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2025/PoseCrafter_ Extreme Pose Estimation with Hybrid Video Synthesis/75323152-3c99-4b86-bd2e-53f0c153bde7_origin.pdf

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2025/PoseCrafter_ Extreme Pose Estimation with Hybrid Video Synthesis/full.md

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+# PoseCrafter: Extreme Pose Estimation with Hybrid Video Synthesis
+
+Qing Mao $^{1,2*}$  Tianxin Huang $^{3}$  Yu Zhu $^{1}$  Jinqiu Sun $^{4}$  Yanning Zhang $^{1\dagger}$  Gim Hee Lee $^{2\dagger}$
+
+$^{1}$ School of Computer Science, Northwestern Polytechnical University
+
+$^{2}$ School of Computing, National University of Singapore
+
+$^{3}$ School of Computing and Data Science, The University of Hong Kong
+
+$^{4}$ School of Astronautics, Northwestern Polytechnical University
+
+maoqing@mail.nwpu.edu.cn ynzhang@nwpu.edu.cn gimhee.lee@nus.edu.sg
+
+https://github.com/maoqingsunny/PoseCrafter
+
+# Abstract
+
+Pairwise camera pose estimation from sparsely overlapping image pairs remains a critical and unsolved challenge in 3D vision. Most existing methods struggle with image pairs that have small or no overlap. Recent approaches attempt to address this by synthesizing intermediate frames using video interpolation and selecting key frames via a self-consistency score. However, the generated frames are often blurry due to small overlap inputs, and the selection strategies are slow and not explicitly aligned with pose estimation. To solve these cases, we propose Hybrid Video Generation (HVG) to synthesize clearer intermediate frames by coupling a video interpolation model with a pose-conditioned novel view synthesis model, where we also propose a Feature Matching Selector (FMS) based on feature correspondence to select intermediate frames appropriate for pose estimation from the synthesized results. Extensive experiments on Cambridge Landmarks, ScanNet, DL3DV-10K, and NAVI demonstrate that, compared to existing SOTA methods, PoseCrafter can obviously enhance the pose estimation performances, especially on examples with small or no overlap.
+
+# 1 Introduction
+
+Accurately estimating the relative pose between two images is a fundamental task in 3D vision, critical for enabling autonomous navigation, robotics, and augmented reality. While modern feature-based [1, 2] or learning-based pipelines [3, 4] perform well when input views share sufficient overlap, their performance deteriorates sharply in the small or no overlap case, owing to the fundamental scarcity of reliable feature correspondences.
+
+To address this issue, InterPose [5] introduced a two-stage strategy: intermediate views are generated using a video interpolation model, and enriched frames selected with a frame selection strategy are provided to the pose estimation model. Although InterPose demonstrated obvious improvements in extreme cases with small overlaps, it faces two core limitations. First, the quality of generated intermediate frames remains a bottleneck. Free and open-source models like DynamiCrafter [6] can generate plausible interpolations near the input image pair but often fail to maintain geometric consistency in the central frames, likely due to the limited overlap between input views. Commercial models like Runway [7] and Luma Dream Machine [8] offer sharper results but still suffer from blur and drift in challenging scenes, in addition to incurring high inference costs. Second, InterPose relies
+
+on a self-consistency score mechanism to select frames, which filters out informative frames across multiple generated video clips. This purely statistical selection strategy is slow and not explicitly aligned with the objectives of pose estimation.
+
+To address these challenges, we propose PoseCrafter—a training-free framework for estimating camera poses from input image pairs with small or no overlap. PoseCrafter comprises two key components: Hybrid Video Generation (HVG) and Feature Matching Selector (FMS). In HVG, we first use the pre-trained video interpolation model DynamamiCrafter [6] to synthesize a coarse video and identify a few reliable "relay" frames. These selected frames are then used to estimate the initial pose and generate high-fidelity intermediate views through a pose-conditioned novel view synthesis model, ViewCrafter [9]. In this work, we find that selecting only the one frame immediately after the start frame and the one frame just before the end frame yields the most effective relay frames. Including additional frames tends to degrade performance due to increased blurriness in the central synthesized frames. More analysis can be found in Sec. 3.2.
+
+In FMS, instead of using statistical scores for frame selection, we propose a simple but effective solution, evaluating synthesized frames based on their feature correspondences with the input image pair to determine their suitability for pose estimation. In detail, we extract local descriptors from each candidate frame and match them to the input image pair, compute RANSAC [10] inlier counts, and select the top  $k$  frames with the highest total inliers.
+
+Extensive experiments on common benchmarks, including Cambridge Landmarks [11], ScanNet [12], DL3DV-10K [13], and NAVI [14] show that PoseCrafter can obviously improve the accuracy of pose estimation on extreme pose image pairs with small or no overlaps, without any requirements for additional training or ground-truth supervision. In summary, our contributions are as follows:
+
+- We propose Hybrid Video Generation(HVG) to synthesize high-fidelity intermediate frames, by effectively coupling a video interpolation model and a pose-conditioned novel view synthesis model.  
+- We develop a Feature Matching Selector(FMS) to deterministically select the most informative frames suitable for pose estimation, eliminating the need for expensive statistical self-consistency scoring in existing works.  
+- We demonstrate that, by integrating HVAC and FMS, our proposed PoseCrafter can achieve SOTA performances across four challenging benchmarks for extreme pose estimation.
+
+# 2 Related Work
+
+Extreme Pose Estimation Traditional relative pose pipelines combine local feature matching [1, 2], RANSAC-based [10] five-point or eight-point solvers, and bundle adjustment [15]. These methods perform well when images share substantial overlap but fail under extreme cases. While deep networks have strengthened individual components [16-19], they still rely on the large overlap. To address cases with small or no overlap, several approaches [20-22, 3] have been proposed. Yang et al. [20] alternate RGB-D scene completion with pose regression, iteratively fusing geometry from both scans; Cai et al. [21] construct dense correlation volumes over synthetic video clips to infer large rotations; and DUSt3R [3] regresses pixel-aligned point maps to jointly recover depth, reconstruction, and pose without camera calibration. Temporal modeling has also been explored. Tang et al. [23] combine attention and recurrent networks for pose prediction. However, each of these methods requires supervised data and training resources. More recently, video-diffusion techniques have been adapted for pose recovery. JOG3R [24] fine-tunes intermediate features of a pre-trained video generation model for SfM-style estimation, InterPose [5] reuses standard diffusion interpolation and a self-consistency scoring scheme to select the most reliable frames, both without retraining the video model. These studies highlight the power of synthesized intermediate views and motivate our PoseCrafter framework.
+
+Generative Video Models Early video synthesis methods relied on generative adversarial networks (GANs) [25] and autoregressive models. GAN-based approaches such as TGAN [26], MoCoGAN [27], and StyleGAN-V [28] extend image GANs to model temporal coherence, but often suffer from frame inconsistencies and require complex architectures. Autoregressive techniques [29, 30] generate videos frame by frame, but they incur high computational costs and error
+
+![](images/b85d815412757a7efbe5758de524b074853d3ef99893a30c6eded161fc003eb9.jpg)  
+Figure 1: Overview of the PoseCrafter pipeline. Starting from an input image pair (left), the Hybrid Video Generation module uses DynamiCrafter to interpolate a short video clip, extracts the most reliable "relay" frames, and refines the sequence using the pose-conditioned ViewCrafter to reduce mid-sequence blur and drift. The Feature Matching Selector then evaluates each synthesized frame based on its feature correspondence with the input pair, selecting the most informative views for pose estimation. These selected frames are then fed into a pose estimation model (e.g. DUSt3R) to estimate the final pose.
+
+accumulation. Diffusion models have recently set a new standard for both image and video synthesis. Video-diffusion frameworks such as VDM [31], Imagen-Video [32], and Make-A-Video [33] generate high-fidelity, temporally coherent sequences via iterative denoising. ViewCrafter [9] proposed by combining video diffusion priors with coarse point-cloud cues to synthesize high-fidelity, pose-controlled novel views from one or a few images. There are also some video generation models that can be used for interpolation that use diffusion to generate smooth, geometry-aware intermediate frames. For example, DynamiCrafter [6] is based on motion-consistent editing. These diffusion-based models outperform prior GAN and autoregressive methods in both visual quality and temporal consistency, making them ideal for downstream tasks such as extreme pose estimation.
+
+# 3 Our Method
+
+As illustrated in Figure 1, given a pair of images with small or no overlap, PoseCrafter estimates their relative camera pose through two complementary stages. In Hybrid Video Generation (Section 3.2), we sequentially combine a video interpolation model, DynamiCrafter, with a pose-conditioned novel view synthesis model, ViewCrafter, to generate refined video frames that significantly reduce mid-sequence blurring and correct structural drift. In the subsequent Feature Matching Selector (Section 3.3), we evaluate the synthesized frames based on their feature correspondences with the input image pair and select the top  $k$  most informative frames for final pose estimation.
+
+# 3.1 Preliminaries
+
+DynamiCrafter DynamiCrafter is a publicly available diffusion model for video synthesis that employs a progressive latent denoising architecture to animate two static images into dynamic sequences [6]. Given an input image pair  $(I_0, I_T \in \mathbb{R}^{H \times W \times 3})$  and an optional text prompt  $\mathcal{P}$ , it generates a dense sequence of intermediate frames using the following formula:
+
+$$
+\left\{I _ {t} \right\} _ {t = 0} ^ {T} = \mathcal {G} _ {D C} \left(I _ {0}, I _ {T}, \mathcal {P}\right),
+$$
+
+where  $\mathcal{G}_{DC}$  denotes the pre-trained DynamiCrafter model. The variable  $t\in \mathbb{Z}^{+}$  denotes the frame index, where  $I_0$  and  $I_{T}$  correspond to the input image pair.
+
+![](images/bc126a117becf76f643d2785fccc0f4192b8fb545003de28e4eddc2dc00cd9c3.jpg)  
+Dc
+
+![](images/2f45f497dd72826f0df640f7ff39c4638a8b195b4528ae3b2c0974d1c30233d0.jpg)  
+0  
+(a) Generated Video Frames
+
+![](images/4dd43fd2b59f90b69a3f7e299ddebe63bc19bb02f37b4452dac8f5045a575df4.jpg)  
+DC  
+(b) Confidence Images  
+Figure 2: Examples of mid-frame blurriness and confidence degradation. (a) presents frames generated by DynamiCrafter (DC) and our proposed method. (b) highlights high-confidence regions identified by DUST3R during pose estimation. Green boxes mark areas affected by blurriness in the DC-generated frames, while red boxes indicate how these regions performed in DUST3R's confidence maps. We observe that the corresponding regions in the DynamiCrafter results exhibit notably low confidence, whereas our method generates frames with higher confidence for DUST3R.
+
+ViewCrafter ViewCrafter is a pose-conditioned diffusion model for novel view synthesis of static 3D scenes, which can generate high-fidelity novel views along an interpolated camera trajectory through input images following the formula:
+
+$$
+\left\{I _ {t} \right\} _ {t = 0} ^ {T} = \mathcal {G} _ {V C} \left(I _ {0}, I _ {T}, \left\{C _ {t} \right\} _ {t = 0} ^ {T}\right),
+$$
+
+where  $\mathcal{G}_{VC}$  denotes the pre-trained ViewCrafter generator.  $\{C_t\}_{t=0}^T$  denotes camera poses alongside the trajectory interpolated between the input image pair.
+
+# 3.2 Hybrid Video Generation
+
+Although InterPose [5] improves pose estimation performance by directly interpolating frames between input image pairs (e.g., using DynciCrafter [6]), the generated sequences often exhibit noticeable blurriness and inconsistencies, particularly in the middle frames. As shown in Figure 2, these blurry regions result in significantly lower confidence during pose estimation with DUSt3R [3], ultimately affecting overall performance. In contrast, ViewCrafter [9] is capable of synthesizing clear, high-fidelity frames, but it requires input images that allow for the estimation of a plausible camera trajectory. To address this issue, we propose Hybrid Video Generation (HVG), which couples DynciCrafter and ViewCrafter. Specifically, we first use DynciCrafter to generate initial interpolated frames and then select a few reliable "relay" frames. These relay frames help ensure a plausible camera trajectory and are subsequently used by ViewCrafter to synthesize high-quality intermediate frames. As shown in Figure 2-Our, intermediate frames generated by our HVG exhibit higher confidence scores in DUSt3R [3], further confirming that HVG contributes positively to pose estimation. The whole process comprises two phases: Robust Relay-Frame Generation, and Pose-Guided Video Refinement.
+
+Robust Relay-Frame Generation In this stage, we use the pre-trained DynamamiCrafter model to interpolate a short video clip from the input image pair (the start frame  $I_0$  and the end frame  $I_T$ ). Although DynamamiCrafter generates plausible interpolations near the input pair, it often fails to maintain geometric consistency in the central frames, weakening feature correspondences and degrading downstream pose estimation. To isolate the most reliable "relay" frames, we conducted a study (Table 1) that evaluated various subsets of interpolated frames. We found that retaining only the start/end frames and their immediate neighbors  $\{I_0, I_1, I_{T - 1}, I_T\}$  minimizes rotation error and
+
+maximizes stability. Consequently, PoseCrafter forwards only these four frames as "relay" frames to the subsequent high-fidelity novel view synthesis stage.
+
+Pose-Guided Video Refinement Given the four reliable relay frames  $\{I_0, I_1, I_{T-1}, I_T\}$ , we first recover their camera poses  $\{C_0, C_1, C_{T-1}, C_T\}$  using the pretrained DUSt3R network. We then interpolate a smooth, dense camera trajectory  $\{C_t\}_{t=0}^T$  by applying spherical linear interpolation to rotations on SO(3) and linear interpolation to translations in  $\mathbb{R}^3$ . Conditioned on this trajectory and the reliable relay frames, ViewCrafter synthesizes high-fidelity intermediate views. This pose-conditioned refinement effectively removes mid-sequence blur and geometric drift, producing crisp, structurally accurate frames that markedly improve feature correspondences for final pose estimation.
+
+Table 1: Relay-frame sampling analysis using mean rotation error (MRE↓). The setting #Frames=2 corresponds to  $\{I_0, I_T\}$ , #Frames=4 corresponds to  $\{I_0, I_1, I_{T-1}, I_T\}$ , #Frames=6 corresponds to  $\{I_0, I_1, I_2, I_{T-2}, I_{T-1}, I_T\}$ , and #Frames=8 corresponds to  $\{I_0, I_1, I_2, I_3, I_{T-3}, I_{T-2}, I_{T-1}, I_T\}$ . The case #Frames=16 uses all frames. Results indicate that #Frames=4 consistently achieves the lowest MRE and the highest stability across datasets.  
+
+<table><tr><td rowspan="2">Dataset</td><td colspan="5">#Frames (n)</td></tr><tr><td>2</td><td>4</td><td>6</td><td>8</td><td>16</td></tr><tr><td>Cambridge Landmarks</td><td>20.56</td><td>14.47</td><td>16.66</td><td>16.87</td><td>17.83</td></tr><tr><td>ScanNet</td><td>19.67</td><td>16.23</td><td>17.03</td><td>17.16</td><td>18.56</td></tr><tr><td>DL3DV-10K</td><td>15.22</td><td>14.27</td><td>14.40</td><td>14.73</td><td>14.52</td></tr><tr><td>NAVI</td><td>7.78</td><td>6.94</td><td>7.18</td><td>9.64</td><td>10.92</td></tr></table>
+
+# 3.3 Feature Matching Selector
+
+Although our proposed Hybrid Video Generation (HVG) produces high-fidelity and visually clear intermediate frames, not all of them are equally beneficial for pose estimation, as some generated content may be inconsistent with the input image pair. InterPose [5] addresses this problem by computing a statistical self-consistency score across multiple separate estimations. However, this approach is both slow and unstable due to the inherent uncertainty introduced by repeated sampling. Moreover, as a purely statistical measure, it does not explicitly ensure that the selected frames are well-suited for pose estimation.
+
+To overcome these drawbacks, we employ a simple but effective deterministic selection strategy based on feature matching, named as Feature Matching Selector (FMS). For each synthesized frame  $I_{t}$ , we extract local descriptors and match them to both the start frame  $I_{0}$  and end frame  $I_{T}$ , then compute RANSAC inlier counts  $N_{0}(t)$  and  $N_{T}(t)$ . Each frame is scored by
+
+$$
+S (t) = N _ {0} (t) + N _ {T} (t),
+$$
+
+and we select the top  $k$  frames whose scores exceed a preset threshold. This inlier-driven criterion avoids the need for repeated estimations and explicitly accounts for geometric consistency with the input image pair, enabling the selection of more informative frames for subsequent pose estimation.
+
+# 4 Experiments
+
+# 4.1 Experiment Setup
+
+Data Preparation Following InterPose [5], we evaluate our method on four common benchmarks: Cambridge Landmarks [11], ScanNet [12], Navi [14] and DL3DV-10K[13]. For Cambridge Landmarks and ScanNet, we select test pairs by sampling images whose relative yaw difference falls into two ranges ( $[50^{\circ} - 65^{\circ}]$  and  $[65^{\circ} - 90^{\circ}]$ ) to evaluate performance under small and no overlap cases. For the object-centric Navi and DL3DV-10K datasets, due to the large object overlap, we adopt a single yaw range of  $[50^{\circ} - 90^{\circ}]$  following InterPose's setting. All images are resized, and center-cropped to  $512 \times 320$  before processing, to adapt to the setting of DynamiCrafter [6].
+
+Evaluation Metrics Following prior work [5], we conduct evaluations using the following metrics:
+
+Mean Rotation Error (MRE) The average geodesic distance between the predicted and the ground-truth rotation, reported in angular.
+
+Mean Translation Error (MTE) The average geodesic distance between the predicted and the ground-truth translation, reported in angular.
+
+Rotation and Translation Accuracy  $(R(\theta), T(\theta))$  Given an angular threshold  $\theta$  (e.g.,  $5^{\circ}, 15^{\circ}, 30^{\circ}$ ), the rotation accuracy  $R(\theta)$  is the fraction of estimates with rotation error below  $\theta$ ; the translation accuracy  $T(\theta)$  is the same definition using translation angular error.
+
+Area Under Curve  $\left(\mathrm{AUC}_{30}\right)$  The normalized area under the rotation or translation error curve from  $0^{\circ}$  to  $30^{\circ}$  provides a compact summary of performance across the full range of angular thresholds. In this work, we report the smaller of the rotation and translation  $\mathrm{AUC}_{30}$  values as the final metric.
+
+# 4.2 Implementation Details
+
+In the hybrid video generation stage, we first generate 16 interpolated frames between each input image pair using DynamamiCrafter. From these, we select 4 frames as reliable relay frames (as described in section 3.2), which are then used by ViewCrafter to render 25-frame sequences for subsequent selection with Feature Matching Selector (FMS). In FMS, we extract 2,000 ORB keypoints per frame and compute RANSAC inlier counts with respect to both the start and end keyframes. The generated frames are then ranked based on their inlier counts, and the top  $k = 6$  frames(excluding the input image pair) are selected for the final pose estimation. All experiments were conducted on a single NVIDIA RTX 6000 GPU to ensure a consistent evaluation environment.
+
+# 4.3 Comparison with State-of-the-Art
+
+To validate our method's effectiveness, we compare it against two closely related baselines: DUSt3R [3] and InterPose [5]. DUSt3r estimates relative pose directly from an input image pair, while InterPose enhances pose estimation results by using videos generated by a pre-trained video model and intermediate frames selected by a self-consistency score. Since InterPose has not been publicly available, we reproduce its pipeline based on the details provided in their paper, and denote it as InterPose‡ for subsequent comparisons. To further assess the impact of video generation quality, we also introduce two variant methods: our method without feature matching selector(Oursw/o FMS), and InterPose without self-consistency score (InterPose‡w/o SCS). In these cases, all of the synthesized frames are used for pose estimation, without specific selection.
+
+# 4.3.1 Quantitative Comparison on PoseCrafter
+
+Tables 2, 3, 4, and 5 present comparative performance results of PoseCrafter against other methods across four benchmark datasets. On outward-facing benchmarks (Cambridge Landmarks and ScanNet), PoseCrafter reduces mean rotation error by approximately  $9.85^{\circ}$  and increases  $\mathbb{R}@\mathbb{30}^{\circ}$  by more than  $10\%$  against InerPose for data with yaw changes between  $[65^{\circ} - 90^{\circ}]$  of Cambridge Landmarks. These improvements demonstrate our pipeline's superiority on extreme pose estimation. Moreover, the comparison between InterPose and PoseCrafter further confirms that our proposed hybrid video generation approach produces frames more suitable for pose estimation than the DynamiCrafter [6] used in InterPose [5].
+
+On center-facing benchmarks (DL3DV-10K and NAVI) with larger cross-image overlaps, PoseCrafter still yields modest but consistent reductions in rotation and translation error, alongside incremental improvements in  $\mathrm{AUC}_{30}$ . Overall, the statistical results across multiple standard benchmarks confirm that our proposed pipeline based on Hybrid Video Generation and the Feature Matching Selector, provides a stable, training-free solution across diverse scenes and baseline conditions.
+
+# 4.3.2 Qualitative Comparison on PoseCrafter
+
+To intuitively assess the effectiveness of our approach, we present qualitative comparisons with DUSt3R and InterPose $\ddagger$  on the previously mentioned benchmarks in Figure 3. In Figure 3, we visualize the input image pairs (with the start frame outlined in blue and the end frame in yellow), point clouds reconstructed by DUSt3R using only the input pairs, intermediate videos generated by InterPose $\ddagger$  and PoseCrafter, and the corresponding estimated poses and reconstructions produced by DUSt3R for each video, respectively. Compared to DUSt3R, which only uses input image pairs,
+
+![](images/53600a4d55ee26080a589e348f17c6e5201be4f746446cd091653d87d47740db.jpg)  
+Figure 3: Qualitative comparisons on common benchmarks. Blue and yellow outlines indicate the start and end frames, respectively. In the DUSt3R reconstruction results, the visualized poses in blue, yellow, and red represent the predicted pose of the start frame, predicted pose of the end frame, and the ground-truth pose of the end frame, respectively.
+
+Table 2: Pose estimation on Cambridge Landmarks. We report rotation recall  $(\mathbb{R}@\theta \uparrow)$ , translation recall  $(\mathrm{T}@\theta \uparrow)$ , mean rotation error  $(\mathrm{MRE}\downarrow)$ , and  $\mathrm{AUC}_{30}\uparrow$  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Input</td><td colspan="5">Yaw range [50°-65°]</td><td colspan="5">Yaw range [65°-90°]</td></tr><tr><td>MRE↓</td><td>R@5°</td><td>R@15°</td><td>R@30°</td><td>AUC30↑</td><td>MRE↓</td><td>R@5°</td><td>R@15°</td><td>R@30</td><td>AUC30↑</td></tr><tr><td>DUSt3R</td><td>Pair</td><td>18.14</td><td>40.34</td><td>71.25</td><td>82.99</td><td>61.98</td><td>51.24</td><td>21.67</td><td>44.67</td><td>51.67</td><td>37.93</td></tr><tr><td>InterPose‡w/o SCS</td><td>DynamiCrafter</td><td>16.11</td><td>42.70</td><td>75.70</td><td>87.35</td><td>65.72</td><td>42.51</td><td>30.67</td><td>42.51</td><td>61.33</td><td>47.18</td></tr><tr><td>InterPose‡</td><td>DynamiCrafter</td><td>13.61</td><td>51.81</td><td>81.50</td><td>83.30</td><td>70.47</td><td>38.87</td><td>36.33</td><td>65.67</td><td>68.33</td><td>55.24</td></tr><tr><td>Oursw/o FMS</td><td>Hybrid video</td><td>13.24</td><td>54.51</td><td>89.24</td><td>92.71</td><td>76.13</td><td>34.87</td><td>31.33</td><td>68.33</td><td>77.67</td><td>56.29</td></tr><tr><td>Ours</td><td>Hybrid video</td><td>11.40</td><td>55.21</td><td>89.93</td><td>93.75</td><td>77.41</td><td>29.02</td><td>36.67</td><td>71.67</td><td>78.33</td><td>60.46</td></tr></table>
+
+Table 3: Pose estimation on ScanNet. We report rotation recall  $(\mathrm{R}@\theta \uparrow)$ , translation recall  $(\mathrm{T}@\theta \uparrow)$ , mean rotation error  $(\mathrm{MRE}\downarrow)$ , mean translation error  $(\mathrm{MTE}\downarrow)$ , and  $\mathrm{AUC}_{30}\uparrow$  
+
+<table><tr><td>Yaw range</td><td>Method</td><td>Input</td><td>R@5°</td><td>R@15°</td><td>R@30°</td><td>T@5°</td><td>T@15°</td><td>T@30°</td><td>MRE↓</td><td>MTE↓</td><td>AUC30↑</td></tr><tr><td rowspan="5">50°-65°</td><td>DUSt3R</td><td>Pair</td><td>43.97</td><td>74.14</td><td>79.31</td><td>25.34</td><td>52.07</td><td>78.45</td><td>19.41</td><td>25.23</td><td>47.37</td></tr><tr><td>InterPose†w/o SCS</td><td>DynamicCrafter</td><td>46.55</td><td>77.59</td><td>85.34</td><td>16.38</td><td>48.10</td><td>64.74</td><td>17.51</td><td>35.25</td><td>42.69</td></tr><tr><td>InterPose†</td><td>DynamicCrafter</td><td>50.86</td><td>81.03</td><td>87.07</td><td>27.58</td><td>61.21</td><td>69.46</td><td>15.15</td><td>23.89</td><td>53.33</td></tr><tr><td>Oursw/o FMS</td><td>Hybrid video</td><td>51.72</td><td>87.07</td><td>93.10</td><td>23.28</td><td>50.62</td><td>67.07</td><td>12.38</td><td>29.02</td><td>45.53</td></tr><tr><td>Ours</td><td>Hybrid video</td><td>53.45</td><td>88.79</td><td>94.83</td><td>33.62</td><td>65.52</td><td>77.69</td><td>10.77</td><td>22.14</td><td>57.03</td></tr><tr><td rowspan="5">65°-90°</td><td>DUSt3R</td><td>Pair</td><td>42.05</td><td>67.05</td><td>70.45</td><td>26.59</td><td>46.59</td><td>53.86</td><td>30.82</td><td>29.99</td><td>36.50</td></tr><tr><td>InterPose†w/o SCS</td><td>DynamicCrafter</td><td>38.64</td><td>62.50</td><td>65.90</td><td>20.45</td><td>39.77</td><td>47.72</td><td>35.18</td><td>58.89</td><td>33.40</td></tr><tr><td>InterPose</td><td>DynamicCrafter</td><td>45.45</td><td>67.05</td><td>71.59</td><td>31.81</td><td>53.41</td><td>64.77</td><td>28.22</td><td>29.52</td><td>45.98</td></tr><tr><td>Oursw/o FMS</td><td>Hybrid video</td><td>46.59</td><td>76.14</td><td>82.95</td><td>23.85</td><td>48.86</td><td>57.95</td><td>22.61</td><td>35.98</td><td>41.72</td></tr><tr><td>Ours</td><td>Hybrid video</td><td>50.00</td><td>77.72</td><td>84.09</td><td>37.50</td><td>63.64</td><td>73.86</td><td>17.02</td><td>29.28</td><td>56.44</td></tr></table>
+
+Table 4: Pose estimation on DL3DV-10K with  $[50^{\circ} - 90^{\circ}]$  yaw range.  
+
+<table><tr><td>Method</td><td>Input</td><td>R@5°</td><td>R@15°</td><td>R@30°</td><td>T@5°</td><td>T@15°</td><td>T@30°</td><td>MRE↓</td><td>MTE↓</td><td>AUC30↑</td></tr><tr><td>DUST3R</td><td>Pair</td><td>34.33</td><td>63.00</td><td>94.66</td><td>27.00</td><td>75.00</td><td>92.67</td><td>13.36</td><td>10.88</td><td>55.58</td></tr><tr><td>InterPosex/o SCS</td><td>DynamicCrafter</td><td>36.33</td><td>64.33</td><td>95.00</td><td>26.00</td><td>76.33</td><td>92.67</td><td>13.32</td><td>11.27</td><td>55.68</td></tr><tr><td>InterPosey/o SCS</td><td>DynamicCrafter</td><td>36.11</td><td>64.33</td><td>97.66</td><td>27.66</td><td>79.67</td><td>95.33</td><td>13.17</td><td>10.76</td><td>56.05</td></tr><tr><td>Oursw/o FMS</td><td>Hybrid video</td><td>38.33</td><td>68.33</td><td>98.33</td><td>30.66</td><td>79.61</td><td>96.67</td><td>12.89</td><td>10.71</td><td>57.16</td></tr><tr><td>Ours</td><td>Hybrid video</td><td>38.10</td><td>70.00</td><td>100.00</td><td>31.33</td><td>81.33</td><td>98.33</td><td>12.73</td><td>10.28</td><td>57.48</td></tr></table>
+
+Table 5: Pose estimation on NAVI for the  $[50^{\circ} - 90^{\circ}]$  yaw range.  
+
+<table><tr><td>Method</td><td>Input</td><td>R@5°</td><td>R@15°</td><td>R@30°</td><td>T@5°</td><td>T@15°</td><td>T@30°</td><td>MRE↓</td><td>MTE↓</td><td>AUC30↑</td></tr><tr><td>DUS3R</td><td>Pair</td><td>64.69</td><td>95.72</td><td>98.05</td><td>62.37</td><td>97.28</td><td>98.22</td><td>7.30</td><td>7.82</td><td>82.37</td></tr><tr><td>InterPose‡w/o SCS</td><td>DynamicCrafter</td><td>45.13</td><td>92.61</td><td>96.11</td><td>57.86</td><td>91.44</td><td>96.50</td><td>11.14</td><td>8.81</td><td>78.63</td></tr><tr><td>InterPose‡</td><td>DynamicCrafter</td><td>66.53</td><td>97.28</td><td>98.83</td><td>67.70</td><td>96.89</td><td>98.84</td><td>6.61</td><td>6.26</td><td>82.80</td></tr><tr><td>Oursw/o FMS</td><td>Hybrid video</td><td>59.53</td><td>97.28</td><td>98.83</td><td>72.26</td><td>95.72</td><td>98.83</td><td>6.93</td><td>6.87</td><td>81.91</td></tr><tr><td>Ours</td><td>Hybrid video</td><td>70.82</td><td>97.67</td><td>98.83</td><td>75.10</td><td>98.44</td><td>99.22</td><td>5.97</td><td>5.46</td><td>83.98</td></tr></table>
+
+Table 6: Runtime and Memory Cost.  
+
+<table><tr><td rowspan="2">Method</td><td colspan="2">Runtime</td><td colspan="2">Memory Cost</td></tr><tr><td>Video Generation</td><td>Pose Estimation</td><td>Video Generation</td><td>Pose Estimation</td></tr><tr><td>InterPose‡</td><td>3.2min</td><td>20.29min</td><td>14.6GB</td><td>3.1GB</td></tr><tr><td>Ours</td><td>3.8min</td><td>0.18min</td><td>22.8GB</td><td>3.6GB</td></tr></table>
+
+PoseCrafter produces significantly cleaner and more complete geometry. In addition, compared to InterPose $\ddagger$ , our method is able to correct blur and pose errors in the middle of the sequence, reducing drift and artifacts in the reconstructed point cloud, thus providing more reliable visual evidence for subsequent pose estimation.
+
+# 4.3.3 Runtime and Memory Cost Discussion
+
+Following the quantitative and qualitative evaluations, we next analyze the efficiency of our approach. Specifically, we compare runtime and memory cost with InterPose $\ddagger$ . InterPose generates 8 video sequences for each image pair and samples 11 frames from each sequence to compute the self-consistency score, resulting in a computationally heavy pipeline. In contrast, our method adopts a streamlined design: we generate only a single hybrid video and apply a deterministic frame selection
+
+Table 7: Ablation study on Hybrid Video Generation. SCS and FMS denote the frame selection strategies from InterPose [5] and ours, respectively.  
+
+<table><tr><td>Method</td><td>Input</td><td>MRE↓</td><td>R@5°</td><td>R@15°</td><td>R@30°</td><td>AUC30↑</td></tr><tr><td>DUSt3R</td><td>Pair</td><td>18.14</td><td>40.34</td><td>71.25</td><td>82.99</td><td>61.98</td></tr><tr><td>InterPose‡w/o SCS</td><td>DynamicCrafter</td><td>16.11</td><td>42.70</td><td>75.70</td><td>87.50</td><td>65.72</td></tr><tr><td>InterPose‡</td><td>DynamicCrafter</td><td>13.60</td><td>51.81</td><td>81.50</td><td>83.30</td><td>70.47</td></tr><tr><td>InterPose‡w/FMS</td><td>DynamicCrafter</td><td>13.02</td><td>52.08</td><td>85.76</td><td>90.63</td><td>73.93</td></tr><tr><td>ViewCrafterw/o FMS</td><td>ViewCrafter</td><td>13.80</td><td>52.78</td><td>82.29</td><td>88.54</td><td>71.12</td></tr><tr><td>ViewCrafterw/FMS</td><td>ViewCrafter</td><td>12.45</td><td>53.82</td><td>84.03</td><td>90.28</td><td>72.82</td></tr><tr><td>Oursw/o FMS</td><td>Hybrid video</td><td>13.24</td><td>54.51</td><td>89.24</td><td>92.71</td><td>76.13</td></tr><tr><td>Oursw/ SCS</td><td>Hybrid video</td><td>12.11</td><td>54.86</td><td>88.54</td><td>91.32</td><td>76.11</td></tr><tr><td>Ours</td><td>Hybrid video</td><td>11.40</td><td>55.21</td><td>89.93</td><td>93.75</td><td>77.41</td></tr></table>
+
+Table 8: Ablation study on feature matching methods used in FMS.  
+
+<table><tr><td>Feature Matching Method</td><td>MRE↓</td><td>R@5°</td><td>R@15°</td><td>R@30°</td><td>AUC30↑</td></tr><tr><td>ORB</td><td>11.40</td><td>55.21</td><td>89.93</td><td>93.75</td><td>77.41</td></tr><tr><td>RoMa</td><td>13.89</td><td>53.13</td><td>88.89</td><td>91.67</td><td>74.76</td></tr><tr><td>LoFTR</td><td>12.41</td><td>54.51</td><td>89.24</td><td>93.40</td><td>76.30</td></tr><tr><td>SIFT</td><td>13.89</td><td>53.13</td><td>88.89</td><td>92.67</td><td>74.77</td></tr><tr><td>SuperPoint</td><td>13.36</td><td>51.74</td><td>89.93</td><td>92.71</td><td>75.48</td></tr></table>
+
+Table 9: Ablation study on different video interpolation models used in Hybrid Video Generation.  
+
+<table><tr><td>Method</td><td>Video Interpolation Model</td><td>MRE↓</td><td>R@5°</td><td>R@15°</td><td>R@30°</td><td>AUC30↑</td></tr><tr><td>DUSt3R</td><td>--</td><td>18.14</td><td>40.34</td><td>71.25</td><td>82.99</td><td>61.98</td></tr><tr><td>Ours</td><td>DynamiCrafter</td><td>11.40</td><td>55.21</td><td>89.93</td><td>93.75</td><td>77.41</td></tr><tr><td>Ours</td><td>ToonCrafter</td><td>12.08</td><td>53.99</td><td>87.16</td><td>89.19</td><td>73.11</td></tr></table>
+
+Table 10: Ablation study on the number of intermediate frames selected by FMS.  
+
+<table><tr><td>#Frames</td><td>MRE↓</td><td>R@5°</td><td>R@15°</td><td>R@30°</td><td>AUC30 ↑</td></tr><tr><td>4</td><td>11.36</td><td>55.90</td><td>89.93</td><td>93.40</td><td>77.59</td></tr><tr><td>6</td><td>11.40</td><td>55.21</td><td>89.93</td><td>93.75</td><td>77.41</td></tr><tr><td>8</td><td>11.93</td><td>55.90</td><td>89.93</td><td>92.10</td><td>76.23</td></tr></table>
+
+strategy based on feature matching. This not only avoids redundant video synthesis but also eliminates repeated self-consistency evaluations.
+
+As summarized in Table 6, our approach substantially reduces runtime in the pose estimation stage while maintaining comparable or even superior accuracy. Although the hybrid video generation incurs slightly higher memory usage than InterPose, the overall cost remains affordable for practical deployment. These results demonstrate that our framework strikes a favorable balance between efficiency and accuracy, underscoring its scalability to real-world applications.
+
+# 4.4 Ablation Studies
+
+In this section, we present ablation studies on the two key components of our framework: Hybrid Video Generation and the Feature Matching Selector. We further investigate the impact of different video generation models and the number of selected frames. All experiments are conducted on the Cambridge Landmarks benchmark under yaw changes of  $[50^{\circ} - 65^{\circ}]$ .
+
+Hybrid Video Generation Table 7 evaluates pose estimation performance for three video-generation variants without any frame selection: DynamiCrafter (InterPose $\ddagger_{\mathrm{w/o SCS}}$ ), ViewCrafter (Viewcrafter $_{\mathrm{w/o FMS}}$ ), and our hybrid video generation (Ours $_{\mathrm{w/o FMS}}$ ). Ours $_{\mathrm{w/o FMS}}$  achieves the lower mean rotation error and higher recall than generated results from DynamiCrafter and ViewCrafter. This confirms that our hybrid video generation strategy, combining the motion-driven
+
+interpolation of DynamiCrafter with the pose-conditioned novel-view synthesis of ViewCrafter, effectively addresses the limitations of each method, enhancing the fidelity of intermediate frames for improved pose estimation.
+
+Frame Matching Selector In Table 8, we evaluate the performance of different keypoint selection algorithms within the Frame Matching Selector (FMS), including RoMa [34], LoFTR [16], ORB [35], SIFT [1], and SuperPoint [36]. We observe that ORB performs best in our case, which may be attributed to its robustness against color blurring and distortions in synthesized frames, making it more effective to select the most informative frames.
+
+Impact of Video Interpolation Model To further validate the generality of our pipeline, we experimented with ToonCrafter [37], a recent interpolation model designed for cartoon-style data but also known for handling large-motion scenarios efficiently. As shown in Table 9, ToonCrafter performs slightly worse than DynamiCrafter, which is likely due to its training bias towards non-photorealistic content. Nevertheless, it still achieves clear improvements over directly using the input image pair. These results confirm that our hybrid pose estimation framework is compatible with a variety of video interpolation backbones, highlighting its flexibility and robustness.
+
+Impact of Selected Frame Count Table 10 analyzes the impact of varying the number of frames  $k$  selected by the FMS module, where  $k$  is 4, 6, and 8 (excluding the input image pair). The results show that  $k = 6$  yields the best overall performance. Using fewer frames may not provide sufficient information for accurate pose estimation, while using more frames can introduce errors due to artifacts in the generated frames.
+
+# 5 Limitation
+
+Although the effectiveness of our method has been validated across multiple diverse benchmarks, there are still certain cases where it may not perform well. For example, in our HVG stage, both the adopted video interpolation model (DynamiCrafter) and the novel view synthesis model (ViewCrafter) face challenges when the start and end frames exhibit significant illumination differences, resulting in synthesized frames with low confidence for subsequent pose estimation. This issue could potentially be mitigated by integrating a relighting model, such as IC-Light [38], to harmonize lighting conditions. In addition, our FMS module also encounters difficulties when the image texture is overly uniform, which hinders reliable feature matching. We will explore these limitations in future work.
+
+# 6 Conclusion
+
+In this work, we propose PoseCrafter, a simple yet effective framework for estimating camera poses from input image pairs with small or no overlap—commonly referred to as extreme viewpoint changes [5]. Estimating poses under such challenging conditions remains a difficult problem, as minimal shared visual content often leads to poor matching and unreliable geometry. Rather than relying solely on video interpolation to synthesize intermediate frames, we introduce Hybrid Video Generation (HVG), which produces clearer and more geometrically consistent frames. HVG couples the vanilla interpolation model DynamamiCrafter with a pose-conditioned novel view synthesis model, ViewCrafter, allowing it to refine and correct structural inconsistencies and reduce mid-sequence blur. To further improve pose estimation accuracy, we also introduce Feature Matching Selector (FMS). This module identifies the most informative frames by evaluating their feature correspondences with the input image pair, ensuring that only geometrically meaningful frames suitable for pose estimation are selected. Through extensive experiments on multiple widely used benchmarks [5], including challenging scenes with extreme viewpoint differences, we demonstrate that PoseCrafter consistently outperforms existing state-of-the-art methods in both accuracy and robustness.
+
+Acknowledgement. This research / project is supported by the National Research Foundation (NRF) Singapore, under its NRF-Investigatorship Programme (Award ID. NRF-NRFI09-0008), and the China Scholarship Council under Grant Number 202306290143. It is also supported by the National Engineering Laboratory for Integrated Aero-Space-Ground-Ocean Big Data Application Technology and by the National Natural Science Foundation of China (NSFC) under Grant Nos. U19B2037, 61901384, and 61971356.
+
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+
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+
+# 6. Experimental Setting/Details
+
+Question: Does the paper specify all the training and test details (e.g., data splits, hyperparameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
+
+Answer: [Yes]
+
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+Guidelines:
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+- The answer NA means that the paper does not include experiments.  
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+
+# 7. Experiment Statistical Significance
+
+Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
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+Answer: [Yes]
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+- The answer NA means that the paper does not include experiments.  
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+
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+- If error bars are reported in tables or plots, The authors should explain in the text how they were calculated and reference the corresponding figures or tables in the text.
+
+# 8. Experiments Compute Resources
+
+Question: For each experiment, does the paper provide sufficient information on the computer resources (type of compute workers, memory, time of execution) needed to reproduce the experiments?
+
+Answer: [Yes]
+
+Justification: In the Experiments section Implementation Details section, the paper introduces the detailed implementation details, including the computing resources, training and evaluation details.
+
+Guidelines:
+
+- The answer NA means that the paper does not include experiments.  
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+
+# 9. Code Of Ethics
+
+Question: Does the research conducted in the paper conform, in every respect, with the NeurIPS Code of Ethics https://neurips.cc/public/EthicsGuidelines?
+
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+
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+
+# 10. Broader Impacts
+
+Question: Does the paper discuss both potential positive societal impacts and negative societal impacts of the work performed?
+
+Answer: [Yes]
+
+Justification: This paper contributes to extreme pose estimation research and extends beyond just extreme pose estimation tasks. In the future, it has the potential to enhance other research fields and benefit human society.
+
+Guidelines:
+
+- The answer NA means that there is no societal impact of the work performed.
+
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+- If there are negative societal impacts, the authors could also discuss possible mitigation strategies (e.g., gated release of models, providing defenses in addition to attacks, mechanisms for monitoring misuse, mechanisms to monitor how a system learns from feedback over time, improving the efficiency and accessibility of ML).
+
+# 11. Safeguards
+
+Question: Does the paper describe safeguards that have been put in place for responsible release of data or models that have a high risk for misuse (e.g., pretrained language models, image generators, or scraped datasets)?
+
+Answer: [NA]
+
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+
+Guidelines:
+
+- The answer NA means that the paper poses no such risks.  
+- Released models that have a high risk for misuse or dual-use should be released with necessary safeguards to allow for controlled use of the model, for example by requiring that users adhere to usage guidelines or restrictions to access the model or implementing safety filters.  
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+- We recognize that providing effective safeguards is challenging, and many papers do not require this, but we encourage authors to take this into account and make a best faith effort.
+
+# 12. Licenses for existing assets
+
+Question: Are the creators or original owners of assets (e.g., code, data, models), used in the paper, properly credited and are the license and terms of use explicitly mentioned and properly respected?
+
+Answer: [Yes]
+
+Justification: The paper cites the original paper that produced the code package or dataset, and follows the licenses for existing assets.
+
+Guidelines:
+
+- The answer NA means that the paper does not use existing assets.  
+- The authors should cite the original paper that produced the code package or dataset.  
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+
+- If assets are released, the license, copyright information, and terms of use in the package should be provided. For popular datasets, paperswithcode.com/datasets has curated licenses for some datasets. Their licensing guide can help determine the license of a dataset.  
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+
+# 13. New Assets
+
+Question: Are new assets introduced in the paper well documented and is the documentation provided alongside the assets?
+
+Answer: [NA]
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+Justification: This paper does not introduce new assets.
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+Guidelines:
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+- At submission time, remember to anonymize your assets (if applicable). You can either create an anonymized URL or include an anonymized zip file.
+
+# 14. Crowdsourcing and Research with Human Subjects
+
+Question: For crowdsourcing experiments and research with human subjects, does the paper include the full text of instructions given to participants and screenshots, if applicable, as well as details about compensation (if any)?
+
+Answer: [NA]
+
+Justification: The paper does not involve crowdsourcing nor research with human subjects.
+
+Guidelines:
+
+- The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.  
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+
+# 15. Institutional Review Board (IRB) Approvals or Equivalent for Research with Human Subjects
+
+Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or an equivalent approval/review based on the requirements of your country or institution) were obtained?
+
+Answer: [NA]
+
+Justification: The paper does not involve crowdsourcing nor research with human subjects.
+
+Guidelines:
+
+- The answer NA means that the paper does not involve crowdsourcing nor research with human subjects.  
+- Depending on the country in which research is conducted, IRB approval (or equivalent) may be required for any human subjects research. If you obtained IRB approval, you should clearly state this in the paper.
+
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+- For initial submissions, do not include any information that would break anonymity (if applicable), such as the institution conducting the review.
+
+# A Camera Pose Estimation Results based on MAST3R
+
+To further validate the generality of PoseCrafter on different pose estimation backbones, we replaced DUSt3R [3] with MASt3R [4], another transformer-based framework augmented with a dense local feature head and efficient sparse matching. We evaluated this configuration on four benchmarks with varying yaw ranges: Cambridge Landmarks  $(50^{\circ} - 65^{\circ})$ , ScanNet  $(50^{\circ} - 65^{\circ})$ , DL3DV-10K  $(50^{\circ} - 90^{\circ})$ , and NAVI  $(50^{\circ} - 90^{\circ})$ . As shown in Table 11 and Table 12, using MASt3R directly for pose estimation results in lower accuracy compared to DUSt3R. A possible explanation is that the sparse matching algorithm employed by MASt3R may be less effective for image pairs with small or no overlap. Nonetheless, our proposed framework consistently improves estimation accuracy over the baseline pose estimation models, including MASt3R. This demonstrates that our approach generalizes well across different pose estimation backbones by synthesizing intermediate frames that are more suitable for pose estimation.
+
+Table 11: Camera pose estimation results on outward-facing datasets (Cambridge Landmarks and ScanNet) based on MAST3R. We report rotation recall  $(\mathrm{R}@\theta \uparrow)$ , translation recall  $(\mathrm{T}@\theta \uparrow)$ , mean rotation error  $(\mathrm{MRE}\downarrow)$ , mean translation error  $(\mathrm{MTE}\downarrow)$ , and  $\mathrm{AUC}_{30}\uparrow$ .  
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">Input</td><td colspan="5">Cambridge Landmarks</td><td colspan="8">ScanNet</td></tr><tr><td>R@5°</td><td>R@15°</td><td>R@30°</td><td>MRE</td><td>AUC30</td><td>R@5°</td><td>R@15°</td><td>R@30°</td><td>T@5°</td><td>T@15°</td><td>T@30°</td><td>MRE</td><td>MTE</td></tr><tr><td>MASt3R</td><td>Pair</td><td>9.03</td><td>43.75</td><td>57.99</td><td>51.61</td><td>36.15</td><td>25.00</td><td>55.17</td><td>62.93</td><td>6.90</td><td>30.17</td><td>48.28</td><td>36.34</td><td>50.13</td></tr><tr><td>Ours(MASt3R)</td><td>Hybrid video</td><td>25.00</td><td>59.03</td><td>69.10</td><td>41.02</td><td>49.83</td><td>31.90</td><td>65.52</td><td>77.59</td><td>18.97</td><td>45.69</td><td>63.79</td><td>29.97</td><td>38.50</td></tr></table>
+
+Table 12: Camera pose estimation results on center-facing datasets (DL3DV-10K and NAVI) based on MAST3R. We report rotation recall  $(\mathbf{R}@\theta \uparrow)$ , translation recall  $(\mathrm{T}@\theta \uparrow)$ , mean rotation error  $(\mathrm{MRE}\downarrow)$ , mean translation error  $(\mathrm{MTE}\downarrow)$ , and  $\mathrm{AUC}_{30}\uparrow$ .  
+
+<table><tr><td>Dataset</td><td>Method</td><td>Input</td><td>R@5°</td><td>R@15°</td><td>R@30°</td><td>T@5°</td><td>T@15°</td><td>T@30°</td><td>MRE</td><td>MTE</td><td>AUC30</td></tr><tr><td rowspan="2">DL3DV-10K</td><td>MASt3R</td><td>Pair</td><td>7.00</td><td>63.67</td><td>97.00</td><td>26.67</td><td>72.67</td><td>91.67</td><td>15.18</td><td>13.31</td><td>53.49</td></tr><tr><td>Ours(MAST3R)</td><td>Hybrid video</td><td>7.67</td><td>68.67</td><td>97.33</td><td>30.00</td><td>76.33</td><td>92.00</td><td>14.09</td><td>12.91</td><td>55.36</td></tr><tr><td rowspan="2">NAVI</td><td>MASt3R</td><td>Pair</td><td>43.97</td><td>93.39</td><td>96.89</td><td>50.97</td><td>89.49</td><td>97.67</td><td>8.30</td><td>7.43</td><td>76.54</td></tr><tr><td>Ours(MAST3R)</td><td>Hybrid video</td><td>43.97</td><td>93.77</td><td>97.28</td><td>51.75</td><td>91.83</td><td>97.28</td><td>7.71</td><td>6.98</td><td>77.26</td></tr></table>
+
+Table 13: Additional comparison with VGGT on Cambridge Landmarks. We report mean rotation error (MRE↓), rotation recall (R@  $\theta$  ↑), and AUC<sub>30</sub> ↑.  
+
+<table><tr><td>Method</td><td>Input</td><td>MRE</td><td>R@5°</td><td>R@15°</td><td>R@30°</td><td>AUC30</td></tr><tr><td>Dust3R</td><td>Pair</td><td>18.14</td><td>40.34</td><td>71.25</td><td>82.99</td><td>61.98</td></tr><tr><td>Ours</td><td>Hybrid video</td><td>11.40</td><td>55.21</td><td>89.93</td><td>93.75</td><td>77.41</td></tr><tr><td>VGGT</td><td>Pair</td><td>20.17</td><td>40.00</td><td>70.17</td><td>82.29</td><td>60.54</td></tr><tr><td>VGGT_Ours</td><td>Hybrid video</td><td>17.88</td><td>42.43</td><td>84.40</td><td>85.76</td><td>65.15</td></tr></table>
+
+# B Additional Comparison with VGGT
+
+To further analyze the generality of our pipeline, we conducted comparative experiments with VGGT [39] on the Cambridge Landmarks dataset under yaw changes of  $[50^{\circ} - 65^{\circ}]$ .
+
+We first evaluated the two models in challenging cases where only image pairs with small or no overlap were provided. As shown in the second and fourth rows of Table 13, DUSt3R consistently outperforms VGGT on such data.
+
+We then integrate these two models into our pipeline and evaluate their performance. As shown in the third and fifth rows, both configurations achieve significant improvements over their directly estimated counterparts. The version using DUSt3R achieves a higher accuracy than the version using VGGT. These results demonstrate that our method is compatible with different pose estimators and consistently enhances their performance.
+
+Overall, DUSt3R appears better suited than VGGT for small- or non-overlapping image pairs, and our framework provides more noticeable improvements when combined with DUSt3R. While fine-tuning VGGT on small-overlap data or adjusting the hyperparameters of our pipeline may further enhance its performance, we leave such extensions for future work.
+
+# C Comparison of DUSt3R Confidence-based Selection and FMS
+
+We compare DUSt3R confidence-based frame selection with our proposed Feature Matching Selector (FMS) to evaluate whether confidence scores can serve as a viable alternative. In this setting, top-ranked frames were selected from hybrid videos using four different confidence thresholds (20%, 40%, 60%, and 80%). The results are summarized in Table 14.
+
+When the threshold was set to  $20\%$  or  $40\%$ , pose estimation accuracy decreased compared to using the full hybrid video sequence. Increasing the threshold to  $60\%$  or  $80\%$  improved performance, but the accuracy still remained lower than that achieved by our proposed FMS.
+
+In terms of efficiency, confidence-based selection introduces substantial overhead, as all video frames must be processed by DUSt3R to compute confidence maps prior to selection. This step incurs significant time and memory costs, and higher thresholds further increase runtime as more frames are selected. By contrast, our FMS requires only a single feature extraction step, immediately identifying the most informative frames with superior efficiency and accuracy. These findings highlight the practical advantages of our proposed FMS over confidence-based selection in both computational efficiency and pose estimation performance.
+
+Table 14: Comparison of DUSt3R confidence-based selection and FMS on Cambridge Landmarks. We report pose estimation results under yaw changes of  $[50^{\circ} - 65^{\circ}]$ . Frames were selected from hybrid videos using four DUSt3R confidence thresholds (20%, 40%, 60%, and 80%). We report mean rotation error (MRE↓), rotation recall (R@ θ ↑), AUC<sub>30</sub> ↑ and pose estimation time.  
+
+<table><tr><td>Method</td><td>MRE↓</td><td>R@5°</td><td>R@15°</td><td>R@30°</td><td>AUC30↑</td><td>Pose Estimation Time</td></tr><tr><td>Conf(20%)</td><td>14.66</td><td>54.17</td><td>85.07</td><td>89.24</td><td>72.45</td><td>2.79min</td></tr><tr><td>Conf(40%)</td><td>14.36</td><td>57.30</td><td>87.15</td><td>90.97</td><td>74.24</td><td>2.91min</td></tr><tr><td>Conf(60%)</td><td>12.35</td><td>54.17</td><td>90.28</td><td>93.06</td><td>76.60</td><td>3.47min</td></tr><tr><td>Conf(80%)</td><td>12.41</td><td>53.47</td><td>90.63</td><td>93.06</td><td>76.46</td><td>4.13min</td></tr><tr><td>Oursw/o FMS</td><td>13.24</td><td>54.51</td><td>89.24</td><td>92.71</td><td>76.13</td><td>2.56min</td></tr><tr><td>Ours</td><td>11.40</td><td>55.21</td><td>89.93</td><td>93.75</td><td>77.41</td><td>0.18min</td></tr></table>
+
+# D Visualization Results of Limitation
+
+Although PoseCrafter achieves robust results across various benchmarks, certain challenging scenes still degrade its performance. In the hybrid video generation (HVG) stage, severe illumination differences between the start and end frames will introduce obvious artifacts in the synthesized intermediate views. The red-boxed regions in Figure 4 highlight these artifacts, which would be marked as low confidence and discarded in the downstream pose estimation backbone, e.g., DUSt3R in this work. Such an obvious removal of information may significantly degrade the final performance. Moreover, in the feature match selector (FMS) module, scenes dominated by uniform or repetitive textures hinder the reliable extraction and matching of key points, resulting in fewer RANSAC [10] inliers and lower pose accuracy. The red lines in Figure 5 show examples of incorrect correspondences in such scenes.
+
+# E More Visualizations of Our Generated Videos
+
+To further illustrate the superiority of our proposed hybrid video generation(HVG), we present additional side-by-side comparisons of intermediate frames produced by DynamiCrafter, ViewCrafter, and PoseCrafter. In Figure 6, DynamiCrafter [6] delivers temporally smooth transitions but exhibits progressive blur and geometric drift in the middle of generated sequences. Although ViewCrafter [9]
+
+![](images/b7df7c00e22c1364d07706a904ded4f1c0217a6e40a9bdae73186d4fdf496f4b.jpg)  
+Figure 4: Hybrid Video Generation artifacts under severe illumination differences. Blue and yellow outlines indicate the start and end frames, respectively. Confidence images denote images filtered with the predicted confidence map in the subsequent DUSt3R model. The red boxes highlight regions affected by artifacts in these cases. We can observe that these regions have quite low confidence.
+
+![](images/779493998b1a47b04ecfd2930a3d96faaea02a405e375cb4f232a711132ecdbb.jpg)  
+Figure 5: Feature Matching Selection failures in low-texture regions. Blue and yellow outlines indicate the start and end frames, respectively. The red and green lines indicate incorrect and correct correspondences, respectively. Incorrect correspondences lead to errors in inlier counting, affecting the accuracy of subsequent frame selection.
+
+can produce sharp results with minimal blur, using only input image pairs with small overlap often leads to structural artifacts and misalignments. To address these limitations, we combine DynamiCrafter and ViewCrafter to complement each other's strengths. Specifically, we first use DynamiCrafter to synthesize intermediate "relay" frames, effectively augmenting the input image pair with frames that have larger overlaps. These relay frames are then passed to ViewCrafter to generate clearer and more geometrically consistent results. As shown in Figure 6, our proposed approach successfully produces frames that are both visually sharp and structurally reliable.
+
+![](images/fa34a4ee603b4196dddea9f4ccf5aa7db0d63278da569fd1b06e29892ef59cfb.jpg)  
+Input Images  
+Figure 6: Comparative video synthesis results. Each row shows intermediate frames synthesized between the same start frame (blue box) and end frame (yellow box), generated by different methods: DynamiCrafter (DC), ViewCrafter (VC), and our Hybrid Video Generation (Ours). DC produces smooth motion but exhibits progressive blur and geometric drift in the middle of sequences (highlighted in red circle). Since VC is sensitive to the pose of the input image pair, it tends to produce structural misalignments in our small-overlap setting (highlighted in red box). By coupling DC and VC together, our method delivers sharp, geometrically consistent video frames throughout, correcting both the blur of DC and the misalignments of VC.
+
+![](images/16fa13caf4e8c791d69cbb315c32966ce7326aafe2e365cd4ada009dfdfeb98e.jpg)  
+Generated Video Frames

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+# Post Hoc Regression Refinement via Pairwise Rankings
+
+Kevin Tirta Wijaya
+
+MPI-INF
+
+kevintirta.w@gmail.com
+
+Michael Sun
+
+MIT
+
+msun415@csail.mit.edu
+
+Minghao Guo
+
+MIT
+
+guomh2014@gmail.com
+
+Hans-Peter Seidel
+
+MPI-INF
+
+hpseidel@mpi-inf.mpg.de
+
+Wojciech Matusik
+
+MIT
+
+wojciech@csail.mit.edu
+
+Vahid Babaei
+
+MPI-INF
+
+vbabaei@mpi-inf.mpg.de
+
+# Abstract
+
+Accurate prediction of continuous properties is essential to many scientific and engineering tasks. Although deep-learning regressors excel with abundant labels, their accuracy deteriorates in data-scarce regimes. We introduce RankRefine, a model-agnostic, plug-and-play post hoc method that refines regression with expert knowledge coming from pairwise rankings. Given a query item and a small reference set with known properties, RankRefine combines the base regressor's output with a rank-based estimate via inverse-variance weighting, requiring no retraining. In molecular property prediction task, RankRefine achieves up to  $10\%$  relative reduction in mean absolute error using only 20 pairwise comparisons obtained through a general-purpose large language model (LLM) with no finetuning. As rankings provided by human experts or general-purpose LLMs are sufficient for improving regression across diverse domains, RankRefine offers practicality and broad applicability, especially in low-data settings.
+
+# 1 Introduction
+
+Accurate prediction of continuous properties is crucial across scientific and engineering disciplines. In molecular-property prediction (MPP), for instance, reliable estimates of physical or chemical attributes can accelerate drug discovery, materials design, and catalyst development. Recent advances in deep learning have enhanced regression models by leveraging large datasets to uncover complex, nonlinear relationships between structured inputs (e.g., molecular graphs, crystal structures) and their associated properties. Yet, unlike computer vision or natural-language processing, where large labeled corpora can be mined or crowd-sourced, many specialized fields face a fundamental bottleneck: acquiring ground-truth labels requires expert-led experiments that are both costly and slow. Consequently, real-world tasks often operate in data-scarce regimes where even 50 labeled samples may be considered plentiful [Sun et al., 2024].
+
+When large-scale labels are unavailable, expert knowledge becomes a valuable but under-utilized asset. One accessible form of such knowledge is relative comparison: pairwise judgments about which of two samples exhibits a higher (or lower) property value. Pairwise rankings convey substantial information, are often easier for human experts to provide, and can even be generated by general-purpose large language models (LLMs), which have shown surprising ranking skills in chemistry and related domains [Sun et al., 2025, Guo et al., 2023].
+
+We introduce RankRefine, a post hoc refinement framework that improves regression predictions by incorporating pairwise rankings. Given a query sample and a small set of labeled references, which can conveniently be drawn from training data, a ranker infers the relative ordering between the query and each reference; these comparisons define a likelihood whose minimization yields a rank-based
+
+property estimate. RankRefine then fuses this estimate with the base regressor's prediction via inverse-variance weighting, all without retraining.
+
+Because RankRefine is largely model-agnostic and requires no architectural changes, it suits low-data, few-shot, and meta-learning scenarios. Leveraging ranking signals from publicly hosted LLMs, it provides substantial improvements in regression accuracy with minimal labeled data and negligible client-side computation. Experiments on synthetic and real-world benchmarks, including multiple MPP tasks, demonstrate that RankRefine consistently boosts predictive performance. Further analysis links its effectiveness to ranking quality, underscoring the promise of LLMs and other expert-informed rankers as practical complements to data-scarce regression models. The source code is available at https://github.com/ktirta/regref.
+
+# 2 Background
+
+# 2.1 Combining Regression and Ranking
+
+Huang et al. [2024] reformulate regression as joint regression-pairwise-ranking objectives and show that the combination improves predictive accuracy. Tynes et al. [2021], Fralish et al. [2023] instead train a regressor to predict pairwise differences in molecular properties; at inference, a query molecule is compared with reference molecules of known labels, and the mean of the predicted differences yields the final estimate. The post hoc method proposed by Gonçalves et al. [2023] refines regression outputs by computing a weighted average of the original prediction and those of its top-k nearest neighbors.
+
+A closely related approach is the consolidation method for document relevance proposed by Yan et al. [2024]. Given a pointwise rating and a set of pairwise comparisons, their post-processor makes minimal adjustments to preserve the ranker-derived inequalities. For a one-dimensional rating  $\hat{y}$  this projection simplifies to
+
+$$
+\hat {y} ^ {*} = \max  \left(\min  (\hat {y}, U), L\right),
+$$
+
+where  $L$  and  $U$  are the lower and upper bounds of the feasible interval.
+
+Preference learning with Gaussian processes [Chu and Ghahramani, 2005, Houlsby et al., 2012, Chau et al., 2022] utilize pairwise data but differ fundamentally from our setting. Preference learning assumes a latent score  $f(x)$  whose absolute scale is irrelevant; the aim is to preserve ordering and learn-to-rank, not to predict calibrated values. In contrast, we target real-world quantities, e.g., solubility or toxicity, and treat pairwise comparisons as auxiliary signals that refine supervised regression into meaningful, calibrated estimates. Similarly, many learning-to-rank approaches [Burges et al., 2005, Yildiz et al., 2020, Tom et al., 2024] may seem related to our work, but they actually address a different problem, i.e., ranking rather than regression.
+
+# 2.2 LLM as a Pairwise Ranker
+
+Large language models (LLMs) have recently been explored in molecular-property prediction and generation [Sun et al., 2025]. Several efforts fine-tune GPT-3- or LLaMA-based models with chemistry-specific prompts [Jablonka et al., 2024, Xie et al., 2024, Jacobs et al., 2024], while MolecularGPT [Liu et al., 2024] is instruction-tuned on 1000 property-prediction tasks and achieves few-shot performance competitive with graph neural networks.
+
+Fine-tuning, however, is resource-intensive and incurs substantial computational overhead. We therefore ask: can general-purpose, publicly hosted LLMs be leveraged directly, without domain-specific adaptation? We hypothesize that such models can supply useful signals when deployed as pairwise rankers.
+
+Human cognition offers an analogue. People often judge quantities either by estimating absolute magnitudes (regression) or by deciding which of two items is greater (ranking). A long-standing hypothesis holds that comparative judgments are easier and less biased [Thurstone, 1927, Miller, 1956, Stewart et al., 2005]. Pairwise tasks impose lower cognitive load [Routh et al., 2023] and avoid scale-interpretation bias [Hoeijmakers et al., 2024]. Because LLMs are pretrained on corpora rich in relative statements and later aligned with human feedback [Zhang et al., 2023, Bai et al., 2022, Rafailov et al., 2023], they may inherit a similar advantage. As a real example, Guo et al. [2023]
+
+![](images/5c0b4bb442d2a11a4056114945de320badba99d030a2465cf336a8aafab8dcc0.jpg)  
+Figure 1: Overview of the RankRefine framework. During training, a regressor is trained using labeled data. At inference, a query sample is paired with reference samples with known properties and compared by an external ranker to produce pairwise rankings. These rankings are used to estimate the query's property value via a rank-based estimator. The final prediction is obtained by fusing the regressor's output and the rank-based estimate using inverse variance weighting.
+
+show that off-the-shelf LLMs rival domain-specific models on chemistry classification and ranking benchmarks, underscoring the promise of pairwise prompting in specialized tasks.
+
+# 3 Method
+
+Our goal is to reduce the test-time error of an existing regressor by fusing its prediction with pairwise-ranking information in a plug-and-play fashion. We present RankRefine, a framework that augments a base regressor with rankings from an external source (e.g., an LLM or a domain expert). RankRefine is largely model-agnostic and applies to any regressor that returns both a point estimate and an uncertainty measure, for example Gaussian processes or random forests.
+
+We assume access to a reference set  $\mathbb{D} = \{(x_i, y_i)\}_{i=1}^k$  with known property values. This reference set can be drawn from the training set. At inference, the regressor predicts the property of a query sample  $x_0$ , giving  $\hat{y}_0^{\mathrm{reg}}$ , while the ranker supplies pairwise comparisons between  $x_0$  and each  $x_i \in \mathbb{D}$ .
+
+# 3.1 RankRefine
+
+Let  $\hat{y}_0^{\mathrm{reg}}\sim \mathcal{N}(y_0,\sigma_{\mathrm{reg}}^2)$  be the regressor's unbiased Gaussian estimate of the true property  $y_{0}$ . A second, rank-based estimate  $\hat{y}_0^{\mathrm{rank}}$  is derived from the comparisons. Under these assumptions, the optimal fusion of the two estimates reduces to the inverse-variance weighting [Cochran and Carroll, 1953], formalized below.
+
+Theorem 3.1 (RankRefine Fusion Theorem) If  $\hat{y}_0^{\mathrm{reg}}$  and  $\hat{y}_0^{\mathrm{rank}}$  are independent, unbiased Gaussian estimators of  $y_0$  with variances  $\sigma_{\mathrm{reg}}^2$  and  $\sigma_{\mathrm{rank}}^2$ , the minimum-variance unbiased estimator is
+
+$$
+\hat {y} _ {0} ^ {*} = \sigma_ {p o s t} ^ {2} \left(\frac {\hat {y} _ {0} ^ {r e g}}{\sigma_ {r e g} ^ {2}} + \frac {\hat {y} _ {0} ^ {r a n k}}{\sigma_ {r a n k} ^ {2}}\right), \quad \sigma_ {p o s t} ^ {2} = \left(\frac {1}{\sigma_ {r e g} ^ {2}} + \frac {1}{\sigma_ {r a n k} ^ {2}}\right) ^ {- 1}. \tag {1}
+$$
+
+See supplementary materials for the proof.
+
+Rank-based estimate. Pairwise probabilities follow the Bradley-Terry model [Bradley and Terry, 1952],  $P(x_{i} \succ x_{j}) = s(y_{i} - y_{j})$  with sigmoid function  $s(z) = (1 + e^{-z})^{-1}$ . Indexing the query as  $i = 0$  and references as  $i > 0$ , we obtain  $\hat{y}_0^{\mathrm{rank}}$  by minimizing the negative log-likelihood
+
+$$
+\hat {y} _ {0} ^ {* \text {r a n k}} = \arg \min  _ {\hat {y} _ {0} ^ {\text {r a n k}}} \left[ - \sum_ {x _ {i} \in \mathbb {A}} \log s \left(\hat {y} _ {0} ^ {\text {r a n k}} - y _ {i}\right) - \sum_ {x _ {j} \in \mathbb {B}} \log \left(1 - s \left(\hat {y} _ {0} ^ {\text {r a n k}} - y _ {j}\right)\right) \right], \tag {2}
+$$
+
+where  $\mathbb{A}$  contains references ranked below  $x_0$  and  $\mathbb{B}$  those ranked above.
+
+Lemma 3.2 (Variance of the rank-based estimate) Let  $\hat{y}_0^{*\text{rank}}$  minimize equation 2. Its variance is approximated by the inverse observed Fisher information [Ly et al., 2017],
+
+$$
+\sigma_ {\text {r a n k}} ^ {2} \approx \left[ \sum_ {y _ {i} \in \mathbb {A} \cup \mathbb {B}} s \left(\Delta_ {i}\right) \left(1 - s \left(\Delta_ {i}\right)\right) \right] ^ {- 1}, \quad \text {w i t h} \Delta_ {i} = \hat {y} _ {0} ^ {* r a n k} - y _ {i}. \tag {3}
+$$
+
+Applying Theorem 3.1 with  $\sigma_{\mathrm{rank}}^2$  from Lemma 3.2 yields  $\hat{y}_0^*$ .
+
+# 3.2 Analysis of RankRefine
+
+We measure performance via the mean absolute error (MAE). For a folded Gaussian derived from a zero-mean Gaussian,  $\mathrm{MAE} = \sqrt{2 / \pi}\sigma$ , so
+
+$$
+\mathrm {M A E} _ {\text {p o s t}} <   \mathrm {M A E} _ {\text {r e g}} \iff \sigma_ {\text {p o s t}} ^ {2} <   \sigma_ {\text {r e g}} ^ {2}.
+$$
+
+Corollary 3.2.1 Any informative ranker with finite variance  $(\sigma_{\text{rank}}^2 < \infty)$  lowers the expected MAE after fusion.
+
+More generally, letting  $\alpha \in [0,1]$  be the desired ratio between post-refinement and the original MAEs,
+
+$$
+\mathrm {M A E} _ {\text {p o s t}} \leq \alpha \mathrm {M A E} _ {\text {r e g}} \Longleftarrow \sigma_ {\text {r a n k}} ^ {2} \leq \frac {\alpha^ {2} \sigma_ {\text {r e g}} ^ {2}}{1 - \alpha^ {2}}. \tag {4}
+$$
+
+Regularization. If the ranker is biased yet over-confident  $(\sigma_{\mathrm{rank}}^2\ll \sigma_{\mathrm{reg}}^2)$ , we temper its variance via
+
+$$
+\sigma_ {\mathrm {r a n k}} ^ {2} \gets \max  \big (\sigma_ {\mathrm {r a n k}} ^ {2}, c \sigma_ {\mathrm {r e g}} ^ {2} \big),
+$$
+
+with user-chosen constant  $c > 0$ .
+
+# 4 Experimental Results
+
+We evaluate RankRefine on synthetic and real-world tasks. After outlining datasets, metrics, and implementation details, we report results in synthetic settings, where ranking oracle is available, and practical settings across multiple domains.
+
+# 4.1 Experimental Setup
+
+We use nine molecular datasets from the TDC ADME benchmark [Huang et al., 2021]: Caco-2 [Wang et al., 2016], Clearance Microsome and Clearance Hepatocyte [Di et al., 2012], log Half-Life [Obach et al., 2008], FreeSolv [Mobley and Guthrie, 2014], Lipophilicity [Wu et al., 2018], PPBR, Solubility [Sorkun et al., 2019], and VDss [Lombardo and Jing, 2016]. We additionally test three tabular regressions: crop-yield prediction from sensor data [Soundankar, 2025], student-performance prediction [Cortez, 2014], international-education cost estimation [Shamim, 2025]. In the human-as-ranker experiment, we use UTKFace [Zhang et al., 2017] for age estimation.
+
+To emulate low-data regimes, we sample 50 training points from above datasets uniformly at random and merge the remainder with the original test split, repeating this re-split over five random seeds.
+
+The primary metric is the mean absolute error (MAE). We report the normalized error
+
+$$
+\beta = \frac {\mathrm {M A E} _ {\text {p o s t}}}{\mathrm {M A E} _ {\text {r e g}}},
+$$
+
+where  $\beta < 1$  indicates improvement.
+
+Suppose that a pairwise ranker  $R$  evaluates a pair of inputs  $(x_{i}, x_{j})$ . The ranker returns  $R(x_{i}, x_{j}) = 0$  if it predicts  $x_{i} \succ x_{j}$ , and  $R(x_{i}, x_{j}) = 1$  otherwise. The pairwise ranker quality can be measured via pairwise ranking accuracy (PRA), defined as,
+
+$$
+\mathrm {P R A} = \frac {1}{| \mathbb {P} |} \sum_ {(i, j) \in \mathbb {P}} \mathbb {I} \left(R \left(x _ {i}, x _ {j}\right) = \mathbb {I} \left(y _ {i} <   y _ {j}\right)\right),
+$$
+
+![](images/9e249c95377fa2ba180c3d2b3cd35b5269b5ea823a88ec40fb33cf9fb26a7f8d.jpg)  
+Figure 2: Empirical validation of the theoretical MAE reduction bound under ideal conditions. For each target improvement factor  $\beta$ , we compute the required ranker variance  $\sigma_{\mathrm{rank}}^2$  using the right-side inequality in Implication 4. We simulate predictions from an oracle regressor  $(\hat{y}_0^{\mathrm{reg}} \sim \mathcal{N}(y_0, 1))$  and an oracle ranker  $(\hat{y}_0^{\mathrm{rank}} \sim \mathcal{N}(y_0, \sigma_{\mathrm{rank}}^2))$ , and compute the fused estimate. The observed postrefinement MAE ratios match the ideal  $\beta$  values, demonstrating the correctness of the fusion rule under Gaussian distribution assumptions.
+
+where  $\mathbb{P} = \{(i,j)|i\neq j\}$  is the set of all comparable pairs with ground-truth labels  $y_{i},y_{j}$ , and  $\mathbb{I}$  is the indicator function which return 1 if the condition is true, and 0 otherwise. Unless stated otherwise, the base model is a random-forest regressor from scikit-learn [Pedregosa et al., 2011] with default hyper-parameters, executed on a single CPU.
+
+# 4.2 Verifying Theoretical MAE Reduction Under Ideal Conditions
+
+To validate Implication 4, we simulate unbiased oracle predictions with known variances. For target factors  $\beta \in \{0.10, 0.20, \dots, 0.90, 0.99\}$ , the required ranker variance  $\sigma_{\mathrm{rank}}^2$  is obtained from the right-side inequality of Implication 4. Synthetic estimates are drawn as  $\hat{y}_0^{\mathrm{reg}} \sim \mathcal{N}(y_0, 1)$  and  $\hat{y}_0^{\mathrm{rank}} \sim \mathcal{N}(y_0, \sigma_{\mathrm{rank}}^2)$ . The fused prediction  $\hat{y}_0^*$  follows Equation 1. Figure 2 confirms that empirical MAE ratios match the prescribed targets.
+
+# 4.3 Effect of Ranker Accuracy and Reference Sample Size on Molecular-Property Prediction with RankRefine
+
+Using the nine TDC datasets, we vary oracle ranker accuracy and the number  $k$  of reference comparisons per query. Figure 3 plots  $\beta$ , the post refinement MAE error divided by the regression error, versus pairwise ranker accuracy. RankRefine consistently lowers error, even with accuracy  $\approx 0.55$  and  $k = 10$ . Increasing the number of pairwise comparisons  $k$  tends to further lower  $\beta$ . We observe that  $k = 20$  is optimal, as the difference between  $k = 20$  and  $k = 30$  is often minimal.
+
+For very accurate rankers ( $>0.95$ ) a slight uptick in  $\beta$  arises from over-confident curvature estimates and extreme solutions when the query is an outlier. For the first source, recall that  $\sigma_{\mathrm{rank}}^2$  is approximated by the second derivative of the negative log-likelihood. This curvature becomes smaller as the ranker accuracy approaches perfection, leading to over-confident estimates. For the second source, consider the case when the query is truly the smallest or largest value among the reference set. This is especially common when  $k$  is small and ranker is accurate. The optimizer may push  $\hat{y}_0^{*\mathrm{rank}}$  toward extreme values that still satisfy pairwise ranking constraints, but overshoot the true property value  $y_0$ .
+
+# 4.4 Cross-Domain Generalization
+
+Applying the same protocol to the three tabular datasets yields Figure 4, whose reductions mirror those in chemistry datasets. The results show that RankRefine generalizes beyond molecular tasks.
+
+![](images/a79f308d4c970a11047cc8fee1c264780307b65d734b51ade48222cc7abe8956.jpg)  
+(a) Caco2
+
+![](images/4f79ff71cb3786b820a709c99366a5a20c545b973ba53e9ad65aadfa68c2a644.jpg)  
+(b) Clearance Microsome
+
+![](images/0316e9103826b0f96b41855862725556fcb236f11081219dab66298e8416d804.jpg)  
+(c) Clearance Hepatocyte
+
+![](images/e3567ab88a31fc9b4b9c0ceea1fa4225546f560d6561918604a6d2cb12ac5ded.jpg)  
+(d) Half Life
+
+![](images/041119d155211e9e3adc3192c457cfb5faaf6e2c03ea9f890f55a19f35a3590b.jpg)  
+(e) FreeSolv
+
+![](images/3fc9213d4142e38f8717b417cf37a93ed5cab89148c495581482a1052e9e09a0.jpg)  
+(f) Lipophilicity
+
+![](images/41760cf438ac848eb88d1cedb563c6cc688264018cc385d7df18c631e0a80a19.jpg)  
+(g) PPBR
+
+![](images/77e07e142b46ea682da47a4a39381ab32dfb8747623457abb1307d2c1bda0a61.jpg)  
+(h) Solubility
+
+![](images/efefe248a18fd565339d8ace9ab342681828be2eb94fa55494d883bbdfa570c5.jpg)  
+(i) VDss  
+Figure 3: Performance of RankRefine on molecular property prediction datasets under varying oracle ranker accuracy and number of reference comparisons. Each plot shows the normalized error  $\beta = \frac{\mathrm{MAE}_{\mathrm{post}}}{\mathrm{MAE}_{\mathrm{reg}}}$  as a function of ranker accuracy, averaged over 5 random splits.  $\beta < 1$  indicates improvements in regression performance over the base regressor.  $k$  is the number of pairwise comparisons for each test molecule. Shaded regions indicate standard deviation. Dashed gray line shows baseline MAE with no refinement. Across most configurations, RankRefine improves regression performance when using a ranker with accuracy as low as 0.55. Increasing  $k$  tends to lower  $\beta$ , but typically the benefits start to diminish beyond  $k = 20$ .
+
+![](images/f96ccce7cd1c505738e29be9af931b93f18ef6dbfc91b04d87480b24579e8709.jpg)  
+(a) International Education Cost
+
+![](images/496cdc7a110bf69507b7db716ecd6ec16438f2b2828c1caa8e01cf61c8af02be.jpg)  
+(b) Smart Farming
+
+![](images/0921b4e3514e7dd773fb74f5d54454c28ce12b63f59b3eb21b63fd1c7cbf3042.jpg)  
+(c) Student Performance
+
+![](images/f58bcda384c177eff36f538914d2db4dd757de135084bd63c290b2edc0701970.jpg)  
+Figure 4: Performance of RankRefine on tabular datasets under varying oracle ranker accuracy and number of reference comparisons. Across most configurations, RankRefine improves regression performance when using a ranker with accuracy as low as 0.55.  
+(a)
+
+![](images/d8c1931bea69264e571430baae45cbfdefedfdb19378fde73f605366c059e234.jpg)  
+(b)  
+Figure 5: (a) Comparison between RankRefine the constrained optimization (projection)-based refinement method of Yan et al. [2024] on molecular property prediction tasks. We report the difference in normalized error,  $\beta_{\mathrm{ours}} - \beta_{\mathrm{projection}}$ . A negative value indicates better performance by RankRefine. Each curve corresponds to a dataset. RankRefine generally outperforms the baseline when the ranker accuracy is between 0.5 and 0.95. (b) We also compare our method to a related post hoc regression improvement method, regression by re-ranking [Gonçalves et al., 2023].
+
+# 4.5 Comparison with Other Baselines
+
+We compare against two post hoc refinement methods: constrained optimization [Yan et al., 2024] and regression by re-ranking (RbR) [Gonçalves et al., 2023]. We implemented the two baselines from scratch, as no publicly available code was provided. We use  $k = 30$  comparisons. Figure 5 displays  $\beta_{\mathrm{ours}} - \beta_{\mathrm{projection}}$  and  $\beta_{\mathrm{ours}} - \beta_{\mathrm{reranking}}$ ; negative values favour RankRefine. Our approach generally outperforms RbR in all datasets. Against the projection-based baseline, RankRefine excels when ranker accuracy lies between 0.50 and 0.95; projection dominates only when the ranker is nearly perfect. This is because, when all pairwise rankings are correct, the projection method strictly enforces the constraints without increasing the absolute error. In such cases, the MAE will either remain unchanged or improved, with the improvements depend primarily on the distribution and resolution of the known labels. Yet, such near-perfect rankers are rare in real-world scenarios. Thus, the robust performance of RankRefine with moderately-accurate rankers offers more practicality. More comparisons with projection-based refinement can be found in the supplementary materials.
+
+# 4.6 Few-Shot Molecular-Property Prediction with LLMs
+
+To evaluate the practical applicability of RankRefine in realistic few-shot settings, we replace the oracle ranker with ChatGPT-4o [OpenAI, 2025], a large language model (LLM). Note that we can
+
+Table 1: PRA and resulting RankRefine performance using ChatGPT-4o as the ranker on six datasets from the TDC ADME benchmark. For each test molecule, 20 training molecules are randomly sampled to form pairwise comparisons. Values are averaged over 3 random splits. Despite moderate pairwise accuracy ( $\sim$ 0.60–0.69), RankRefine consistently improves regression performance, demonstrating the viability of LLM-based rankers in low-data domains.  
+
+<table><tr><td>Dataset</td><td>Lipophilicity</td><td>Solubility</td><td>VDss</td></tr><tr><td>Pairwise Ranking Accuracy</td><td>0.622 ± 0.008</td><td>0.693 ± 0.035</td><td>0.605 ± 0.010</td></tr><tr><td>β</td><td>0.957 ± 0.012</td><td>0.934 ± 0.048</td><td>0.895 ± 0.053</td></tr><tr><td>Dataset</td><td>Caco2</td><td>Half Life</td><td>FreeSolv</td></tr><tr><td>Pairwise Ranking Accuracy</td><td>0.660 ± 0.013</td><td>0.602 ± 0.014</td><td>0.681 ± 0.050</td></tr><tr><td>β</td><td>0.970 ± 0.027</td><td>0.971 ± 0.005</td><td>0.937 ± 0.012</td></tr></table>
+
+Table 2: Performance of RankRefine when using human participants as both direct estimators and pairwise rankers on a facial age estimation task. The base error  $(\mathrm{MAE}_{\mathrm{reg}})$  corresponds to the raw human estimate error. Each test face is compared to 15 reference faces via human-judged pairwise comparisons. RankRefine improves prediction accuracy by refining each estimate based on human-provided rankings.  
+
+<table><tr><td>MAEreg</td><td>Pairwise Ranking Acc.</td><td>β</td></tr><tr><td>6.343 ± 0.610</td><td>0.759 ± 0.052</td><td>0.954 ± 0.046</td></tr></table>
+
+still evaluate the ranking accuracy of the LLM through oracle for the purpose of analysis. For each test molecule, we randomly sample 20 reference molecules from the training set and ask ChatGPT-4o to perform pairwise comparisons (e.g., "Which molecule is likely to have higher solubility?"). The model is queried using textual molecular descriptions, SMILES [Weininger, 1988]. The details of the prompt is provided in the supplementary materials.
+
+Table 1 summarizes ChatGPT-4o ranking accuracy and the resulting  $\beta$  on six TDC datasets. Even moderate accuracies ( $\approx 0.62 - 0.69$ ) yield tangible MAE gains, underscoring both the robustness and practicality of our method.
+
+One natural concern when employing a pretrained LLM as a ranker is whether it simply memorizes from training data which item (e.g., a molecule) has a higher or lower property value (e.g., solubility) compared to others. To test this, we conducted an additional evaluation on a private compound-activity dataset consisting of 75 compounds with IC50 labels measured against a specific target protein complex. This dataset is unpublished, and therefore, not part of any LLM training corpora, ruling out direct memorization. On this dataset, ChatGPT-4o achieves  $60.14\%$  pairwise ranking accuracy, indicating generalization capability and not simple memorization.
+
+# 4.7 Human Age Estimation with Pairwise Self-Correction
+
+RankRefine can potentially be used in an interactive, human-in-the-loop scenarios, where domain experts act as the pairwise rankers. As a proof of concept, we conduct a user study on the age estimation task. Details about the user study is available in the supplementary materials.
+
+Table 2 reports a UTKFace user study where 6 participants are asked to: (1) estimate the age of 17 individuals from their corresponding pictures, and (2) perform pairwise judgments to 15 individuals in the reference set. Pairwise judgments raise ranking accuracy to 0.76 and cut MAE by  $\approx 5\%$ , illustrating RankRefine's value for expert self-correction.
+
+# 4.8 Effects of Noisy Variance Estimates
+
+We study the effect of noise in the ranker variance estimate on the Solubility dataset using  $k = 30$  and  $k = 40$ . We add uniform perturbations sampled from  $[-b, +b]$  to the estimated ranker variance before fusion. As shown in Figure 6, performance degradation becomes noticeable when  $b \geq 5$ , which is more than three times the standard deviation of the ranker variance estimates. For reference, the mean and standard deviation of the estimated ranker variance are  $2.358 \pm 1.079$ .
+
+![](images/661b3dc0fb6a45717623bb1ea5a56930c42a1abce28c4a6faecb35f0b74d88d9.jpg)  
+(a)  $\mathrm{k} = {30}$
+
+![](images/ce04d9cea60c5f34117fef847052d9ef1392720f21630da62c0a423255f09979.jpg)  
+(b)  $\mathrm{k} = {40}$  
+Figure 6: Impact of noisy ranker variance estimate on the regression performance in Solubility dataset. Uniform noise from  $[-b, +b]$  is added to the estimated ranker variance. Performance starts to degrade when  $b \geq 5$ , more than 3 times the standard deviation of the ranker variance estimate.
+
+# 4.9 Effects of Biased Regressor
+
+We systematically inject constant bias into an otherwise unbiased regressor. Specifically, we uniformly draw ground-truth labels  $y_0 \sim U(0,1)$ , and set predictions by injecting zero-mean Gaussian noise  $\hat{y}_0^{reg} = y_0 + \epsilon$ , such that MAE ≈ 1SD where SD is the standard deviation of the ground-truth labels. We then add a constant offset,  $B$ , increasing in magnitude from 0% to 70% of the label standard deviation (SD). We report the refined-to-original MAE ratio,  $\beta$ , for varying ranker accuracies. Table 3 in Appendix D shows that  $\beta$  worsens as bias increases, but remains < 1 up to  $B = 60\%$  SD, indicating that RankRefine remains effective even under substantial regressor bias.
+
+# 4.10 Effects of Biased Sampling
+
+We study the effects of non-uniform sampling of references, in particular, when the references are clustered. Similar to the biased regressor experiment, we generate synthetic predictions with ground-truth label range [0, 1]. We then restrict the reference labels to increasingly narrow subranges of the ground-truth label range, centered around the midpoint of the range. The reference set bias,  $RB = x\%$ , means that the reference labels cover only (100 - x)% of the full ground-truth range. For example, an  $RB = 10\%$  means the reference labels range is [0.05, 0.95]. Table 4 in Appendix E suggests that RankRefine performance is best when the reference set spans the full ground-truth labels' range (i.e.,  $RB = 0\%$ ), but clustered sets still yield substantial gains. For example, at  $RB = 90\%$  and ranker accuracy = 60%,  $\beta = 0.8842$ , an 11.58% improvement.
+
+Furthermore, we evaluate biased sampling in two challenging settings: (i) disjoint: reference labels are in  $[-1,0]$  or  $[1,2]$  while queries are in  $[0,1]$ ; and (ii) partial overlap: reference labels are in  $[-0.5, 0.5]$  or  $[0.5, 1.5]$ , while queries are in  $[0,1]$ . This simulates a distribution shift, where the distribution of the reference labels is different from the distribution of the query labels. Despite the challenging setups, RankRefine improves the base regressor when the ranker is moderately accurate (i.e.,  $\geq 65\%$  in the disjoint case,  $\geq 55\%$  in the partial overlap case). More details are available in Table 5 in Appendix E.
+
+# 5 Limitations
+
+While RankRefine demonstrates strong empirical performance, it has a number of limitations:
+
+- Our theoretical analysis assumes that both the regressor and rank-based estimates have unbiased, Gaussian-distributed errors and are independent. Despite the empirical robustness of our method, its assumptions may not hold in practice, particularly in the presence of heavy-tailed or skewed noise.  
+- RankRefine depends on well-calibrated uncertainty estimates from the regressor and a trustworthy estimate of ranker variance (via Equation 3). Miscalibration in either component can reduce or even negate the performance gains.  
+- Our oracle experiments assume uniformly random ranking errors; however, real-world rankers may exhibit systematic biases, for example consistently failing on extreme values which can skew the fusion process.  
+- RankRefine uses the Bradley-Terry model by treating true property values as proxies for latent scores, which differs from its original use where latent scores are learned to explain probabilistic pairwise outcomes. While practical, this introduces a modeling mismatch. A possible solution is to learn a mapping from a standard Bradley-Terry latent scores to labels on a holdout set and apply it during inference
+
+# 6 Future Work
+
+Future work can extend RankRefine in several promising directions. One avenue is to replace the Bradley-Terry likelihood with richer stochastic-transitivity models that better capture structured or systematic errors in the ranker. Another important direction involves incorporating Bayesian or conformal calibration layers to automatically correct misestimated variances and improve reliability. Beyond scalar predictions, RankRefine could potentially be extended to handle multivariate or structured targets, such as full pharmacokinetic profiles. Finally, leveraging rationale from language models could improve the interpretability of the ranking process and facilitate richer forms of expert feedback in decision-critical domains.
+
+# 7 Conclusion
+
+We introduced RankRefine, a plug-and-play, post hoc framework that injects pairwise-ranking signals into any uncertainty-aware regressor. Theoretically, we proved that inverse-variance fusion with a rank-based estimator lowers the expected mean absolute error (MAE) whenever the ranker variance is finite. Empirically, oracle simulations generally follows the theory, and experiments on nine molecular-property benchmarks plus three diverse tabular tasks showed consistent improvements even with ranker accuracies of around  $55\%$  and as few as 10 comparisons. ChatGPT-4o rankings yielded measurable MAE drops on six ADME datasets, and a user study demonstrated similar self-correction for human age estimation. Compared with a projection baseline, RankRefine prevailed whenever ranker accuracy lay in the realistic 0.50–0.95 range, underscoring its robustness and broad applicability.
+
+# References
+
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+Michael Sun, Gang Liu, Weize Yuan, Wojciech Matusik, and Jie Chen. Foundation molecular grammar: Multi-modal foundation models induce interpretable molecular graph languages. In International Conference on Machine Learning. PMLR, 2025.  
+Taicheng Guo, Bozhao Nan, Zhenwen Liang, Zhichun Guo, Nitesh Chawla, Olaf Wiest, Xiangliang Zhang, et al. What can large language models do in chemistry? a comprehensive benchmark on eight tasks. Advances in Neural Information Processing Systems, 36:59662-59688, 2023.
+
+Pin-Yen Huang, Szu-Wei Fu, and Yu Tsao. Rankup: Boosting semi-supervised regression with an auxiliary ranking classifier. In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024. URL https://openreview.net/forum?id=d21PM1Aczs.  
+Michael Tynes, Wenhao Gao, Daniel J Burrill, Enrique R Batista, Danny Perez, Ping Yang, and Nicholas Lubbers. Pairwise difference regression: a machine learning meta-algorithm for improved prediction and uncertainty quantification in chemical search. Journal of chemical information and modeling, 61(8):3846-3857, 2021.  
+Zachary Fralish, Ashley Chen, Paul Skaluba, and Daniel Reker. Deepdelta: predicting admet improvements of molecular derivatives with deep learning. Journal of cheminformatics, 15(1):101, 2023.  
+Filipe Marcel Fernandes Gonçalves, Daniel Carlos Guimarães Pedronette, and Ricardo da Silva Torres. Regression by re-ranking. Pattern Recognition, 140:109577, 2023.  
+Le Yan, Zhen Qin, Honglei Zhuang, Rolf Jagerman, Xuanhui Wang, Michael Bendersky, and Harrie Oosterhuis. Consolidating ranking and relevance predictions of large language models through post-processing. In Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing, pages 410-423, 2024.  
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+Neil Houlsby, Ferenc Huszar, Zoubin Ghahramani, and Jose Hernández-lobato. Collaborative gaussian processes for preference learning. Advances in neural information processing systems, 25, 2012.  
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+Gary Tom, Stanley Lo, Samantha Corapi, Alan Aspuru-Guzik, and Benjamin Sanchez-Lengeling. Ranking over regression for bayesian optimization and molecule selection. arXiv preprint arXiv:2410.09290, 2024.  
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+Ryan Jacobs, Maciej P Polak, Lane E Schultz, Hamed Mahdavi, Vasant Honavar, and Dane Morgan. Regression with large language models for materials and molecular property prediction. arXiv preprint arXiv:2409.06080, 2024.  
+Yuyan Liu, Sirui Ding, Sheng Zhou, Wenqi Fan, and Qiaoyu Tan. Molecularargpt: Open large language model (llm) for few-shot molecular property prediction. arXiv preprint arXiv:2406.12950, 2024.  
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+George A Miller. The magical number seven, plus or minus two: Some limits on our capacity for processing information. *Psychological review*, 63(2):81, 1956.  
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+Jennifer Routh, Sharmini Julita Paramasivam, Peter Cockcroft, Sarah Wood, John Remnant, Cornélie Westermann, Alison Reid, Patricia Pawson, Sheena Warman, Vishna Devi Nadarajah, et al. Rating and ranking preparedness characteristics important for veterinary workplace clinical training: a novel application of pairwise comparisons and the elo algorithm. Frontiers in Medicine, 10: 1128058, 2023.  
+Eva JI Hoeijmakers, Bibi Martens, Babs MF Hendriks, Casper Mihl, Razvan L Miclea, Walter H Backes, Joachim E Wildberger, Frank M Zijta, Hester A Gietema, Patricia J Nelemans, et al. How subjective ct image quality assessment becomes surprisingly reliable: pairwise comparisons instead of likert scale. European Radiology, 34(7):4494-4503, 2024.  
+Shengyu Zhang, Linfeng Dong, Xiaoya Li, Sen Zhang, Xiaofei Sun, Shuhe Wang, Jiwei Li, Runyi Hu, Tianwei Zhang, Fei Wu, et al. Instruction tuning for large language models: A survey. arXiv preprint arXiv:2308.10792, 2023.  
+Yuntao Bai, Andy Jones, Kamal Ndousse, Amanda Askell, Anna Chen, Nova DasSarma, Dawn Drain, Stanislav Fort, Deep Ganguli, Tom Henighan, et al. Training a helpful and harmless assistant with reinforcement learning from human feedback. arXiv preprint arXiv:2204.05862, 2022.  
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+William G Cochran and Sarah Porter Carroll. A sampling investigation of the efficiency of weighting inversely as the estimated variance. Biometrics, 9(4):447-459, 1953.  
+Ralph Allan Bradley and Milton E Terry. Rank analysis of incomplete block designs: I. the method of paired comparisons. Biometrika, 39(3/4):324-345, 1952.  
+Alexander Ly, Maarten Marsman, Josine Verhagen, Raoul PPP Grasman, and Eric-Jan Wagenmakers. A tutorial on fisher information. Journal of Mathematical Psychology, 80:40-55, 2017.  
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+Ning-Ning Wang, Jie Dong, Yin-Hua Deng, Min-Feng Zhu, Ming Wen, Zhi-Jiang Yao, Ai-Ping Lu, Jian-Bing Wang, and Dong-Sheng Cao. Adme properties evaluation in drug discovery: prediction of caco-2 cell permeability using a combination of nsga-ii and boosting. Journal of chemical information and modeling, 56(4):763-773, 2016.  
+Li Di, Christopher Keefer, Dennis O Scott, Timothy J Strelevitz, George Chang, Yi-An Bi, Yurong Lai, Jonathon Duckworth, Katherine Fenner, Matthew D Troutman, et al. Mechanistic insights from comparing intrinsic clearance values between human liver microsomes and hepatocytes to guide drug design. European journal of medicinal chemistry, 57:441-448, 2012.  
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+OpenAI. Chatgpt-4o, 2025. URL https://chatgpt.com/.  
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+
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+
+Answer: [Yes]
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+
+- The answer NA means that the core method development in this research does not involve LLMs as any important, original, or non-standard components.  
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+
+# A Extended Proof
+
+# A.1 RankRefine is a minimum-variance unbiased estimator
+
+Suppose that we have two independent unbiased estimates of the same parameter  $y_0$ ,
+
+$$
+\hat {y} _ {0} ^ {\text {r e g}} \sim \mathcal {N} (y _ {0}, \sigma_ {\text {r e g}} ^ {2}), \quad \hat {y} _ {0} ^ {\text {r a n k}} \sim \mathcal {N} (y _ {0}, \sigma_ {\text {r a n k}} ^ {2}),
+$$
+
+and we want to form a linear combination of the two estimates,
+
+$$
+\hat {y} _ {0} ^ {*} = w \hat {y} _ {0} ^ {\mathrm {r e g}} + (1 - w) \hat {y} _ {0} ^ {\mathrm {r a n k}}, \tag {5}
+$$
+
+our goal is to choose  $w \in [0,1]$  such that the variance is minimized.
+
+For two independent random variables  $X$  and  $Y$ ,  $\operatorname{Var}(aX + bY) = a^2 X + b^2 Y$ . The post-fusion variance of the unbiased estimates is then,
+
+$$
+\sigma_ {\text {p o s t}} ^ {2} = w ^ {2} \sigma_ {\text {r e g}} ^ {2} + (1 - w) ^ {2} \sigma_ {\text {r a n k}} ^ {2}. \tag {6}
+$$
+
+To minimize  $\sigma_{\mathrm{post}}^2$  with respect to  $w$ , we take the derivative and solve for,
+
+$$
+\frac {d}{d w} \left(w ^ {2} \sigma_ {\text {r e g}} ^ {2} + (1 - w) ^ {2} \sigma_ {\text {r a n k}} ^ {2}\right) = 0,
+$$
+
+$$
+2 w \sigma_ {\text {r e g}} ^ {2} - 2 (1 - w) \sigma_ {\text {r a n k}} ^ {2} = 0
+$$
+
+$$
+2 w \sigma_ {\mathrm {r e g}} ^ {2} = 2 (1 - w) \sigma_ {\mathrm {r a n k}} ^ {2}
+$$
+
+$$
+w \sigma_ {\text {r e g}} ^ {2} = (1 - w) \sigma_ {\text {r a n k}} ^ {2} \tag {7}
+$$
+
+$$
+w \sigma_ {\text {r e g}} ^ {2} = \sigma_ {\text {r a n k}} ^ {2} - w \sigma_ {\text {r a n k}} ^ {2}
+$$
+
+$$
+w \sigma_ {\text {r e g}} ^ {2} + w \sigma_ {\text {r a n k}} ^ {2} = \sigma_ {\text {r a n k}} ^ {2}
+$$
+
+$$
+w \left(\sigma_ {\text {r e g}} ^ {2} + \sigma_ {\text {r a n k}} ^ {2}\right) = \sigma_ {\text {r a n k}} ^ {2}.
+$$
+
+Therefore,
+
+$$
+w = \frac {\sigma_ {\text {r a n k}} ^ {2}}{\sigma_ {\text {r e g}} ^ {2} + \sigma_ {\text {r a n k}} ^ {2}}, \quad (1 - w) = \frac {\sigma_ {\text {r e g}} ^ {2}}{\sigma_ {\text {r e g}} ^ {2} + \sigma_ {\text {r a n k}} ^ {2}}. \tag {8}
+$$
+
+Substituting the weights in Equation 6 with Equation 8, we obtain the RankRefine post-fusion variance in Equation 1,
+
+$$
+\begin{array}{l} \sigma_ {\text {p o s t}} ^ {2} = \left(\frac {\sigma_ {\text {r a n k}} ^ {2}}{\sigma_ {\text {r e g}} ^ {2} + \sigma_ {\text {r a n k}} ^ {2}}\right) ^ {2} \sigma_ {\text {r e g}} ^ {2} + \left(\frac {\sigma_ {\text {r e g}} ^ {2}}{\sigma_ {\text {r e g}} ^ {2} + \sigma_ {\text {r a n k}} ^ {2}}\right) ^ {2} \sigma_ {\text {r a n k}} ^ {2} \\ = \frac {(\sigma_ {\mathrm {r a n k}} ^ {2}) ^ {2} \sigma_ {\mathrm {r e g}} ^ {2} + (\sigma_ {\mathrm {r e g}} ^ {2}) ^ {2} \sigma_ {\mathrm {r a n k}} ^ {2}}{(\sigma_ {\mathrm {r e g}} ^ {2} + \sigma_ {\mathrm {r a n k}} ^ {2}) ^ {2}} \\ = \frac {\sigma_ {\text {r a n k}} ^ {2} \sigma_ {\text {r e g}} ^ {2} \left(\sigma_ {\text {r a n k}} ^ {2} + \sigma_ {\text {r e g}} ^ {2}\right)}{\left(\sigma_ {\text {r e g}} ^ {2} + \sigma_ {\text {r a n k}} ^ {2}\right) ^ {2}} \tag {9} \\ = \frac {\sigma_ {\text {r a n k}} ^ {2} \sigma_ {\text {r e g}} ^ {2}}{\sigma_ {\text {r a n k}} ^ {2} + \sigma_ {\text {r e g}} ^ {2}} \\ = \left(\frac {1}{\sigma_ {\text {r e g}} ^ {2}} + \frac {1}{\sigma_ {\text {r a n k}} ^ {2}}\right) ^ {- 1} \\ \end{array}
+$$
+
+Similarly, substituting the weights in Equation 5 with Equation 8, we get the RankRefine estimate in Equation 1,
+
+$$
+\begin{array}{l} \hat {y} _ {0} ^ {*} = \frac {\sigma_ {\mathrm {r a n k}} ^ {2}}{\sigma_ {\mathrm {r e g}} ^ {2} + \sigma_ {\mathrm {r a n k}} ^ {2}} \hat {y} _ {0} ^ {\mathrm {r e g}} + \frac {\sigma_ {\mathrm {r e g}} ^ {2}}{\sigma_ {\mathrm {r e g}} ^ {2} + \sigma_ {\mathrm {r a n k}} ^ {2}} \hat {y} _ {0} ^ {\mathrm {r a n k}} \\ = \frac {\sigma_ {\text {r a n k}} ^ {2} \sigma_ {\text {r e g}} ^ {2}}{\left(\sigma_ {\text {r e g}} ^ {2} + \sigma_ {\text {r a n k}} ^ {2}\right) \sigma_ {\text {r e g}} ^ {2}} \hat {y} _ {0} ^ {\text {r e g}} + \frac {\sigma_ {\text {r e g}} ^ {2} \sigma_ {\text {r a n k}} ^ {2}}{\left(\sigma_ {\text {r e g}} ^ {2} + \sigma_ {\text {r a n k}} ^ {2}\right) \sigma_ {\text {r a n k}} ^ {2}} \hat {y} _ {0} ^ {\text {r a n k}} \tag {10} \\ = \frac {\sigma_ {\text {p o s t}} ^ {2}}{\sigma_ {\text {r e g}} ^ {2}} \hat {y} _ {0} ^ {\text {r e g}} + \frac {\sigma_ {\text {p o s t}} ^ {2}}{\sigma_ {\text {r a n k}} ^ {2}} \hat {y} _ {0} ^ {\text {r a n k}} \\ = \sigma_ {\text {p o s t}} ^ {2} \left(\frac {\hat {y} _ {0} ^ {\text {r e g}}}{\sigma_ {\text {r e g}} ^ {2}} + \frac {\hat {y} _ {0} ^ {\text {r a n k}}}{\sigma_ {\text {r a n k}} ^ {2}}\right) \\ \end{array}
+$$
+
+# A.2 Analysis of RankRefine
+
+Corollary 3.2.1 is obtained from:
+
+$$
+\begin{array}{l} \sigma_ {\text {p o s t}} ^ {2} <   \sigma_ {\text {r e g}} ^ {2} \iff \left(\frac {1}{\sigma_ {\text {r e g}} ^ {2}} + \frac {1}{\sigma_ {\text {r a n k}} ^ {2}}\right) ^ {- 1} <   \sigma_ {\text {r e g}} ^ {2}, \\ \Longleftrightarrow \frac {1}{\sigma_ {\text {r e g}} ^ {2}} + \frac {1}{\sigma_ {\text {r a n k}} ^ {2}} > \frac {1}{\sigma_ {\text {r e g}} ^ {2}}, \tag {11} \\ \Longleftrightarrow \frac {1}{\sigma_ {\mathrm {r a n k}} ^ {2}} <   0, \\ \Longleftrightarrow \sigma_ {\text {r a n k}} ^ {2} <   \infty . \\ \end{array}
+$$
+
+For an unbiased Gaussian estimates  $\hat{y}_0\sim \mathcal{N}(y_0,\sigma^2)$ , the expected error is,
+
+$$
+\begin{array}{l} \mathbb {E} \left(\left| \hat {y} _ {0} - y _ {0} \right|\right) = \mathbb {E} \left(\left| y _ {0} + \epsilon - y _ {0} \right|\right), \quad \text {w i t h} \epsilon \sim \mathcal {N} (0, \sigma^ {2}) \tag {12} \\ = \mathbb {E} (| \epsilon |). \\ \end{array}
+$$
+
+Since  $\epsilon$  is a Gaussian distribution, then  $|\epsilon|$  follows the half-Gaussian distribution with an expected value equals to  $\sqrt{2/\pi}\sigma$ . The subsequent  $\beta$  bound in Equation 4 is obtained from:
+
+$$
+\begin{array}{l} \mathrm {M A E} _ {\text {p o s t}} \leq \beta \mathrm {M A E} _ {\text {r e g}} \iff \sigma_ {\text {p o s t}} \leq \beta \sigma_ {\text {r e g}}, \\ \Longleftrightarrow \quad \sigma_ {\text {p o s t}} ^ {2} \leq \beta^ {2} \sigma_ {\text {r e g}} ^ {2}. \\ \Longleftrightarrow \left(\frac {1}{\sigma_ {\text {r e g}} ^ {2}} + \frac {1}{\sigma_ {\text {r a n k}} ^ {2}}\right) ^ {- 1} \leq \beta^ {2} \sigma_ {\text {r e g}} ^ {2} \\ \Longleftrightarrow \frac {1}{\sigma_ {\text {r e g}} ^ {2}} + \frac {1}{\sigma_ {\text {r a n k}} ^ {2}} \geq \frac {1}{\beta^ {2} \sigma_ {\text {r e g}} ^ {2}} \tag {13} \\ \Longleftrightarrow \frac {1}{\sigma_ {\text {r a n k}} ^ {2}} \geq \frac {1 - \beta^ {2}}{\beta^ {2} \sigma_ {\text {r e g}} ^ {2}}, \\ \Longleftrightarrow \sigma_ {\text {r a n k}} ^ {2} \leq \frac {\beta^ {2} \sigma_ {\text {r e g}} ^ {2}}{1 - \beta^ {2}} \\ \end{array}
+$$
+
+# B Additional Experimental Details
+
+# B.1 Prompt for obtaining pairwise rankings from ChatGPT-40
+
+We use the following prompt to query ChatGPT-4o to predict the pairwise rankings for the Lipophilicity dataset.
+
+# Identity
+
+You are an expert in chemistry and biology. Given a short description of a molecular property and two molecular SMILES, you can determine if Molecule A has greater property value than Molecule B or not.
+
+# Instructions
+
+* The list of pairwise molecules is given in two CSV files: "test_A.csv" and "test_B.csv". These are two different lists that you need to perform rank prediction on. The first line is the header.
+
+* You cannot use external cheminformatics library to directly predict the property.
+
+* You can design your own heuristics, comparing atom types, bonds, and other important information to make your predictions.
+
+* Before you start designing the heuristics, briefly explain the property and what influence its values. Incorporate this prior knowledge into your heuristic.
+
+* You are given 5 examples in the prompt. Make sure your heuristics in general is aligned with the given examples. Pay attention to the examples, especially because some properties have greater effects when its values are lower.
+
+* You should output CSV files titled "test_pred_A.csv" and "test_pred_B". The header is "molecule_a, molecule_b, is_agreater".
+
+* Only output 0 or 1 for "is_agreater". 0 means that the property value of molecule A is less than that of Molecule B. 1 means that the property value of molecule A is greater than that of Molecule B
+
+* In addition to the output CSV file, you should output the first and last molecule pairs, in both CSV A and CSV B, to the chat. Briefly explain your answer for these three molecule pairs.
+
+# Examples
+
+<user_query>
+
+The property of interest is lipophilicity, the ability of a drug to dissolve in a lipid (e.g. fats, oils) environment.
+
+Examples:
+
+CC(C)Cn1c  $(= 0)$  n(C)c  $(= 0)$  c2c  $(= 0)$  N3CC[C@@H] (0)C3)c(Oc3cccc4cccccc34)sc21, CC(C)  $(\mathsf{C}(= 0)\mathsf{O})$  c1ccc(C(0)CCCN2CCC(C(0)(c3ccccc3)c3cccccc3)CC2)cc1,
+
+1
+
+$0 = \mathrm{C(Nc1cccc1Cl)c1cc[nH]n1}$ $0 = C(Nc1ccc(Nc2ccc(NC (=0)c3cccc3)c3c2C (=0)c2cccccc2C3=0)c2c1C (=0)c1cccccc1C2=0)c1cccccc1$  0
+
+Cn1c2cccccc2c2cc(NC  $(= 0)$  CCc3ccncc3)ccc21,
+
+Cc1cc(0CCCS(C)  $(= 0) = 0)$  cc(C)c1-c1cccc(COc2ccc3c(c2)OC[C@H]3CC  $(= 0)$  0)c1, 1
+
+Cc1ccnc2nc(C  $(= 0)$  Nc3nccs3)nn12,
+
+Cc1cc(0CCCCS(C)  $(= 0) = 0)$  cc(C)c1-c1cccc(COc2ccc3c(c2)OC[C@H]3CC  $(= 0)0)$  c1, 0
+
+$0 = \mathrm{C(NCc1ccc(OC(F)(F)F)cc1)C1c2cccc2C(= 0)N1CC1CC(F)(F)C1}$  COCCCCO1ccnc(C[S+]（[0-]）c2nc3cccc3[nH]2)c1C,
+
+1
+
+</user_query>
+
+![](images/e56487149c209215357a5cc4929d264622d58f75790d05bedb5c6d77aa000471.jpg)  
+Image 1  
+Who looks older?  
+010J  
+Wledge 1  
+Who looks older?  
+  
+0
+
+![](images/0d36e5668e6abbbbcb2975a3d9c57b9967e07a5ebeb6a3fafa6179858393bf76.jpg)
+
+01
+
+![](images/b8de399ab1eb0b0e8f771f473630d7ce5fec9d291c3b89c319473a6e2c09c794.jpg)  
+图1  
+Who looks older?  
+#
+
+![](images/81e7f10cbc37083df9e517f977a83d68f1d70d666551f646100f851d0b89916d.jpg)  
+imageJ
+
+![](images/32284ee41b8d0b65473aeded01aba276f588b2f3420624bbc77e245d522d2981.jpg)  
+image  
+  
+Who looks older?  
+01OJ
+
+![](images/12cc43862b09208c0ed4dae812e7a0904496b08c083ea8ab23483e0ed913b06e.jpg)  
+Image J
+
+![](images/7f051232a5b3c69801be7ab255a5453c8efb2e73e7468e1cb329c093084858a3.jpg)  
+Image 1  
+Who looks older?  
+#
+
+![](images/98290551cb616f8bc1c76fe97553c07f63424b7159f6047aa1c592acf6e13f4d.jpg)
+
+![](images/27025f85eac71f59c405463010cfc4c00910e5c06b5940c290263d5b88e86512.jpg)  
+Image 1  
+  
+Who looks older?  
+I OJ
+
+![](images/2e1a8a5a070c643fe87c3c299befb9934a1aa3ce4cdf074db74d5cbb62e54191.jpg)  
+Image J
+
+![](images/67e882532f363729b9f9c427078318c44560ea5e30766401b865b6817d235981.jpg)  
+age1  
+Who looks older?  
+#
+
+![](images/d8f05d47e03250e8bb9a31a2edd0f58718fe6173b862a5ed623dbb32b17c247a.jpg)  
+(a)  
+  
+  
+  
+(b)
+
+![](images/0419f62251c594c253e9e26e69ae190b0084c01cab45daf8a4cdd16e3b874f6c.jpg)  
+Image1  
+$\therefore m = \frac{3}{11}$
+
+![](images/08e0f639dc16166839f998fbe5ea80def240a87938dc30ba882bdd5e735ce50e.jpg)  
+Image J  
+who looks older  
+#  
+Figure 7: Partial interface used in the user study. Participants first estimate the age of each test individual, then make pairwise judgments on who appears older between the test individual and reference individuals of the same UTKFace gender label.
+
+![](images/e641986cbec45ceefc5fe477c151313da244e4fc92ee984b81e53f539b099f62.jpg)  
+Image 1
+
+![](images/c3774ab6d7b896c42ea59dcedf52ad053ba85ddeec4e2b141c9970f7443edcd4.jpg)
+
+# B.2 User Study
+
+The user study uses age estimation on the UTKFace dataset as a regression task. Six participants estimate the ages of 17 individuals from facial images. Each test individual is then paired with 15 disjoint reference individuals, and participants judge who appears older in each pair based solely on facial appearance. To prevent fatigue, the total number of comparisons is limited to  $17 \times 15 = 255$ . A screenshot of the Streamlit app used in the study is shown in Figure 7.
+
+# C More Comparisons with the Projection-based Approach
+
+Figure 8 highlights how performance varies between RankRefine and the projection-based approach as the number of reference samples increases. While the projection-based method benefits from high-accuracy rankers or minimal references, RankRefine demonstrates stronger robustness in lower-accuracy regimes, particularly as the number of reference samples  $k$  increases.
+
+# D Ablation: Biased Regressor
+
+We inject constant bias  $B$  into an otherwise unbiased regressor, where the magnitude of the offset is measured as a percentage of the ground truth labels standard deviation. RankRefine offers improvement even when the regressor is biased (e.g., 60% of the SD of the ground truth labels)
+
+Table 3: RankRefine performance, measured in  $\beta$  (lower is better),on a biased regressor.  
+
+<table><tr><td>Ranker Accuracy</td><td>50%</td><td>55%</td><td>60%</td><td>65%</td><td>70%</td></tr><tr><td>Bias (B) = 0% SD</td><td>0.8911</td><td>0.8436</td><td>0.8694</td><td>0.8668</td><td>0.8949</td></tr><tr><td>B = 10% SD</td><td>0.8995</td><td>0.8800</td><td>0.8623</td><td>0.8602</td><td>0.8969</td></tr><tr><td>B = 20% SD</td><td>0.9084</td><td>0.8869</td><td>0.8704</td><td>0.8704</td><td>0.9047</td></tr><tr><td>B = 30% SD</td><td>0.9224</td><td>0.8997</td><td>0.8844</td><td>0.8861</td><td>0.9192</td></tr><tr><td>B = 40% SD</td><td>0.9409</td><td>0.9172</td><td>0.9059</td><td>0.9071</td><td>0.9395</td></tr><tr><td>B = 50% SD</td><td>0.9645</td><td>0.9403</td><td>0.9329</td><td>0.9343</td><td>0.9654</td></tr><tr><td>B = 60% SD</td><td>0.9942</td><td>0.9702</td><td>0.9649</td><td>0.9670</td><td>0.9967</td></tr><tr><td>B = 70% SD</td><td>1.0291</td><td>1.0062</td><td>1.0022</td><td>1.0049</td><td>1.0326</td></tr></table>
+
+![](images/6ca22a4ab94de39573d0f5ec2ea08c0726386ac27dd74cb3b87029bc0882fd27.jpg)  
+(a)  $\mathrm{k} = 3$
+
+![](images/5acd515a190a759bf2170d4994ac773a7b841f6954fa9b6d58bf5bf9fa6fc216.jpg)  
+(b)  $\mathrm{k} = 5$
+
+![](images/ad19275a08b66dcd1ee3a6214b9b116042f0f7289c8918a55131d7a7e3f59626.jpg)  
+(c)  $\mathrm{k} = 7$
+
+![](images/65bdf60611417bb2be86afbb137773ce4e4a5913a8c024f83912c25c59979014.jpg)  
+(d)  $\mathrm{k} = {10}$
+
+![](images/e5823a6d1ee399e1a13eeb406508fe60165b5babb802908f026bf9c1aa63c2d4.jpg)  
+(e)  $\mathrm{k} = {20}$
+
+![](images/a8c2c469ef12c04546c5f693d1315fb109195d2b14501cbcb920fc7603e0892f.jpg)  
+(f)  $\mathrm{k} = {30}$  
+Figure 8: Comparison of RankRefine and the projection-based approach across varying reference sample sizes  $k$ . The projection-based method performs better with high ranker accuracy or very few references, while RankRefine excels when accuracy is below  $70\%$  for  $k = 7$ ,  $80\%$  for  $k = 10$ ,  $90\%$  for  $k = 20$ , and  $95\%$  for  $k = 30$ . Since RankRefine can leverage general-purpose LLMs, collecting more pairwise rankings can be done efficiently as long as the reference set is sufficiently large.
+
+# E Ablation: Biased Sampling
+
+We restrict the reference set range to increasingly narrow subsets of the ground truth label range ([0, 1]), simulating clustered or biased samples. The reference set bias,  $RB = x\%$ , means that the reference labels cover only (100 - x)% of the full ground-truth range. For example, an  $RB = 10\%$  means the reference labels range is [0.05, 0.95]. Best performance is achieved when the reference set spans the entire range of the ground truth labels, but clustered reference sets still provide substantial regression improvements.
+
+Table 4: RankRefine performance, measured in  $\beta$  ,with non-uniform sampling of the reference set.  
+
+<table><tr><td rowspan="2">Ranker Accuracy
+Reference Set Bias (RB) = 0% range</td><td>50%</td><td>55%</td><td>60%</td><td>65%</td><td>70%</td></tr><tr><td>0.8828</td><td>0.8706</td><td>0.8343</td><td>0.8443</td><td>0.8598</td></tr><tr><td>RB = 10% range</td><td>0.9034</td><td>0.8731</td><td>0.8493</td><td>0.8529</td><td>0.8768</td></tr><tr><td>RB = 20% range</td><td>0.9078</td><td>0.8753</td><td>0.8366</td><td>0.8694</td><td>0.9002</td></tr><tr><td>RB = 30% range</td><td>0.9076</td><td>0.8701</td><td>0.8439</td><td>0.8733</td><td>0.9280</td></tr><tr><td>RB = 40% range</td><td>0.9143</td><td>0.8767</td><td>0.8618</td><td>0.8824</td><td>0.9414</td></tr><tr><td>RB = 50% range</td><td>0.9253</td><td>0.8786</td><td>0.8640</td><td>0.8769</td><td>0.9480</td></tr><tr><td>RB = 60% range</td><td>0.9349</td><td>0.8858</td><td>0.8712</td><td>0.8929</td><td>0.9546</td></tr><tr><td>RB = 70% range</td><td>0.9385</td><td>0.8919</td><td>0.8770</td><td>0.8957</td><td>0.9597</td></tr><tr><td>RB = 80% range</td><td>0.9551</td><td>0.8984</td><td>0.8798</td><td>0.8943</td><td>0.9558</td></tr><tr><td>RB = 90% range</td><td>0.9664</td><td>0.9042</td><td>0.8842</td><td>0.9035</td><td>0.9631</td></tr></table>
+
+To test the impact of distribution shift between reference and query, we created two challenging scenarios where the reference labels and query labels are drawn uniformly from different range values:
+
+- Disjoint distributions: reference labels in  $[-1,0]$  or  $[1,2]$ , query labels in  $[0,1]$ . We averaged the results of the two cases, that is, between ref = [-1, 0], query = [0, 1] and ref = [1, 2], query = [0, 1].
+
+- Partial overlap: reference labels in  $[-0.5, 0.5]$  or  $[0.5, 1.5]$ , query labels in  $[0, 1]$ . We averaged the results of the two cases, that is, between ref =  $[-0.5, 0.5]$ , query =  $[0, 1]$  and ref =  $[0.5, 1.5]$ , query =  $[0, 1]$ .
+
+The results in 5 shows that RankRefine still improves the base regressor when the ranker is moderately accurate, even when the distribution of the reference labels is different from the query.
+
+Table 5: RankRefine performance, measured in  $\beta$  ,for disjoint and partially overlapping reference set.  
+
+<table><tr><td>Ranker Accuracy</td><td>50%</td><td>55%</td><td>60%</td><td>65%</td><td>70%</td></tr><tr><td>Disjoint</td><td>1.2906</td><td>1.1629</td><td>1.0170</td><td>0.9437</td><td>0.9219</td></tr><tr><td>Partial Overlap</td><td>1.0160</td><td>0.9465</td><td>0.8700</td><td>0.8607</td><td>0.8898</td></tr></table>

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