning. The detector-order cycle 7 uses motion-planning seed 5 after five failed seeds. Cycle 8 ends with a release-confirmation timeout. 1 2 3 4 5 6 7 8 GraRe GN Figure 23: Candidate-distribution loop for GN Scene 4. Columns are cycles 1–8, with the GraRe order above the detector order. Each panel renders up to 50 collision-free post-NMS candidates used by the successful planning seed. Candidates associated with the hand-camera gripper or lying within 20 m of the fitted tabletop are omitted from the display. GraRe colors candidates by the re-ranking score, while GN uses detector confidence. Blue denotes a low score and red a high score within each panel. Later columns also reflect the scene states produced by the preceding executions in each closed-loop run. Figure 24: Cycle-level rank of the grasp executed by GraReGNGraRe_GN in Scene 4. Each vertical segment compares the same executed candidate under π^D and πRπ^R; smaller ranks are better, and labels give the candidate count K. GraRe changes the top-ranked candidate in the first six cycles. In these cycles, the candidates ultimately selected for execution move from detector-order ranks 21, 24, 12, 10, 20, and 11 to re-ranked positions 11, 3, 2, 4, 1, and 2, respectively. In the final two cycles, the candidate sets contain only three or four candidates and both orders retain the same top-ranked candidate. This trace shows that the ranking changes observed on the benchmark also occur during closed-loop robot execution. (a) Initial scene (b) Empty observation (c) Detector order π^D (d) Re-ranked order πRπ^R Figure 25: Closed-loop trace for GN Scene 4. The first cycle starts from the RGB observation in (a). After eight sensor-confirmed transfers, the observation in (b) contains no segmented objects and starts the two-frame empty-scene confirmation. Panels (c) and (d) compare the unchanged candidates under the detector order and re-ranked order, respectively. Colors run from blue (low score) to red (high score) within each order. M.3 Additional Hard-Scene Loops The next six loops extend the execution trace to the three hard scenes. In every panel, GraRe is shown above the detector order; the column header reports the paired logged cycles as Rci/DcjR\,c_i/D\,c_j. Pose panels show the selected execution pose after collision checking and planning. Candidate panels show up to 50 post-NMS candidates after the visualization-only removal of candidates associated with the hand-camera gripper or lying within 20 m of the fitted tabletop. Candidate colors are normalized within each panel, with blue denoting lower and red higher scores. Figure 26: Selected execution-pose loop for SBG Scene 8. The detector-order run ends with two objects remaining, whereas the GraRe run clears the scene. Figure 27: Candidate-distribution loop for SBG Scene 8 using the same logged cycles as Fig. 26. The candidate set contracts to three detector-order candidates while two objects remain; GraRe reaches an empty observation after its ninth executed cycle. Figure 28: Selected execution-pose loop for GN Scene 9. GraRe completes the scene in eight successful attempts, while the detector-order run contains repeated failures and leaves one object. Figure 29: Candidate-distribution loop for GN Scene 9 using the same logged cycles as Fig. 28. Both rows retain dense candidate sets early in the run, but their score orderings select different execution poses as the scene state evolves. Figure 30: Selected execution-pose loop for EG Scene 10. GraRe clears the scene in nine successful attempts; the detector-order run succeeds in five of twelve attempts and leaves two objects. Figure 31: Candidate-distribution loop for EG Scene 10 using the same logged cycles as Fig. 30. GraRe maintains a progressively smaller set of displayed candidates as objects are removed, while the detector-order row continues through a longer run with residual objects. Figure 32: Candidate-count evolution for the three hard-scene loops after the same visualization-only nuisance mask. Horizontal labels give the paired GraRe/detector-order cycle indices. Counts may exceed 50 because the loop panels display at most the first 50 retained candidates. Figure 32 shows that incomplete detector-order runs do not share a single late-stage candidate regime. At the final sampled detector-order cycle, SBG Scene 8 and EG Scene 10 retain only three and ten candidates while objects remain, indicating limited candidate coverage. In contrast, GN Scene 9 still retains 56 candidates around its final object, so its incomplete outcome cannot be attributed to a lack of generated choices. GraRe clears all three scenes across these distinct regimes. M.4 Planning Trace We use the instrumented Scene 4 run to compare how the two candidate orders affect downstream planning and sensor-confirmed cycle completion. Order Comp. Sens. Plans Fail. Retries End state πRπ^R 8 8 8 0 0 Cleared π^D 7 6 13 5 5 Release timeout Table 25: Logged execution and planning events. Complete cycles return the robot to the observation view. Sensor counts complete cycles confirmed by the gripper state. Plans counts calls to the motion planner. The re-ranked run completes eight sensor-confirmed transfers and two empty confirmations without a failed plan or retry. The detector-order run completes seven return-to-view cycles, six of which are sensor-confirmed, and requires five planning retries. In cycle 7, motion-planning seeds 0–4 produce no feasible path and seed 5 completes the cycle; cycle 8 reaches the release stage but ends with a gripper-open confirmation timeout. The trace links the changed candidate order to fewer repeated planning failures and a cleared terminal state. M.5 Online Latency We time the same instrumented Scene 4 runs to separate GraRe computation from physical robot execution. Measurement π^R π^D Complete timed cycles 8 7 GraRe re-ranking (ms) 15.3 [11.7, 23.9] – Total compute (s) 0.825 [0.632, 1.249] 0.758 [0.616, 0.843] Robot execution (s) 33.38 [20.57, 51.16] 32.19 [21.86, 51.59] Table 26: Online RTX 2060 latency as mean [minimum, maximum]. Total compute excludes visualization, serialization, and the incomplete detector-order cycle. CUDA-synchronized timing gives 15.3 ms for GraRe re-ranking on average, and total compute remains below one second for both orders. Robot motion exceeds 32 s per completed cycle and dominates runtime, while five planning retries extend detector-order cycle 7 to 68.63 s. The re-ranking overhead is therefore small relative to physical execution and can be offset by avoiding repeated planning attempts. Appendix N Qualitative Failure Analysis (Q4) The qualitative examples in the main paper are interpreted together with the transition statistics and feature ablations. In the illustrated beneficial cases, GraRe replaces a colliding detector top-ranked grasp with a candidate whose local points support contacts on both closing sides. Candidate features are particularly important for EG: removing them lowers Average AP by 5.46/4.91 points on RealSense/Kinect. Harmful success-to-failure transitions are most frequent on Similar scenes, while the Novel examples show GraRe promoting plausible candidates that require higher friction. GraRe therefore often repairs detector-confidence misranking but can still overpromote geometrically plausible yet less robust grasps.

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