$\pi^3$: Permutation-Equivariant Visual Geometry Learning
Authors: Yifan Wang
Jianjun Zhou
Haoyi Zhu
Wenzheng Chang
Yang Zhou
Zizun Li
Junyi Chen
Jiangmiao Pang
Chunhua Shen
Tong He
Venue: ICLR 2026 Poster (2026)
Keywords: Permutation-Equivariance
3D reconstruction
Reference-Free
Camera Pose Estimation
Depth Estimation
Primary area: applications to computer vision, audio, language, and other modalities
TL;DR: $\pi^3$ is a feed-forward model that reconstructs 3D geometry without a fixed reference view, making it more robust and accurate for tasks like camera pose and depth estimation.

Abstract: We introduce $\pi^3$, a feed-forward neural network that offers a novel approach to visual geometry reconstruction, breaking the reliance on a conventional fixed reference view. Previous methods often anchor their reconstructions to a designated viewpoint, an inductive bias that can lead to instability and failures if the reference is suboptimal. In contrast, $\pi^3$ employs a fully permutation-equivariant architecture to predict affine-invariant camera poses and scale-invariant local point maps without any reference frames. This design not only makes our model inherently robust to input ordering, but also leads to higher accuracy and performance. These advantages enable our simple and bias-free approach to achieve state-of-the-art performance on a wide range of tasks, including camera pose estimation, monocular/video depth estimation, and dense point map reconstruction. Code and models are available at https://github.com/yyfz/Pi3.

Published as a conference paper at ICLR 2026
33 PERMUTATION-EQUIVARIATT VISUAL GEOMETRY LEARNING
Yifan Wang Jianjun Zhou 2,34 Haoyi Zhu
Wenzheng Changl.3 1.2
Yang Zhou 2.6
Zizun Li Junyi Chen 1.2 Jiangmiao Pang2 Chunhua Shen*
Tong H 2,37
Shanghai Jiao Tong University Shanghai AI Laboratory Shanghai Innovation Institute
"Zhejiang University University of Science and Technology of China https: //g/ttttubb www.eoo///o.....ee 2
Fudan University
M
AYADS
Camera Pose Estimation
Sintel
NYI1-2 Cop2
SanNet
DTC
Estimation
Point Mia Lnninttoo
KITTI
ETRED
MEERO
Sintel
Viden Depth Estimation
BoNN
VGGT
FLARE
Fast3R
Figure 1: अ effectively reconstructs diverse set of open-domain images feed- forward manner, encompassing various scenes such indoor, outdoor, and aerial-view, as well as cartoons, with both dynamic and static content.
"Equal Contribution.
1 "ooresponniig Author. Email: 900gma

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Published as a conference paper at ICLR 2026
ABSTRACT
We introduce n,, a feed-forward neural network that offers a novel approach to visual geometry reconstruction, breaking the reliance on a conventional fixed ref- erence view. Previous methods often anchor their reconstructions to designated viewpoint, an inductive bias that can lead to instability and failures if the refer- ence is suboptimal. In contrast, π employs a fully cermutation-equivee chitecture to predict invariant camera poses and scale- invariant local point maps without any reference frames. This design not only makes our model inher- ently robust input ordering, but also leads to higher accuracy and performance. These ad advantages enable our simple and bias-free approach to achieve state-of- the-art performance on wide range of tasks, including camera pose estimation, nonocular/video depth estimation, and dense point map reconstruction. Code and models are available at Pi3.
ar-
INTRODUCTION
Visual geometry reconstruction, long-standing and fundamental problem in computer vision, holds substantial potential for applications such as augmented reality (Engel et al., 2023), robotics (Zhu al., 2024), and autonomous navigation (Mur-Artal et al., 2015). While traditional methods ad- dressed this challenge using iterative optimization techniques like Bundle Adjustment (BA) (Hartley & Zisserman, 2003), the field has recently seen remarkable progress with feed-forward neural net- works. End-to-end models like DUS:3R (Wang et al., 2024) and its successors have demonstrated the power of deep learning for reconstructing geometry from image pairs (Leroy al., 2024; Zhang et al., 2024), videos, multi-view collections (Yang et al., 2025; Zhang et al., 2025; Wang et al., 2025a).
Despite these advances, critical limitation persists in both classical and modern approaches: the reliance on selecting a single, fixed reference view. The camera coordinate system of this chosen view is treated as the global frame of reference, practice inherited from traditional Structure from- Motion (SfM) (Hartley& & Zisserman. 2003; Cui et al., 2017; Schonberger & Frahm, 2016; Pan et al., 2024) or Multi-view Stereo (MVS) (Furukawa et al., 2015; Schönberger al., 2016). We contend that this design choice introduces an unnecessary inductive bias that fundamentally constrains the performance and robustness of feed-forward neural networks. As we demonstrate empirically. this reliance on an arbitrary reference makes existing methods, including the state-of-the-ar (SOTA) VGGT (Wang et al., 2025a), highly sensitive to the initial view selection. A poor choice can lead to dramatic degradation in reconstruction quality, hindering the development of robust systems (Figure 2).
To overcome this limitation, we introduce T (Figure 1), a robust, accurate, and fully permutation-equiiariant method that elimi- nates reference view-based biases in vi- sual geometry learning. 3 accepts var- ied inputs-includdig single images, video se- quences, unordered image sets from static or dynamic scenes-withou designating a ref- erence view. Instead, our model predicts an affine-invariant camera pose and scale- invariant local pointmap, with the pointmap be- ing defined in that frame's 's own camera coor- dinate system. By eschewing order-dependent components like frame index positional em- beddings and employing a transformer archi- tecture that alternates between view-wise and global self-attention (similar to (Wang et al., 2025a)), T3 achieves true permutation equiv- ariance. This guarantees a consistent one-to- to- one mapping between visual inputs and the re-
Performance Comparison
Reference Selection
Avorge Erse ower Rete))
VGGT
VOGT (2NN12 lege
Olars (hvg:A11
Fran Iolo
ACC 1855 COMP : EUT
Packresnn dag ACE E-627
ACT 8 COMP 1-I1E (Clan)
COMP COMPI:E34 11224
VGGT
Figure 2: Performance comparison across dif- ferent reference frames. While previous meth- ods, even with DINO-based selection, show in- consistent results, 3 consistently delivers supe- rior and stable performance, demonstrating its ro- bustness.
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constructed geometry, making the model inher-
ently robust to imput order and immune to the reference view selection problem (Table 7).
Our design yields significant advantages. Primarily, it is substantially more robust. Unlike previous methods, our approach demonstrates minimal performance degradation and a low standard deviation when the reference frame is altered (Figure 2 and Table 4.4). Furthermore, it enhances reconstruction accuracy over earlier methods that rely on a reference view.
Through extensive experiments, T establishes new SOTA across numerous benchmarks and tasks. For example, it achieves comparable performance to existing methods like MoGe (Wang et al., 2025c) in monocular depth estimation, and outperforms VGGT (Wang al., 2025a) in video depth estimation and camera pose estimation. On the Sintel benchmark, π reduces the camera pose estimation ATE from VGGT's 0.167 down to 0.074 and improves the scale-aligned video depth absolute relative error from 0.299 to 0.233. Furthermore, л is both lightweight and fast, achieving an inference speed of 57.4 FPS compared DUSt3R's s 1.25 FPS and VGGT's 43.2 FPS. Its ability to reconstruct both static and dynamic scenes makes it robust and optimal solution for real-world applications.
In summary, the contributions of this work are as follows:
We are the first to systematically identify and challenge the reliance on fixed reference view in visual geometry reconstruction, demonstrating how this common design choice introduces a detrimental inductive bias that limits model robustness and performance.
We propose 8 novel, fully permutation-equivariee Our model predicts affine-invrriant camera poses and scale-invariant pointmaps in purely relative, per-view manner, completely removing the need for global coordinate system.
architecture that eliminates this bias.
We demonstrate through extensive experiments that n establishes a new state-of-the- on a wide range of benchmarks for camera pose estimation, monocular/video depth estimation, and pointmap reconstruction, outperforming prior leading methods.
2
RELATED WORK
2.1 TRADITIONAL 3D RECONSTRUCTION
Reconstructing 3D scenes from images is foundational problem in computer vision. Classical crnuture-from-Motioo (SfM) (Hartley & Zisserman, 2003; Cui et al., 2017: Schon-
methods, such berger & Frahm, 2016; Pan et al.. 2024) and Multi-View Stereo (MVS) (Furukawa et al., 2015; Schönberger et al., 2016), have achieved considerable success. These techniques leverage the prin- ciples of multi-view geometry to establish feature correspondences across images, from which they estimate camera poses and generate dense 3D point clouds. Although robust, particularly in con- trolled environments, these methods typically rely complex, multi-stage pipelines. Moreover, they often involve time-consuming iterative optimization problems, such as Bundle Adjustment (BA), to jointly refine the 3D structure and camera poses.
2.2 FEED-FORWARD 3D RECONSTRUCTION
Recently, feed-forward models have emerged as powerful alternative, capable of directly regress- ing the 3D structure of a scene from set of images in single pass. Pioneering efforts in this domain, such as Dust3R (Wang et al., 2024), focused on processing image pairs to predict a point cloud within the coordinate system of the first camera. While effective for two views, scaling this to larger scenes requires a subsequent global alignment step, a process that can be both time-consuming and prone to instability.
Subsequent work has focused on overcoming this limitation. Fast3R (Yang et al., 2025) represents a significant advance by enabling simultaneous inference thousands of images, thereby eliminating the need for a costly and fragile global alignment stage. Other approaches have explored simplifying the learning problem itself. For instance, FLARE (Zhang al., 2025) decomposes the task by first predicting camera poses and then estimating the scene geometry. VGGT (Wang et al., 2025a) leverages nulti-task learning and large-scale datasets achieve superior accuracy and performance.
3

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Prevdius Matholi
OT
Frame-wiss ViT
Aggregstion
Decoder
Tyen
Reference Indicating
Gomeery rORTERS NEP conndanke
Key Features
(Oarg)
Robust
Aggregation
Accurate
Gaasdry zákini refaesee
Figure 3: Unlike prior methods that designate reference view by concatenating a special token (Type A) or adding learnable embedding (Type B), ा achieves permutation equivariance by elim- inating this requirement altogether. Instead, it employs relative supervision, making our approach inherently robust to the order of input views.
unifying characteristic these methods a paradigm largely inherited from classical SfM-is their reliance on anchoring the predicted 3D structure designated reference frame. Our work departs from this paradigm by presenting a fundamentally different approach.
3 METHOD
3.1
PERMUTATION- -EAIIIIONN-EUVVRRAANT ARCHITECTURE
To ensure our model's output invariant to the arbitrary ordering of input views, we designed our network ò to be ietiuaaatioo-eeivaiiinntt
Let the input be a sequence of N images. S (II...., ... IN). where each image R2 #xx33 The network o maps this sequence to a corresponding tuple of output sequences:
Φ(S) ((T Tx), (X....., XN), (C....., C,))
(1)
Here, T, E SE(3) C 4 is the camera pose, X; E "xxx3 is the associated pixel-aligned 3D point map represented in its own camera coordinate system, and C, "x is the confidence map of X, each corresponding to the input image I,
For any permutation æ, let P- be an operator that permutes the order of a sequence. The network satisfies the ienuutaaioo-euivariian property:
o (Pr (o(S))
This means that permuting the input sequence, P=(S) (Ia(I))... (.())), results in identically permuted output tuple:
Pa (o(S)) ((T (1)) (I).,
".,o)....TTT..).. TR(N)), (X (()):.... X X<(N)), (Ca()) Cx(M)))
This property guarantees consistent one-to-one correspondence between each image and its respec- tive output (e.g., geometry pose). This design offers several key advantages. First, reconstruction quality becomes independent of the reference view selection, contrast to prior methods that suffer from performance degradation when the reference view changes. Second, the model becomes more robust to uncertain or noisy observations. These claims are empirically validated in Section 4.
To realize this equivariance in practice, our implementation (illustrated in Figure 3) omits all order-dependent components, such as positional embeddings used to differentiate between frames and specialized learnable tokens that designate reference view, like the camera tokens found in VGGT (Wang et al., 2025a). Our pipeline begins by embedding each view into a sequence of patch tokens using DINOv2 (Oquab al., 2023) backbone. These tokens are then processed through
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Published as a conference paper at ICLR 2026
series of alternating view-wise and global self-attention layers, similar to (Wang al., 2025a), before a final decoder generates the output. The detailed architecture of our model provided in Appendix A.I.
3.2 SCALE-INVARIANT LOCAL GEOMETRY
For each imput image I, our network predicts the geometry pixel-aligned 3D point map X, Each point cloud imitially defined in its own local camera coordinate system. A well-known challenge in monocular reconstruction is the inherent scale ambiguity. To address this, our network predicts the point clouds up to an unknown, yet consistent, scale factor across all N images of given scene.
Consequently, the training process requires aligning the predicted point maps, IX....., X N with the corresponding ground-truth (GT) set, ;XI....XNN: This aligmment is accomplished by solving for single optimal scale factor, s", which minimizes the depth-weighted L1 distance across the entire image sequence. The optimization problem is formulated as:
N HxW
arg min Σ
Σ
Xi.illi
(4)
Here, Kz,y E R denotes the predicted 3D point at index j of the point map X,. Similarly, x,, is its ground-truth counterpart X, The term Fig is the ground-truth depth, which is the z-component of Xi.j This problem is solved using the ROE solver proposed by (Wang et al., 2025c).
Finally, the point cloud reconstruction loss, fpainss defined using the optimal scale factor s":
N HxW
pointss
|| Ri, -x,,
(5)
3NHW
Zi.j
To encourage the reconstruction of locally smooth surfaces, we also introduce a normal loss follow- ing Wang et al. (2025c), Lnormll For each point in the predicted point map X,, normal vector ú, computed from the cross product of the vectors to its adjacent neighbors on the image grid. We then supervise these normals by minimizing the angle between them and their ground-truth counterparts nt.j:
Lnormal
arccos (n nij)
NHW
We supervise the predicted confidence map C, using a Binary Cross-Entropy (BCE) loss, denoted Ceont- The ground-truth target for each point is set to if its LI reconstruction error, 1 K4,jllu is below a threshold e, and 0 otherwise.
8
z.,
3.3 AFHINE-INAARIAN CAMERA POSE
The model's permutation equivariance, combined with the inherent scale ambiguity of multi-view reconstruction, implies that the output camera poses (TI,..., Tw) are only defined up bitrary similarity transformation. This specific type of affine transformation consists of rigid transformation and single, unknown global scale factor.
To resolve the ambiguity of the global reference frame, we supervise the network on the relative poses between views. The predicted relative pose Ti,, from view j to is computed as:
T Timj T.
Each predicted relative pose Ti-s is composed of a rotation Rç,, SO(3) and a translation t._, E R While the relative rotation is invariant to this global transformation, the relative trans- lation's ' magnitude ambiguous. We resolve this by leveraging the optimal scale factor, s", that is computed by aligning the predicted point map the ground truth (as detailed in previous section).
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Published as a conference paper at ICLR 2026
This single, consistent scale factor is used to rectify all predicted camera translations, allowing to directly supervise both the rotation and the correctly-scabee translation components.
The camera loss Leam is weighted sum of a rotation loss term and translation loss term, averaged over all ordered view pairs where # j:
cam
Σ (Era(t,))) Luama N(N 1) 2
(8)
where À is hyperparameter to balance the two terms.
Following Dong et al. (2025), we use angle loss for rotation and Huber loss for translation, The rotation loss minimizes the geodesic distance (angle) between the predicted relative rotation R: and its ground-tran truth target Rçe-:
Tr (Riss) -1
(i,( = arccos
2
For the translation loss, we compare our scaled prediction against the ground-truth relative transla- tion, tz---. We use the Huber loss, H.s. for its robustness outliers:
Lanos (i.j) Has(stiasss (
(10)
Furthermore, our reference-free formulation is particularly well-suited capturing the intrinsic structure of camera trajectories. Our affine-invariant camera model builds a key insight: real- world camera paths are highly structured, not random. They typically lie on a low-dimensional manifold- for instance, camera orbiting object moves along a sphere, while car-mounted camera follows curve.
We quantitatively analyze the structure of the predicted pose distributions Fig- ure 4. The eigenvalue analysis confirms that the variance of our predicted poses is concentrated along significantly fewer principal components than VGGT, validat- ing the low-dimensional structure of our output. We discuss this further in Ap- pendix A.3.
Position Eigenvalues
Rotation Eigenvalues
Don
Eigensite
Eigenalls
CA
PCT
PC2
PC1
PC
PC7
Trincipal Compenent Index
Principel Componerr Index
Figure 4: Comparison of predicted pose distribu- tions. Our predicted pose distribution exhibits clear low-dimensional structure.
3.4 MODEL TRAINING
Our model is trained end-to-end by minimizing a composite loss function, L, which is a weighted sum of the point reconstruction loss, the confidence loss, and the camera pose loss:
L = Ppinnss + Anormal + Acont + Acam
(11)
To ensure robustness and wide applicability, we train the model on a large-scale aggregation of 15 diverse datasets. This combined dataset provides extensive coverage of both indoor and outdoor en- vironments, encompassing wide variety of scenes from synthetic renderings to real-world captures.
The specific datasets include GTA-SIM (Wang Shen, 2020), CO3D (Reizenstein et al., 2021),
WildRGB-D (Xia et al., 2024), Habitat (Savva al., 2019), ARKitScenes (Baruch al., 2021),
TartanAir (Wang et al., 2020), ScanNet (Dai et al., 2017). ScanNet++ (Yeshwanth et al., 2023),
BlendedMVG (Yao et al., 2020), MatrixCity (Li al., 2023), MegaDepth (Li & Snavely, 2018),
Hypersim (Roberts et al., 2021), Taskonomy (Zamir et al., 2018), Mid-Air (Fonder & Van Droogen-
broeck, 2019), and an internal dynamic scene dataset. Details of model training can be found in Appendix A.2.
4 EXPERIMENTS
We report quantitative results of our method on four tasks: camera pose estimation (Sec. 4.1), point map estimation (Sec. 4.2), video depth estimation and monocular depth estimation (Sec. 4.3).

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Published as a conference paper at ICLR 2026
Table 1: Camera pose estimation. RRA, RTA, AUC are evaluated with threshold of 30 degrees.
RealEsttelOK
CaStv22 (S06a)
Stntel
TUM- mom-iis
ScanNet (seea)
Methoad
ALCC
RKA.
1
ALCT
ATTEL
MP9-11
AT1:1
R.
Rassk (Ying al. 2025)
95,05
81.26
57.49
91.11
73.63
0.331
13:75
0.0M0
0.101
1,425
0.155
0.125
3.491
CUTER (Wang al. 3025b)
98.62
05.10
$1.47
96.19
92.69
75.62
0.217
0.070
0.66
0.347
0.315
0.411
0.094
0.022
0.629
FLARE (Chong atal. 2005)
99.00 0M
05.25
M0307
16-18
91.75
73.99
0.200
0158
3015
0.005
0.013
0.675
1096
11971
VGGT (Wagg et 20254)
02:02
03.13
77.62
08.96
92.13
$8.59
0.167
0.62
0.491
0.812
0.010
0
0.25
0.05
0.382
x² (Ours)
99.99
05.62
$5.90
59.85
97.33
35.41
0.074
0.940
0.382
9.044
0,009
0,312
10031
0.013
1.347
Across all tasks, our method achieves state-of-the-art (SOTA) comparable performance against existing feed-forward 3D reconstruction methods. Visualized point maps are given in Figure 5 and Figure (in Appendix) as qualitative results.
To validate the effectiveness of our design, We also conduct several analyses: (I) a robustness evaluation against input image sequence permutations (Sec. 4.4), (2) an ablation study on scale- invariant point maps and affine-invarian camera poses (Sec. 4.5).
4.1 CAMERA POSE ESTIMATION
We assess predicted camera pose using two distinct sets of metrics: angular accuracy (follow- ing (Wang et al., 2023; 2024; 2025a)) on RealEsttae 10K (Zhou et al., 2018) and Co3Dv2 (Reizen- stein et al., 2021) datasets, and distance error (following (Zhao et al., 2022; Zhang et al., 2024; Wang et al., 2025b)) on Sintel (Bozic et al., 3021). TUM-dynamics (Sturm et al., 2012) and ScanNet (Dai et al., 2017). Details about the metrics can be found in Appendix A.5.
As shown in Table I, our method sets a new SOTA benchmark in zero-shot generalization on Sintel and MaalEstatelOK. and achieves competitive SOTA results alongside VGGT on TUM-dynamics, and the in-domaín Co3Dv2 and ScanNet datasets. These results underscore our model's strong generalization capabilities while maintaining excellent performance on familiar data distributions.
4.2 POINT MAP ESTIMATION
Following CUT3R (Wang et al., 2025b), we evaluate the quality of reconstructed multi-view point maps on the scene-level 7-Scenes (Shotton et al., 2013) and NRGBD (Azinović et al., 2022) datasets under both sparse and dense view conditions (different in sampling strides). We also extend our eval- uation to the object-centric DTU (Jensen et al., 2014) and scene-level ETH3D (Schops et al., 2017) datasets. Predicted point maps are aligned to the ground truth using the Umeyama algorithm for coarse Sim(3) alignment, followed by refinement with the Iterative Closest Point (ICP) algorithm.
Consistent with prior works (Azinović et al., 2022; Wang et al., 2024; Wang & Agapito, 2024: Wang et al., 2025b), we report Accuracy (Acc.). Completion (Comp.), and Normal Consistency (N.C.) in Table 2 and Table These results highlight the strong generalization capability of our method in a scenarios, sparse and dense view settings (Table 2), as well as object-level and scene-level scales (Table 3).
broad spectrum of 3D reconstruction tasks, proving robust across synthetic and
Table 2: Point map estimation 7-Scenes and NRGBD
7-Scemes
NRGBD
Method
View
Acc.
Comp. 1
NC.
Acc.
Comp.
NC. 1
Moan
Med.
Mean
Med.
Mcan
Mod.
Mcan
Mcd.
Mcan
Med.
Mcan
Med.
Past3k (Yang al., 2025)
0.095
0.065
0.144
0.089
0.673
0.759
0.135
0.091
0.163
0.104
0.759
0.877
CUTTRR (Wing al., 2025h)
0.093
0.049
0.102
0.051
0.704
0.805
0.104
0.041
0.079
0.031
0.822
0.968
FLARE (Zhang et al., 2025)
0.085
0.057
0,145
0.107
0.696
0.780
0.053
0.024
0.051
0.025
0.877
0.988
VGGT (Wang al., 2025a)
0.044
0.056
0.033
0.733
0.845
0.029
0.038
0.890
0.981
(Ours)
0.047
0.029
0.075
0.049
0.742
0.84]
0.026
0.015
0.028
0.014
0.916
0.992
Fast3R (Yang al., 2025)
0.040
0.017
0.0%6
0.018
0.644
0.725
0.030
0.016
0.790
0.934
CUT3R (Wang al., 2025b)
0.023
0.010
0.027
0.008
0.669
0.764
0.086
0.037
0.048
0.017
0.800
0.953
FLARE (Zhang et al., 2025)
dense
0.019
0.007
0.026
0.013
0.684
0.785
0.023
0.011
0.018
0.008
0.882
0.986
VGGT (Wang al., 2025a)
0.022
0.026
0.666
0.760
0.017
0.010
0.015
0.005
0.893
(Ours)
0.016
0.007
0.022
0.011
0.689
0.792
0.015
0.068
0.013
0.005
0.898
0.987
Table 3: Point map estimation DTU and ETH3D
DTU
ETH3D
Method
Acc.
Comp.
N.C. f
Acc. 4
Comp. J
N.C. 1
Mean
Med.
Mean
Med.
Mean
Med.
Mean
Med.
Med.
Meun
Med.
Fast3R (Yang al., 2025)
3.340
1.919
2.929
1.125
0.671
0.755
0.832
0.691
0.978
0.683
0.667
0.766
CUT3R (Wang et al., 2025b)
4.742
2.600
3.400
1.316
0.679
0.764
0.617
0.525
0.747
0.579
0.754
0.848
FLARE (Zhang 2025)
2.541
1.468
3.174
1.420
0.684
0.774
0.464
0.338
0.664
0.395
0.744
0.864
VGGT (Wang et al., 2025a)
1.338
0.779
1.896
0.992
0.676
0.766
0.280
0.185
0.305
0.182
0.853
0.950
(Ours)
1.198
0.646
1.849
0.607
0.678
0.768
0.194
0.131
0.210
0.128
0.883
0.969
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Table 4: Video depth estimation on Sintel, Bonn and KITTL FPS evaluated on KITTI using one A800 GPU.
Sintel
Bonn
KITTI
Method
Params
Abs Rel
8 < 1.25 1
Abs Rel 1
8 < 1.25
Abs Rel
5 1.25
FPS
DUSER (Wang et al., 2024)
571M
0.662
0.434
0.151
0.839
0.143
0.814
1.25
MAS:3R (Leroy al., 2024)
689M
0.558
0,487
0.188
0.765
0.115
0.848
1.01
MonST3R (Zhang et al., 2024)
571M
0.399
0.519
0,072
0.957
0.107
0.884
1.27
FastR (Yang et al., 2025)
648M
MVDUS13 (Tang et al., 2024)
661M
0.805
0.283
0.426
0.357
0.456
0.342
0.69
CUT3R (Wang et al., 20255)
793M
0.417
0.507
0.078
0.937
0.122
0.876
6.98
Acther (Team al., 2025)
5.57B
0.324
0,502
0.273
0.594
0.056
0.978
6.14
Fl FLARE (Zhang et al., 20255
1.40B
0.729
0.336
0.152
0.790
0.356
0.570
1.75
VGGT (Wang et al., 2025a)
1.26B
0.638
0.057
0.966
0.062
0.969
(Ours)
959M
0.233
0.664
0.049
0.975
0.038
0.986
57.4
Input Images
Ground Truth
Ours
VGGT
FLARE
Fast3R
Figure 5: Qualitative comparison of multi-view 3D reconstruction. Compared other multi- frame reconstruction methods, T produces cleaner, more accurate and more complete reconstructions with fewer artifacts.
4.3 DEPTH ESTIMATION
Following the methodology of CUT3R (Wang et al., 2025b), we report the Absolute Relative Error (Abs Rel) and the prediction accuracy at threshold of 8 < 1.25 of our method on the tasks of video depth estimation and monocular depth estimation, using the Sintel (Bozic et al., 2021), Bonn (Palaz- zolo et al., 2019), and KITTI (Geiger et al., 2013) datasets. NYU-v2 Silherman et al. (2012) is additionally used for monocular depth estimation.
Video depth estimation. In this setting, video depth sequences are aligned to the ground truth with a scale per sequence. As reported in Table 4, our method achieves new SOTA performance across all three datasets within feed-forward 3D reconstruction methods. Notably, it also delivers exceptional efficiency, running at 57.4 FPS on KITTI, significantly faster than VGGT (43.2 FPS) and Aether (6.14 FPS), despite having a smaller model size.
Monocular depth estimation. In this setting, each depth map aligned independently its ground truth with scale factor. As reported in Table 5, our method achieves state-of-the-ar results among multi-frame feed-forward reconstruction approaches, even though it is not explicitly optimized for fongle-frame depth estimation. Meanwhile, it performs competitively with MoGe (Wang et al., 2025c;d), one of the top-performing monocular depth estimation models.
4.4 ROBUSTNESS EVALUATION
key property of our proposed architecture is permutation equivariance, ensuring that its outputs robust variations in the input image sequence order. To empirically verify this, conduct
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Table 5: Monocular depth estimation
Sintel
Bonn
KITTI
NYU-22
Method
Ahs Rell
d 1.25
Ahs Rel:
d < 1.25
Abs Rell
5 < 1.25
Abs Rell
6 < 1.25
DUS:R (Wang et al., 2024)
0.488
0.532
0.139
0.832
0.109
0.873
0.081
0.909
MASI3R (Leroy al., 2024)
0.413
0.569
0.123
0.833
0.077
0,948
0.110
0.865
MonST3R (Zhang et ol., 2024)
0.402
0.525
0.069
0.954
0.098
0.895
0.094
0.887
FasER (Yang al., 2025)
0.544
0.509
0.169
0.79
0.120
0.861
0.093
0.898
CUT3R (Wang al., 2025b)
0.418
0.520
0.058
0.967
0.097
0.914
0.081
0.914
FLARE (Zhang al., 2025)
0.606
0.402
0.130
0,836
0.312
0.513
0.089
0.898
VGGT (Wang et al., 2025a)
0.335
0.599
0.053
0.970
0.082
0.947
0.056
0.951
MoGe
0.273
0.695
0.050
0.976
0.049
0,979
0.055
0.952
-t (Rarget al, 20156
6:73
-0059
-095
-0051
0.97
00055
0997
(Ours)
0.277
0.614
0.044
0.976
0.060
0.971
0.054
0.956
Table 6: Standard deviation of point cloud estimation
DTU
ETH3D
Method
Acc. std. +
Comp. std. J
N.C. std.
Acc. std. 4
Comp. std.
N.C.
std.
Mean
Med.
Mean
Mod.
Mean
Med.
Moan
Med.
Mcan
Med.
Mean
Med.
Fast3R (Yang al., 2025)
0.578
0.451
0.677
0.376
0.007
0.009
0.182
0.205
0.381
0.273
0.047
0.072
FLARE (Zhang et al., 2025)
0.720
0.494
1.346
1.134
0.009
0.012
0.171
0.187
0.251
0.188
0.048
0.053
VGGT (Wang 2025a)
0.033
0.022
0.054
0.036
0.007
0.007
0.049
0.040
0.062
0.042
0.022
0.015
(Ours)
0.003
0.002
0.006
0.003
0.001
0.001
0.000
0.000
0.000
0.000
0.001
0.000
experiments on the DTU (Jensen et al., 2014) and ETH3D (Schops et al., 2017) datasets. For each
sequence of length N, we create N different input orderings, by making each of the N frames the first frame in the sequence in turn. We then compute the standard deviation of the metrics across these N runs. We then compute the standard deviation of the reconstruction metrics across these N outputs. A lower standard deviation indicates higher robustness to input order variations.
As reported in Table 4.4, our method achieves near-zero standard deviation across all metrics on DTU and ETH3D, outperforming existing approaches by several orders of magnitude. For in- stance, on DTU, mean accuracy standard deviation is 0.003, while VGGT reports 0.033. On ETH3D, our model achieves effectively zero variance. This stark contrast highlights the limita- tions of redereeceefraame-deeeddeee Our results provide compelling evidence that the proposed architecture is genuinely permutation- equivariant, ensuring consistent and indee-indeeendentt 3D reconstruction.
methods, which exhibit significant sensitivity input order.
4.5 ABLATION STUDY
To validate the effectiveness our proposed components, we conducted an ablation study by sys- tematically removing features from our complete model. We define two ablated variants of our full model: Model 2, which lacks the affine-invariant camera pose modeling, and Model 1, which lacks both affine-invariant poses and scale-invariant pointmaps. See Appendix A.6 for more details.
The comparative results for pointmap estimation across three datasets are presented in Table 7. We found that scale-invariant pointmap modeling does not yield significant performance gains on indoor datasets like 7-Scenes and NRGBD. For outdoor data, however, the performance improve- ment is substantially more pronounced. This observation is consistent with previous studies on acale-invarian depth, which have shown that outdoor scenes are more significantly affected by scale ambiguity. Furthermore, we observed that affine-invariant camera pose modeling consistently en- hances the final performance. More importantly, unlike Model 1 and Model 2, its inclusion renders Consequently, the model becomes robust to both the order of
the model permutation-equivarine input frames and the selection of the reference view.
Table 7: Ablation study on the key components of our model. We show how the performance metric improves as each component added to the baseline.
ETH3D
7-Scemes
NRGBD
Comp.
N.C.
Comp
Camp. 1
N.C
Mean
Med.
Mean
Med.
Med.
Med.
Med.
Med.
Med.
Meun
Med.
Mean
Med.
0.229
0.150
0.166
0.103
0.930
0.010
0.010
31009
0.854
0.018
0,025
0.359
0.977
Model
0.197
0.118
0.118
0,065
0.820
0.443
0,020
0.009
0,000
0.837
0.031
0,018
0,023
0
0.361
0.978
Model
0U143
0.957
0.009
3.009
0,843

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5 CONCLUSION
In this work, we introduced π², a feed-forward neural network that presents a new paradigm for visual geometry reconstruction by eliminating the reliance on a fixed reference view. By leveraging a fully permutation-cquivariann architecture, our model is inherently robust to input ordering and leads higher accuracy. This design choice removes a critical inductive bias found in previous methods, allowing our simple yet powerful approach to achieve state-of-the-ee performance on wide array of tasks, including camera pose estimation, depth estimation, and dense reconstruction. T demonstrates that effrence-frre systems are not only viable but can lead to more stable and versatile 3D vision models.
ACKNOWLEDGMENTS
This work supported by Shanghai Artificial Intelligence Laboratory.
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A APPENDIX
A.1
ARCHITECTURE DETAILS
The encoder and alternating attention modules are the same as those in VGGT (Wang et al., 2025a), with the exception that we use only 36 layers for the alternating attention module, whereas VGGT uses 48. The decoders for camera poses, local point maps, and confidence scores share the same architecture but do not share weights. This architecture is a lightweight, 5-layer transformer that applies self-attention exclusively to the features of each individual image. Following the decoder, the output heads vary by task. The heads for local point maps and confidence scores consist of simple MLP followed by pixel shuffle operation. For camera poses, the head is adapted from Reloc3r (Dong et al., 2025) and uses an MLP, average pooling, and another MLP. The rotation initially predicted in 9D representation (Levinson et al., 2020) and is then converted to 3x3 rotation matrix via SVD orthogonalization
A.2 TRAINING DETAILS
We train 3 in two stages, process similar to Dust3R (Wang et al., 2024). First, the model is trained on low resolution of 224 x 224 pix- els. Then, it is fine-tuned on images of random resolutions where the total pixel count be- tween 100,000 and 255,000 and the aspect ra- tio is sampled from the range [0.5, 2.0]. a strat- egy similar to MoGe (Wang et al., 2025c). We use a dynamic batch sizing strategy similar to VGGT. In the first stage, sample 64 images per GPU, and in the second stage, we sample 48 images per GPU. Each batch is composed of
VOGT
ceuro
Figure 6: Comparison of predicted pose dis- tributions. We visualize the predicted pose dis- tributions in 3D space. अ shows a clear low- dimensional structure, while VGGT's distribution scattered.
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Table 8: Comparison with VGGT when trained from scratch.
ETH3D
7-Scenes
NRGB
Method
Acc.
Comp.
Acc. 4
Comp.
Acc. 4
Comp.
0.618
0.453
0.064
0.068
0.071
0.047
VGGT (Wang et al., 2025a)
0,563
0.449
0.057
0.046
0.060
0.042
global proxy
0.418
0.266
0.059
0.071
0.052
0.035
2 to 24 images. Each training stage runs for 80 epochs, with each epoch comprising 800 iterations. Our final model is not trained from scratch. Instead, we initialize the weights for the encoder and the alternating attention module from the pre- trained VGGT model, and we keep the encoder frozen during training. We train the first stage on 16 A100 GPUs and the second stage on 64 A100 GPUs. For our loss function, we the weights for each component as follows: Anoeal = 1.0, Acont = 0.05, Aeam = 0.1, and Auans - 100.0. The imple- mentation of our normal loss follows that of MoGe, and the resolution for aligning the local point map loss is set to 4096. Regarding optimization, we set the initial learning rate for all model compo- nents to 5 x 10-5, We employ a OneCycl eLR scheduler, where the learning rate anneals from its maximum value down to a minimal value over the entire training duration following a cosine curve. We use the same learning rate and scheduler settings for both stages. The confidence head is not trained jointly with the other modules. Instead, after completing the two main training stages, freeze the rest of the network and train the confidence head isolation. This final stage converges rapidly, typically within a few epochs, without impacting the model's overall performance. We use gradient clipping with a norm of 1.0.
A.3 DISCUSSION FOR PREDICTED POSE DISTRIBUTION
In Figure 6, we analyze the geometric properties of the learned representations by visualizing the distribution of predicted camera poses. In this plot, the spatial coordinates (z, y. 2) correspond to the translation component, while the rotation is encoded into the RGB color space. Specifically, we convert each predicted rotation matrix into an axis-angle vector, normalize its components to the range [0, 1], and map them to the Red, Green, and Blue channels. The visualization reveals striking contrast: while VGGT's distribution appears scattered and random, our predictions form a distinct low- oow-dimensional structure. This suggests that our model effectively captures the underlying geometric manifold, which is likely a key factor contributing to its superior performance.
A.4 COMPARISON WITH VGGT
This section details an experiment designed soiely for fair comparison against VGGT (Wang et al., 2025a). A direct comparison is challenging because training our model from scratch with only its core objectives (camera poses and local pointmaps) leads to suboptimal convergence, whereas VGGT's design incorporates a multi-task learning setup.
We attribute this difficulty to the "cold start" problem inherent in relative pose supervision. Unlike reference-anchoree methods, our approach generates highly coupled N x N relative constraints, which are significantly more unstable to optimize from completely random initialization.
To address this, we introduce an auxiliary head to predict global pointmap relative to a reference frame, using a loss analogous to Eq. 3.2. Crucially, while the reference view is used via cross- attention in this head, it serves purely as a proxy task to decouple geometry learning and stabilize the optimization landscape. Our final model remains fully permutation-equivarrantt,
We train both our adapted model and VGGT under these identical, multi-task conditions: from scratch (except for DINOv2 encoders) the same data, at 224 224 resolution for 80 epochs (800 steps/epoch). We use the same data as described in Section 3.4.
As shown in Table 8, once the optimization stability is ensured by the global proxy, T significantly outperforms the VGGT baseline on ETH3D and NRGB benchmarks. Note that while our model can be trained from scratch effectively with this proxy, utilize VGGT initialization in our main experiments to maximize computational efficiency and leverage the large-scale data priors captured in the pre-trained weights.
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Input Images
Ours
VOGT
FLARE
Fast3R
Figure 7: Qualitative comparison of in-the-wild multi-view 3D reconstruction. π demonstrates superior robustness on challenging in-the-wild sequences, consistently producing more coherent and complete 3D structures for both dynamic and complex static scenes compared to other ferd-forward approaches.
A.5 CAMERA POSE EVALUATION METRICS
Angular Accuracy Metrics. Following prior work (Wang al., 2024; 2025a), evaluate predicted camera poses on the scene-level RealEstate10K (Zhou et al., 2018) and object-centric Co3Dv2 (Reizenstein al., 2021) datasets, both featuring over 1000 test sequences. For each quence, we randomly sample 10 images, form all possible pairs, and compute the angular errors of the relative rotation and translation vectors. This process yields the Relative Rotation Accuracy (RRA) and Relative Translation Accuracy (RTA) at given angular threshold (e.g. 30 degrees). The Area Under the Curve (AUC) of the min(RRA..RTA)-tbreshett curve serves as a unified metrie. All methods in Table have been trained on Co3Dv2, while RealEstate 10K is excluded from trainset except for CUT3R (Wang al., 2025b).
Distance Error Metrics. Following (Wang et al., 2025b), we report the Absolute Trajectory Error (ATE), Relative Pose Error for translation (RPE-t), and Relative Pose Error for rotation (RPE-r) on the synthetic outdoor Sintel (Bozic et al., 2021) dataset, well the real-world indoor TUM- dynamics (Sturm et al., 2012) and ScanNet (Dai et al., 2017) datasets. Predicted camera trajectories aligned with the ground truth via a Sim(3) transformation before calculating the errors. All meth- ods in Table have seen ScanNet or ScanNet++ (Yeshwanth et al., 2023) samples during training time. Zero-shot pose estimation accuracy is evaluated on Sintel and TUM-dynamics for all methods.
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A.6 ABLATION DETAILS
The primary difference between our full model and the ablated models (Model and Model 2) is that the latter two incorporate a camera token. This token is essential for distinguishing the refer- ence view, as the model is no longer cermutation-equivariaa after the removal of the uffine-ivariaan camera pose modeling. At each iteration, the camera token is concatenated with a randomly selected reference view before the ineennatin-attention module similar to (Wang et al., 2025a). We compute an angle loss for rotation and Huber loss for translation between the predicted and ground-truth poses in the reference view's coordinate system for Model and Model 2. While Model 1 and Model 2 share an identical architecture and parameter count, their key distinctions lie in the loss calculation and normalization processes. For Model 1, neither perform alignment during the loss computation for the predicted pointmap nor do we normalize the pointmap itself. We found that ap- plying normalization in this specific case led to anomalous and significantly degraded performance, a phenomenon also observed in prior work (Wang et al., 2025a). In contrast, the predicted local pointmaps are normalized for both Model and the full model.
For a fair comparison, all models were trained for 80 epochs. with 800 iterations per epoch, on images with a resolution of 224 224. They shared the same initialization procedure as our final model: we loaded pre-trained weights for the VGGT encoder and alternating alternaingg-atentioon attenntinn layers, and kept the encoder frozen throughout training. For the 7-Scenes and NRGBD datasets, we use the same dense view setting as in the previous section.
A.7 ADDITIONAL EVALUATION
Camera pose estimation with tighter angular thresholds. Following the protocol of VGGT (Wang et al.. 2025a), Tab. primarily reports the RRA, RTA, and AUC metries using relaxed angular threshold of 30" However, to better assess precision, we also examine tighter thresholds, such as 5 and 15e used by Fast3R (Yang al., 2025) and FLARE (Zhang al., 2025). Accordingly, in Tab. 9, we present a full set of RRA, RTA, and AUC metries across thresholds of 1 3 5", 10, and 15,, evaluated on RealEstate 10K. Our T model demonstrates robust and consistent performance even with these more demanding constraints.
Table 9: Camera pose estimation with tighter angular thresholds on RealEstate10K
RRA (t)
(1)
AUC (7)
Method
03
45
87
1:15
12
03
05
0.10
05
81
63
12.5
Q:10
@55
Fast3k Yang et al., 2025)
$4.30
87.24
94.73
97.90
98.46
5.47
24.56
39.23
59.29
69.11
3.77
13.67
22.36
37.33
46.71
CUTSR (Wang 2025b)
78.63
96.06
98.15
99.31
99.63
16.23
51.43
67.44
$2.98
88.93
13.40
33.39
45.63
61.78
70.15
FLARE (Zhang 2025)
70.99
97.11
98.98
99.44
43.33
62.39
82.29
25.67
38.47
57.20
67.02
VGGT (Wang al.,, 2025a)
97.05
39.93
60.61
x² (Ours)
85.19
97.56
98.83
99.63
99.86
27.57
63.57
78.32
$3.69
92.02
24.87
47.28
58.63
72.11
78.39
Point map estimation with Chamfer Distance(CD). To further evaluate the quality of the point map estimation, we additionaly calculate the Chamfer Distance metric, which defined as the mean value of the Accuracy (Acc.) and Completion (Comp.) terms. The results across all evaluation datasets are reported in Tab. 10.
Table 10: Point map estimation with Chamfer Distance.
7-Seees-paree
7-Scene-drnie
NRGBD-quae
NRGBD-dene
ETHDD
Method
EiDemoon
(1i-mall
[11mmaon]
CDonsd]
CDonscre]
CDomal]
LiDmmon.
(3i-mol.
[31-mran]
(Tomvd)
[Domeis]
CDonad]
Faatlk Ylaag et 2025)
0/25
0.009
4.021
Hi ABB (hhang al. 3075)
0.115
0/881
6833
0.000
0.012
0.001
01000
0/00
1.858
1.405
0.564
0.377
VOGT (Wong al. 3075a)
8,88
0.06
[1000
01085
0.00
00015
0007
1.699
11881
0.767
0.177
72 (Dun))
0.06
6,819
IU079
8J826
6.813
R003
0
1.422
11626
0.199
6128
Monocular depth estimation compared with Depth Anything V2 (Yang et al., 2024), one of the
SOTA models for monocular depth estimation. We evaluate it on our standard benchmarks with input resolution 518, following CUT3R (Wang al., 2025b) protocol. As shown in Tab. 11, 3 achieves comparable performance to the specialized DAv2, despite being designed for generalist multi-view reconstruction.
16

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Published as a conference paper at ICLR 2026
Table 11: Monocular depth estimation.
Sintel
Bonn
KITTI
NYU-v2
Method
Abs Rel,
1.25 f
Abs Relf
1.25
Abs Rell
5 1.25
Abs Rell
1.25
DA (Yang al., 2024)
0.541
0.126
0.090
0.921
metic inforr
0.372
-0.26
-00997
-9912
-0081
netric outior
0.488
00477
-.186
0.66
0.500
0019
0.372
0.89
MoGe
0.273
0.695
0,050
0.976
0,049
0,979
0.055
0.952
V1 (Wing ata 2025)
-0.23
0.005
0.050
11976
-0054
0997
-0055
0.55
(Wing 20250)
(Ours)
0.277
0.614
0.044
0,976
0.060
0.971
0.054
0.956
A.8
LIMITATIONS
Our model demonstrates strong performance, but also has several key limitations. First, it is unable handle transparent objects, as our model does not explicitly account for complex light transport phenomena. Second, compared to contemporary diffusion- based approaches, our reconstructed ge- ometry lacks the same level of fine-grat ane-ggrined detail. Finally, the point cloud generation relies on simple upsampling mechanism using an MI. with pixel shuffling. While efficient, this design can introduce noticeable grid-like artifacts, particularly in regions with high reconstruction uncertainty.
A.9 LLM USAGE STATEMENT
In the preparation of this manuscript, utilized Large Language Model (LLM) writing assistant. The LLM's role was strictly limited to improving the manuscript's clarity, correcting grammatical errors, and refining the overall language for professional academic standards. All sei- entific contributions, including the core ideas, methodology, experimental design, and interpretation of results, are the original work of the authors.
17


Reviews:
[{"review_id": "N0hcvl3nGf", "reviewer": "Reviewer_urpi", "summary": "This paper proposes $\\pi^3$, a feedforward model for pose estimation and point cloud prediction. It investigates the limitations of previous feedforward reconstruction models, such as VGGT, whose performance depends on the selection of the reference view. To address this issue, the proposed method removes the reference-view-dependent design in the model architecture and introduces a relative camera pose loss and a local point loss. Experimental results show that the proposed method effectively resolves the aforementioned problem and achieves state-of-the-art performance.", "questions": "- For monocular depth estimation, how does the performance compare with SOTA models such as DepthAnythingv2? Besides, what is the input image resolution used for depth estimation?\n- Since the MLP head with pixel shuffling introduces grid-like artifacts, why does the proposed method still adopt this design instead of using DPT heads as in previous methods?\n\nI will raise my score if the authors can provide reasonable clarifications regarding initialization and the effect of adding the global loss.", "limitations": "", "rating": 6, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "- The paper addresses an interesting and important problem: the dependence of previous feedforward reconstruction models on reference view selection. The proposed method provides a simple yet effective solution.\n\n- The proposed model achieves SOTA performance on both pose estimation and reconstruction tasks.", "weaknesses": "- Some parts of the paper lack proper citations:\n    - The normal loss is identical to that in MoGe, but no citation is provided.\n    - The camera pose estimation module and loss function are the same as in Reloc3r, yet there is no citation in Section 3.3.\n\n- The proposed method requires weight initialization from VGGT, which makes the comparison with other methods, such as VGGT itself, somewhat unfair. Table 8 shows results when both models are trained from scratch; however, it remains unclear how the model performs when trained from scratch only with the local point and pose losses. Furthermore, can the model trained from scratch with the added global loss achieve performance comparable to the version initialized from VGGT?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "IMEswvGxFL", "reviewer": "Reviewer_ghyt", "summary": "This paper proposes a VGGT-like model that achieves superior performance across multiple tasks, including pose estimation, depth estimation, and point map estimation.\n\nThe performance improvement stems from a novel permutation-invariant model design. Previous methods such as Dust3R, Mast3R, and VGGT rely on a predefined reference frame during estimation, making them sensitive to frame selection and limiting their robustness. In contrast, this work attains permutation invariance by removing all frame order–dependent positional encodings and introducing a scale-invariant point map loss together with an affine-invariant pose loss.\n\nStrengths: The proposed idea is both novel and insightful, supported by thorough and comprehensive experiments.\n\nWeaknesses: No major issues are identified in this paper.", "questions": "How is the rotation mapped to xyz in Figure 6? What's the rotation representation?", "limitations": "", "rating": 10, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "1. Novel and insightful idea: The paper makes an insightful observation about the limitation of defining a reference frame in prior models. The proposed approach to eliminate this dependency is technically sound and straightforward to implement.\n2. Comprehensive experiments: The method is evaluated across multiple applications on widely used datasets. Reporting standard deviations in Table 6 is a valuable addition that strengthens the credibility of the results.\nWell-presented paper: The paper is clearly written and easy to follow. Figures and tables are well designed, effectively supporting the main arguments and improving readability.", "weaknesses": "I don't see any major issues in this work.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "OfDVpOdTOU", "reviewer": "Reviewer_DanB", "summary": "This paper introduces a novel permutation equivariant architecture for feed-forward 3D reconstruction. To achieve permutation equivariance, positional embeddings used to differentiate between frames and learnable tokens that denote a reference view are not used. The structure is straightforward, while the performance is impressive on various tasks.", "questions": "1. To compute the scale $s$ that aligns ground truth and prediction, the other solution is to use umeyama to align the ground truth and predicted camera poses. Different form optimizing Eq. 4, this solution looks simpler. Did the authors try this?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "1. The paper is well-written and easy to follow. \n\n2. The paper addresses the limitation of existing feed-forward 3D reconstruction pipelines, where one view is selected as a reference view and the performance may degrade if the reference view changes. \n\n3. The performance in camera pose estimation, monocular/video depth estimation, and pointmap reconstruction, is state-of-the-art. \n\n4. Ablation study verifies the permutation equivariance of Pi3.", "weaknesses": "1. Camera pose estimation: In addition to using large angular threshold (30 degrees), more strict thresholds, e.g. 5 degrees, 10 degrees, should be used to illustrate the rotation accuracy. \n\n2. Point-map evaluation: \n    * On both DTU and ETH3D, the numbers of VGGT are very different from those in the original paper. Could the authors explain the reason? \n    * Since the authors already provide accuracy and completeness, it makes sense to further add Chamfer distance/F-score, which is the best metric to evaluate the overall reconstruction quality. \n\n3. In Table 6, CUT3R heavily relies on the sequential/temporal information. Thus, it is not a very good baseline here.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)