Interpretable 3D Neural Object Volumes for Robust Conceptual Reasoning
Authors: Nhi Pham
Artur Jesslen
Bernt Schiele
Adam Kortylewski
Jonas Fischer
Venue: ICLR 2026 Poster (2026)
Keywords: Interpretability
Robustness
3D-aware classification with concepts
Sparse volumetric object representation
3D consistency
Primary area: interpretability and explainable AI
TL;DR: We introduce CAVE: Concept-Aware Object Volumes for Robust and Interpretable Image Classification

Abstract: With the rise of deep neural networks, especially in safety-critical applications, robustness and interpretability are crucial to ensure their trustworthiness. Recent advances in 3D-aware classifiers that map image features to volumetric representation of objects, rather than relying solely on 2D appearance, have greatly improved robustness on out-of-distribution (OOD) data. Such classifiers have not yet been studied from the perspective of interpretability. Meanwhile, current concept-based XAI methods often neglect OOD robustness. We aim to address both aspects with CAVE - Concept Aware Volumes for Explanations - a new direction that unifies interpretability and robustness in image classification. We design CAVE as a robust and inherently interpretable classifier that learns sparse concepts from 3D object representation. We further propose 3D Consistency (3D-C), a metric to measure spatial consistency of concepts. Unlike existing metrics that rely on human-annotated parts on images, 3D-C leverages ground-truth object meshes as a common surface to project and compare explanations across concept-based methods. CAVE achieves competitive classification performance while discovering consistent and meaningful concepts across images in various OOD settings.

Published as a conference paper at ICLR 2026
INTERPRETABLE 3D NEURAL OBJECT VOLUMES FOR ROBUST CONCEPTUAL REASONING
Nhi Pham' ! Artur Jesslen", Bernt Schiele', Adam Kortylewski Jonas Fischer!.
Max Planck Institute for Informatics, Saarland Informatics Campus, Germany
University of Freiburg, Germany
CISPA Helmholtz Center for Information Security, Germany Equal senior advisorship
(a) Explicit AD-Aware Concept Representation
(b) Robustness vs, Interpretability Trade-off
CAVE (Ours)
OOD Accuracy (Robustness
Better
LFC
Teafist
w/ ground trath pases w/t ground-irvus iirth 3D poses
ProboPhitt
Spatial Localisation (Interpretabilitt)
Figure 1: CAVE Concept Aware Volumes for Explanations. (a) We learn 3D object volumes (left), here ellipsoids, with concept representations. Each concept captures distinct local features of objects (color coded). At inference (right), these concepts are matched with 2D image features, achieving robust and interpretable image classification. (b) CAVE achieves the best robustness vs. interpretabilityy tradeoff across methods (higher is better on both axes). Here, we measure robustness with OOD accuracy (%) on Occluded Pascal3D+ (Wang al., 2020), and interpretability with concept spatial localisation (i.e., how well an explanation generated by method overlaps with ground-trufe -tuuh aoman-annotated object parts Pascal-Part (Chen al., 2014); defined in App. G.2).
ABSTRACT
With the rise of deep neural networks, especially in safety-critical applications, robustness and interpretability are crucial to ensure their trustworthiness. Recent advances in awa-a classifiers that map image features to volumetric representa- tion of objects, rather than relying solely on 2D appearance, have greatly improved robustness on -iddtr--iittiittinn (OOD) data. Such classifiers have not yet been studied from the perspective of interpretability. Meanwhile, current concept-basee based XAI methods often neglect OOD robustness. We aim address both aspects with new direction that uni- fies interpretability and robustness in image classification. We design CAVE as robust and inherently interpretable classifier that learns sparse concepts from 3D object representation. We further propose 3D Consistency (3D-C), a metric measure spatial consistency of concepts. Unlike existing metries that rely on human-annotated parts on images, 3D-C' leverages ground-truth object meshes common surface to project and compare explanations across concept- concept-based based methods. CAVE achieves competitive classification performance while discover- ing consistent and meaningful concepts across images in various OOD settings. Code is available at github.
CAVE Concept Aware Volumes for Explanations
INTRODUCTION
Deep neural networks (DNNs) have achieved impressive performance in diverse domains ranging from healthcare to autonomous driving. However, their decision maaiinn processes remain largely opaque and often rely spurious correlations (Noohdani al., 2024). In high-stake applications,

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Underwater
Fog
Shape
Context
3D Consistency
OOD Imput
NOVUM+ICE
TesNet
Ours
Figure 2: CAVE (Ours) discovers consistent concept for Motorbike images under challenging OOD nuisances in OOD-CV dataset. Columns correspond to inputs with different OOD nui- sances: underwater, fog, shape, and context. Rows show attributions from NOVUM + ICE (best post-hoc), TesNet (best ad-hoc) and Ours. CAD mesh (right) visualises the class-level 3D consis- tency of a concept, where highlighted regions visualise the aggregated concept attributions across test images. CAVE produces more consistent and localised explanations, NOVUM ICE and Tes- Net detect concepts inconsistently under nuisances. See App. LI for full qualitative comparison.
for instance, in the medical domain, autonomous systems judicial justice, ensuring both inter- pretability and robustness is not just desirable - it is essential for safety and trustworthiness. To overcome such issues and make networks have been proposed in the scope of explainable AI (XAI). Notably, post-hoc methods generate concept-based explanations for pre-trained networks, providing insights into their decision-making process without altering the underlying architecture (Fel et al., 2023b; Ancona et al., 2018; Erion al., 2021; Hesse et al., 2021; Fel al., 2023a). However, such methods only approximate the model's computations, and thus do not provide faithful explanation. In contrast, another line of research enforces interpretability directly during training, making aspects of the model inherently interpretable and ensuring that the explanations remain faithful to its computations (Chen et al., 2019; Nauta et al., 2023a; Alvarez Melis & Jaakkola, 2018: Nauta et al., 2021; Oikarinen et al., 2023). Yet, these models are often not designed with robustness in mind (cf. Fig. lb).
transparent and interpretable, various approaches
DNNs real-world scenarios typically encounter distribution shifts over time such as occlusions, or adverse weather conditions in the case of autonomous driving. If the model is not OOD-robust, any explanations extracted from the model representation are unreliable. In fact, under foggy weather or changing contexts, most methods often fail to identify consistent and meaningful explanations (cf. Fig. 2). In an orthogonal line of research, incorporating 3D compositional object representations into the training pipeline significantly improves OOD robustness, yet these classifiers remain inherently opaque, leaving a critical gap in understanding their decision making (Jesslen et al., 2024). They are also restricted training settings where ground-truth 3D poses are available. This landscape exposes key gap in the interpretability and robustness of image classification. We address it with CAVE classification that is both OOD-robust and inherently interpretable. CAVE builds on the idea of representing each class with a neural object volume (NOV) introduced in NOVUM (Jesslen et al., 2024), where simple shapes such cuboids spheres densely distributed with Gaussian fea- tures on the surface. These Gaussian features are then aligned with the latent image features for classification. While this improves OOD robustness, these dense features remain opaque and offer
Concept Aware Volumes for Explanations - framework for image
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little semantic insights. CAVE overcomes this by representing objects with ellipsoid NOVs, from which a sparse dictionary of high-level concepts learned (cf. Fig. la). Additionally, we leverage zero-shot estimated object orientation from Wang al. (2025b), thereby alleviating the reliance on pose annotations during training in 3D-aware architectures such as NOVUM. Once concepts are learned, they can be attributed to pixel spaces for explanations. Standard attribution methods such as layer-wise relevance propagation (LRP) however unfaithfully leak relevances in 3D-aware archi- tectures with non-standard layers. We modify LRP account for volumetric representations such as NOVs in 3D-aware architectures, while also ensuring its relevance conservation property.
For concept evaluation, existing consistency metrics often assume that learned concepts are aligned with hunan-annotated object parts (Huang et al., 2023; Behzadi- Khormouuj & Oramas, 2023), even though good model performance does not require such alignment. We thus propose 3D consistency (3D-C), which uses ground-truth 3D object meshes as common surface to project and compare concepts, allowing consistency to be measured without relying on part annotations. In summary, main contributions include:
(i) CAVE as a robust and inherently-intepreaable -nterpretaable image classifier through ellipsoid NOVs. Our concept basis is spatially aaware and its explanations are model-faithfil
(ii) an adaptation of LRP for concept attribution in classifiers with volumetric representations, (iii) and novel part-annotation-free consistency metric 3D-C that captures the spatial coher- ence of concepts across viewpoints and OOD nuisances. In comparision to various XAI methods, both post-hoc and inherently interpretable approaches, CAVE shows a favorable balance of OOD robustness and interpretability, with improvements across metrics such as OOD accuracy, object coverage, spatial localisation, and concept consistency.
2 RELATED WORK
Leveraging 3D supervision. 3D information is useful for 2D feature representations in downstream tasks like segmentation and depth estimation, but these require rich multi-view data (Yue et al., 2024; Hou et al., 2021; Fu et al., 2024). Recently, NOVUM pioneers using 3D information for robust classification, by considering 3D pose information to fit cuboid NOVs to an image (Jesslen et al., 2024). This line of work forms the basis of our approach.
Learning without 3D supervision. In 3D-aware image classifiers such as NOVUM, model train- ing requires ground-truth 3D pose annotations to align NOVs with the object in the image. This requirement significantly limits applicability, as such annotations are expensive to obtain and often unavailable in real-world datasets. Recent work proposes zero-shot object orientation estimation models, e.g., Orient- Orient-Anything (Wang et al., 2025b), which extract pose information given an input image. CAVE adopts such pose estimators to remove the need for annotated 3D poses in training. Concept-based explanations. A major line of work in XAI focuses discovering concept rep- resentations. Post-hoc concept extraction methods such as CRAFT (Fel et al., 2023b; 2024) and ICE (Zhang et al., 2021) factorise model activations to uncover latent concepts, while MCD (Viel- haben et al., 2023) uses sparse subspace clustering to identify concept subspaces, and PCX (Dreyer et al., 2024) learns concepts from relevance maps. These approaches offer implicit interpretability, and only approximate its computation (i.e., not model-faithful) A different class of approaches makes the model predictions themselves explicitly interpretuble by design. Concept Bottleneck Models (CBMs) (Koh et al., 2020; Oikarinen et al., 2023) introduce a dedicated concept layer whose units correspond to ity. Similarly, prototype-bad based networks such as ProtoPNet (Chen et al., 2019) and its follow-up works (Wang et al., ;021; Nauta et al., 2023a; Wang et al., 2025a) learn prototypical image features whose presence is used for prediction, offering explicit visual interpretability through prototype pro- jection. CAVE is faithfull-b bysiil--b-deiigge and implicitly interpretable: its internal units arise through un- supervised discovery rather than explicit semantic prototype supervision. We therefore compare CAVE with both post-hoe concept discovery methods (CRAFT, ICE, MCD, PCX) and faithful-by- design interpretable models (LF-CBM, ProtoPNet, TesNet. PiP-Net, MGProto). This allows us to assess concept quality across implicit versus explicit approaches, while comparing predictive per- formance among beyhhuul-b--eeignn models.
concepts, thus providing explicit semantic interpretabil-
Evaluating concept explanations. Prior works assess concepts along several axes: (i) spatial lo- calisation to ground-truft -ruth bounding boxes masks, (ii) object coverage, i.c. how well they attend to different parts of the object, and (iii) consistency across instances (Huang et al., 2023; Behzadi- Khormouji & Oramas, 2023; Huang et al., 2024; Zhu et al., 2025). Such metrics are limited for two
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reasons: they require human-annotaiee annotated object parts, and model training often optimises for task per- formance rather than part alignment. To complement these metrics, we propose 3D-C, a consistency measure of concept across samples without requiring part annotations.
PRELIMINARIES! NEURAL OBJECT VOLUMES (NOVS) AND NOVUM
In this section, we provide a recap of neural object volumes (NOVs) and NOVUM (Jesslen al., 2024), as they are essential for defining our method CAVE in Section 4. Notations. In a supervised setting, an image classifier consists of a feature extractor E(-) and classification layer ((-). Given an input image I R H x xC the feature extractor produces a
feature map F. {x) E IR H xw xW"x"', Here, H' v H and W < W denote the spatial dimension of the latent representation of x and need not correspond to pixel resolution. C" denotes the number of latent channels. We use f; (x) to indicate the 1.2-normalised latent feature vector for the i-th pixel of feature map F2 in raster order. The classification decision computed as y = 6(F2).
Neural Object Volumes (NOVs). NOV volumetric approximation of an object class y (cf. Fig. 3), and consists of set of K 3D Gaussians. In NOVUM, the NOVs are instantiated as cuboids
with Gaussians evenly distributed on their surface. The k-th Gaussian defined by its center puy 3 with fixed unit variance, and is associated with an 12-normalised feature vector By (k) E RCC.
Hence, each Gaussian in a NOV is assigned a fixed 3D coordinate on the surface of canonical object shape and form a structured volumetric representation. We define the matrix of Gaussian features for the object class y as Gy E RK'C', which have the same channel dimension C" as latent features Fg from the backbone model and will be later used to match with the Fg. Extending this notation, the complete matrix of Gaussian features across all N object classes can be represented as G [91: G2: ... GNl E R NK'C" During training of NOVUM, these NOVs G are learned to align with latent image features Fa, orienting the volumes through ground-truth 3D pose annotations (see also Appendix for training objectives). Intuitively, matching image latent features Gaussian features guided by the pose annotations aligns the image representation with the canonical 3D object geometry, allowing Gaussians to correspond consistent object geometry.
Classification with NOV' in NOVUM is done through feature matching between the back- bone image features Fz and the set of learned 3D object representation NOVs G. This opera- tion aligns each feature fi E Fz with the most similar Gaussian feature across G. The logit for class is computed by summing over all spa- tial locations where feature f; is matched Gaussian feature of
Gonssian & E Gear
Grussian
Concept M Baar
Baa Gear
Sy = O(F2, Gy) Σ max f: "
(1)
The class with the highest score Sy is the pre- dicted label y" This formulation gives rise to 3D-aware classification through bag-of-words feature matching mechanism, where image fea- tures are directly compared against 3D-aware Gaussian features. However, this classification process remains inherently opaque. The num- ber of Gaussian features involved in the match- ing step the order of thousands makes it difficult interpret which features contribute to the final decision (cf. Fig. 3, left). In the next Section 4, we describe our method CAVE, which replace dense Gaussian features and instead operates on a sparse dictionary of representative Gaussian fea- tures. We refer to these representations as concept-based NOVs, an interpretable concept basis for 3D-aware classification (cf. Fig. 3, right).
NOVUM
CAVE (Ours)
Figure 3: CAVE adopts ellipsoid NOVs and pro- duces a sparse set of concepts that replace the dense thousands of Gaussians in NOVUM, thus providing more interpretable explanations.
4 CAVE: CONCEPT-AWARE VOLUMES FOR EXPLANATIONS
Our goal is to build an image classifier with two key properties: (i) robust classification in OOD settings, and (ii) inherently interpretable model predictions. While specific solutions exist for each
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(a) Extract Image Features
(b) Interpretable Concept-based Neural Object Volumes
[Ma Hewi- - HTmial
Inpur 1
Now
Ryss
F
Spus 0.0004
Scar 0.99
STeain
(c) Classification with Concept Matching Eq. (2) for Each Class
Figure 4: CAVE Concept Aware Volumes for Explanations, framework for robust conceptual
reasoning and classification through 3D-aware concept-based neural object volumes (NOVs). In this visual illustration, colors indicate the top-5 concepts within each class. For classification, CAVE combines (a) extracted image features Fz and (b) interpretable concept-aware NOVs H. through a bag-of- word concept matching (c) with equation 2, where each feature fa Fz is best aligned with H by cosine similarity. Correct classification happens when many image features activates Car concepts, while concepts other classes fail to align with any feature (crossed-oul arrows).
property individually, combining them remains far from trivial. Building upon NOVUM, our method leverages volumetric object representations to simultaneously achieve both robustness and inter- pretability. In Section 1. we show how to extract a sparse set of interpretable concepts from dense Gaussian features on NOVs, which then form our concept-based NOV' for inherently interpretable classification. Figure 4 gives an overview of our method CAVE. We further attribute these concepts from the model prediction, through these concept- based NOVs, the imput image for explanations using our modified LRP. Then, in Section 4.2, we discuss how to improve learning NOVs through more expressive shapes and introducing weak 3D supervision with estimated poses for CAVE, thus extending its applicability to settings without ground-truth 3D pose annotations.
4.1 IDENTIFYING AND ATTRIBUTING CONCEPTS THROUGH NOVs
From NOVs to Concept-Based NOVs. To achieve an inherently interpretable NOV-based classifier, we identify a meaningful concept basis from each NOV and replace the latter with these concepts (cf. Fig. 4b). Formally, for a NOV Gy E Kx'' of class y, we formulate our class class-wise concept extraction problem through the lens of dictionary learning (Mairal et al., 2014; Fel et al., 2024):
(W : Hy)) = arg min 1|9, - WyH,, H,, l| Wy,H,,
where the weight matrix WH RKXD and the dictionary of D concept vectors Hij [n(") ..... h (DITT DxC' minimize the dlement-wise distance between our Gaussian features Sy and W. In the case of hard clustering, the weight matrix W reduces to a discrete assign- ment matrix, where each row is one-hot encoding that corresponds only one concept. This allows clustering to be much more interpretable than methods with less sparse weight matrices. We adopted K-Means clustering for its balance of accuracy, concept sparsity, and alignment to the learned NOVs. We refer to our ablation on concept extraction methods in Appendix J.
The extracted concept dictionary H. is now seen as a sparse and interpretable concept-based NOV to replace the original dense NOV G, (cf. Fig. 3). We modulate the original feature matching o(Fa,9 () in NOVUM with concept matching Φ( F,, H) that establishes correspondences between F& and new volumetric representation H. = [H H4;.... Hy] E R DDCC" Eq. (1) thus becomes
Sy = ((F2, Hly) )= = Σ max fo n0) fe-1
(2)
D
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2D Image
(a) Cuboid
(b) Sphere
(c) Ellipsoid
(d) Prototype CAD
More accurate shape approximation
NOV shapes for approximating object class Bicycle. Here Gaussians are evenly dis- tributed on the surface of each volumetric type.
Figure 5:
This reformulation, illustrated in Fig. 4b-c, enables feature matching against a compact and inter- pretable concept set instead of thousands of Gaussians, yielding sparser representations, stronger robustness, and more confident predictions compared to NOVUM (cf. Fig. 7). Both fr and h.)) are L2-normalised. Thus each dot product f: hgy in Eq. (2) is a cosine similarity in [-1, 1] which defines latent feature- crancet-concept alignment. Importantly, the score in Eq. (2) is computed exactly from activations of these volumetric concepts, preserving the faithfulness that NOVUM (Jesslen et al., 2024) also has while adding interpretability through sparse concept representations. These concepts emerge implicitly as geometrically grouuddd units through unsupervised clustering of Gaussian fea- tures, while poototype-based methods and CBMs learn concepts explicitly.
Attributing concepts with NOV-aware LRP. We aim to provide interpretable explanations on the input-level for our NOV-based concepts H. thereby demonstrating the model's reasoning through neural volumetric concepts. To achieve this, we build on LRP, well-established attribution method that traces relevances from the model's 's prediction back to the input pixels (Bach al., 2015; Ot- suki et al., 2024). A key principle of LRP is the conservation property, which requires the total relevance to remain constant throughout the network (Otsuki et al., 2024). However, we empiri- cally find that when directly applied to NOV-based architectures, LRP fails to uphold this property and instead unfaithfully leaks relevances (cf. Appendix Fig. I1). We address this by introducing a redistribution rule that preserves the conservation property through the concept-matchie 6(F,, H)), ensuring that the total relevance assigned to input pixels equals that at the concept level Ener, Rí: = ΣnER (h) Ry- This NOV-aware extension allows to correctly attribute predictions through volumetric concepts with LRP, enabling robust and reliable concept explana- tions even under challenging OOD conditions. Full derivation is provided in Appendix C.
operator
4.2 EXTENDING NOVs: WEAK 3D SUPERVISION AND MORE EXPRESSIVE SHAPES
Learning with weak 3D supervision. One notable limitation of NOV-based classifiers is that they assume access to ground-truth 3D pose annotations during training (Jesslen et al., 2024). Here, relax this requirement by training CAVE with estimated object orientations from Orient- Anything (Wang et al., 2025b). While the weaker supervision introduces some performance drop, especially under OOD nuisances (ef. Appendix E2), it shows that NOV-based classifiers can operate without explicit pose annotations, allowing for better scalability. Unless stated otherwise, we use CAVE with estimated poses for fair comparison ad-hoc baselines in our setting.
More accurate shape approximation. Typically, NOV-based classifiers such as NOVUM use sim- ple shapes such as cuboids and spheres, which provide a coarse volumetric approximation of objects. We broaden the scope by adapting NOVs to more expressive geometries: ellipsoids and prototype CADs (cf. Fig. 5), which serve basis for our concept extraction. We adopt ellipsoid NOVs in setup, given their favorable trade-off between OOD accuracy and interpretability (cf. Appendix H).
3D CONSISTENCY OF CONCEPTS
Evaluating concept consistency is challenging. Prior works often rely on part annotations (Huang et al., 2023; Behzadi- -hormouui Oramas, 2023; Huang et al., 2024), which do not necessarily reflect what models actually learn, since training optimises task accuracy rather than alignment with pre-defined parts. Object geometry, however, provides a natural reference: meaningful, it should consistently map to the same semantic region of the object under different poses or OOD factors. We call this property 3D consistency (3D-C) (cf. Fig. 6, in-distribution). For instance, the concept "front part of motorbike" is consistent if its attributions refer to the same part under distribution shifts such as weather, shape, or context (cf. Fig. 2, OOD). Our 3D-C thus complements existing metrics with principled alternative independent of part annotations.
a concept is

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Cabinet
Bicycle
Forldijt
Busket
Ax
NOVUM ICE
Less Conssitent
3D-C1
0.28
0.15
0.14
0.15
0.12
TesNer
3D-C1
0.13
0.07
0.11
0.07
0.08
More Consistent
Ours
3D-C1
0.46
0.24
0.20
0.30
0.25
Figure 6: CAVE (Ours) produces most consistent concepts across different classes, compared to NOVUM + ICE (best post-hoc) and TesNet (best ad-hoc). We highlight how consistent concept by aggregating concept relevance scores from class-wise test images onto object mesh, and report class-wise 3D-C scores below each row. Higher 3D-C means more consistent mapping to the same region. See Tab. for full quantitative comparison with baselines.
To compute the 3D-C score of a concept h in class y. we project its positive attributions A+ (x, h) E B. HxW from test images x E X, the CAD model of class y, This projection ground-truth 3D poses when available, and estimated poses from Orient-Any Anything (Wang et al., 2025b) otherwise. Formally, we define the mapping Ωy : # x + 11,,,, where Qy denotes the set triangles in the CAD model of class y that represents the object's surface. Given concept and an input image x of class y, Sly maps the positive attribution map A+ h), onto the corresponding oriented CAD of all projected attributions falling onto it. We denote by (i, a pixel position in A (x, h) and by A (xay,, /t) the positive attribution given to this pixel. Concretely, define the output vector Q2y (A+ + (a,, h)) component-wis as:
model and aggregates, for each triangle q Qy: the
Σ
A A
(KJ))P
where p)()) is the set of pixel positions (i,j) whose projection falls onto triangle E 2g of the CAD model of class y. For each concept we normalise the concept attribution A A+ (x. h) such that Eosse "!) (I....W) A (Zig. h) = 1. The 3D-C score for concept h across X, is defined as:
3D-C(X,,h)
= h)
Σ X
(2,(A*(z,))) (A+ b))),
(4)
which is normalised to [0, 1], where ny is the number test images in X, in which concept is present. We exclude concepts that occur in fewer than 7 % of test images of class y (here, choose 50), as they may appear spuriously consistent when evaluated on too few test samples. See Appendix D for further details on visualisation of concept consistency on object meshes.
EXPERIMENTS
Datasets and metrics. We evaluate CAVE with weak 3D supervision classification accuracy and 3D-C in two settings: (i) in-distribution on Pascal3D+ (Xiang et al., 2014) and large-scale ImageNet3D (Ma et al., 2024), and (ii) OOD OccludedP3D+ (Wang et al., 2020) (3 occlusion levels on Pascal3D+) and OOD-CV (Zhao et al., 2022) (nuisances in pose, shape, context, texture, and weather). We further assess spatial localisation (weighted loU with attributions) and object

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Locolise 1
Coverage
Conzistency (3D-C)
Models
Pascal-Par Part
Pascal3D+
ImageNeec3
OccludedPIDe
OOD-CV
Post- hot-h
NOVUM + CRAFT (Pel et al., 20236)
0.18
0.42
0.28
0.26
0.15
0.15
NOVUM MCD (Vielhuhen et 2023)
0.15
0.34
0.16
0.25
0.11
0.14
NOVUM ICE (Zhang al., 2021)
0.12
0.44
0.28
0.27
0.15
0.15
NOVUM
(Dreyer at.,, 2024)
0.11
LF-CBM (Olkarizen et al., 2023)
0.20
0.56
0.15
0.14
0.13
0.11
Ad-boc
ProtoPPeet (Chen et al., 2019)
0.22
0.43
0.19
0.13
0.21
0.09
TenNet (Wang 2021)
0.25
0.44
0.20
0.18
0.18
0.12
PIP-Net (Nauta al.,
0.12
0:09
MGiProto (Wang 2025a)
0.25
0.35
0.19
0.16
0.07
CAVE (Ouns)
0.28 (2: 0.001)
0.80 0.002)
0.49 (1L: 0.001)
0.40
(= 0.001)
0.23 (d 0.006)
0:24 (2L: 0.002)
CAVE (with fall 3D supervision)
0.28 (+) 0.001)
0.87 0.002)
0.42 (+: 0.001)
0.43 (= 0.00033
0.23 (+ 0.010)
0.26 (+: 0.001)
Table I: Concept interpretability evaluation using spatial localisation (whether concepts align with human-annotated parts), object coverage (extent of concept coverage over the object), and 3D consistency (3D-C) (concept stability across 3D viewpoints, independent of part annotations). CAVE trained with full 3D supervision (ground-truie 3D poses) are shown in gray text. Our CAVE produces concepts that are spatially localised, sufficiently diverse to cover the object, and robustly consistent across in-distribution and OOD settings. We report our results across 10 random seeds.
In-distribution
Out-of-distribation (OOD)
Wo Ground-truth
Models
3D Pose
Pascal3D+
ImageNet3D
Occluded P3D+
OOD-CV
LF-CBM (Oikarinen et al., 2023)
Yes
98.4
83.3
66.4
23.5
ProtoPNet (Chen ul., 2019)
Yes
97.4
74.0
60.5
71.2
TesNet (Wang et al., 2021)
Yes
97.6
77.9
63.8
70.1
Net-Net (Nauta et ul., 2023a)
Yes
95.7
$1.0
68.6
60.0
MGProto (Wang al., 2025a)
Yes
97.2
64.2
73.8
72.3
CAVE (Ours)
Yes
99.0 (+ 0.03)
84.6
0.02)
76.8 (+ 0.51)
80.3 (+ 0.27)
CAVE (with full 3D supervision)
No 99.4 (# 0.02)
88.5 (+ 0.03)
81.3 (= 0.30)
84.0 (+ 0.21)
NOVUM (with full 3D supervision)
No
99.5
88.3
81.7
81.3
Table 2: Classification accuracy (%, 1) comparison. We compare CAVE (Ours) trained with no 3D supervision (using Orient-Anything (Wang et al., 2025b)) against inherently interpretable models across both in-distribution and OOD datasets. Best and second best are highlighted. CAVE and NOVUM with full supervision. i.e., ground-truth 3D poses, are shown in gray text. CAVE achieves consistently higher accuracy, especially in OOD settings. CAVE with weak supervision delivers competitive accuracy without ground-truth 3D pose, with only a modest gap to full supervision. We report our results as the mean (+a, where a is standard deviation) across 10 random seeds.
coverage (concept comprehensiveness) on Pascal-Part (Chen et al., 2014), and concept faithfulness to model's predictions (Wang et al., 2024; Böhle et al., 2022; Rudin, 2019; Adehayo et al., 2018). See also Appendix G for dataset and metric details.
Baselines. We apply common post-hoe concept- based methods CRAFT (Fel et al., 2023b), MCD (Vielhaben et al., 2023), ICE (Zhang et al., 2021), )), and PCX (Dreyer et al., 2024) on NOVUM to make it concept-iinterppeaablle We also consider L.FCBMM (Oikarinen et al., 2023), and the proto- type learning approaches ProtoPNet (Chen et al., 2019). TesNet (Wang et al., 2021), PIP-Net (Nauta et al., 2023a), and MGProto (Wang al., 2025a), which are all inherently interpretable. We use ResNet-50 backbone for all methods. Post-hoe basclines extract concepts from NOVUM activa- tions. Unless explicitly stated, CAVE is learned with weak 3D supervision. The number of concepts per class is fixed to = 20 across methods. See further implementation details in Appendix G.
6.1 CAVE DISCOVERS SPATIALLY CONSISTENT CONCEPTS
Both NOVUM (Jesslen et al., 2024) and CAVE are faithful-by-dests since their predictions de- compose exactly over internal units (Gaussian features in NOVUM, region-level concepts in CAVE). CAVE achieves implicit interpretability by learning sparse, structured concept units from NOVUM's fine- fine-grained Gaussian features, effectively grouping them into geometrically-mennnge
concepts.
We evaluate concepts on: (i) spatial localisation, (ii) object coverage to measure the extent of con- cept comprehensiveness, and (iii) 3D-C to assess concept consistency across settings (Tab. 1). On Pascal-Part, CAVE with weak 3D supervision still provides stronger concept localisation and coverage than both ad-hoc baselines and post-hoc methods applied to NOVUM with full 3D super- vision. In particular, CAVE discovers diverse concepts that sufficiently cover average 80% of the object, whereas the next best method LF-CBM reaches only ~ 56%. We hypothesise that this higher coverage also supports CAVE in identifying concepts, for example, under occlusion.
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For 3D-C, post-hoe methods ICE and CRAFT benefit from the 3D supervision in NOVUM and extract more spatially consistent concepts compared to inherently interpretable baselines on in- distribution data. Their consistency, however, remains lower than CAVE's. In OOD scenarios, all methods show a decline in consistency. CAVE maintains the highest scores and thus comparatively shows that its concepts are more stable under distribution shifts. While only roughly approximated through an ellipsoid, CAVE's concepts still consistently map to meaningful and diverse regions on the object mesh, even under OOD shifts in Fig. and complex structures in Fig. 6.
6.2 CAVE MAINTAINS COMPETITIVE CLASSIFICATION ACCURACIES
The goal of CAVE is to be both robust and interpretable. We measure robustness in terms of OOD accuracy on OccludedP3DD and OOD-CV, and further report accuracy on in-distribution Pascal3D+ and ImageNet3D (cf. Tab. 2). We compare only to inherently interpretable methods, omitting post- hoc methods as they do not modify the underlying classification of NOVUM.
Across all datasets, CAVE with ground-truth 3D poses achieves performance competitive with NOVUM, even slightly surpassing it on large-scale ImageNet3D (+0.2%) and OOD-CV (+2.7%), while using much sparser representations. With weak supervision (no ground-truth 3D poses), CAVE shows comparatively mild drops in performance on ImageNet3D and OOD-CV relative to ground truth pose supervision. In the following, we report CAVE without ground-truth 3ID poses. On in-distribution Pascal3D+, all methods perform relatively well. However, when scaling to Ima- geNet3D, prototypical networks sharply degrade, with even the strongest TesNet almost 8% lower than CAVE (vs. 1.4% gap on the comparably small Pascal3D+). Under occlusion ranging 20 80% of the image in OccludedP3D+, CAVE outperforms the competitors by around 10%. Similarly, on OOD-CV, CAVE performs best (80.4% acc) with LF-CBM a distant second (73.5% acc) and other methods performing much worse. In summary, CAVE provides unique combination of inherent interpretability and robustness to OOD data unmatched by existing work.
6.3 ABLATIONS
Consistency across concept count. We study how the spatial consistency of concepts varies with the number of class-wise concepts D. As shown in Tab. 3, our 3D-C scores improve with more concepts under heavy occlusion, but overall remain stable across concept counts across settings.
Pascal3D+
ImageNet3D
OccludedP3D+
OOD-CV
Concept count
in-dist.
inst
22 40%% occ.
[40 60%] occ.
[00
80%% occ.
avg.
OOD muisumees
==
0.38 (1: 0.004)
0.42 (2: 0,002)
0.27 (:: 0.002)
0.22 (:: 0,01)
0.17 (1 0.01)
(:22 0.005)
0.24 (2: 0.003)
D 10
0.39 (1: 0.003)
0.41 (#: 0.001)
0.28 (4: 0.003)
0.21 (3: 0.005)
0.19 0.02)
0.23 0.007)
0.24 0.001)
0.40 0.001)
0.0013
0.29 0.002)
(1: 0.002)
0.20
0.006)
0.24 0.012)
D 40
0.41 (t: 0.004)
0.40 0.001)
0.29 (#: 0.001)
0.22 ( +: 0.001)
0.21 (# 0.01)
0.24( 0.003)
0.23 (4 0.001)
Table 3: 3D-C across concept count per class D E {5, 10, 20, 40) of our CAVE with weak 3D supervision. The results are reported as mean (#t) across 10 random seeds.
Sparsity-accuracy tradeoff. We study the effect of varying the number of class-wise concepts D in CAVE (5-90) compared to NOVUM's fixed ~ Gaussians per class (cf. Fig. 7a, b). CAVE achieves competitive accuracy with far fewer concepts, with a knee around = 20, yielding ~98% sparser representations that match or even slightly exceed NOVUM's performance, especially under OOD shifts. CAVE also produces more confident predictions with clearer class separation (Fig. 7c).
NOV-aware LRP. Our NOV-aware LRP yields spatially coherent attributions, even under OOD conditions such as snow and heavy occlusion, whereas vanilla LRP (Bach al., 2015) and Grad- CAM (Selvaraju et al., 2017) produce scattered explanations (cf. Fig 8). Empirically, vanilla LRP unfaithfully leaks relevance compared to our formulation (cf. Appendix Fig. Il). Our full ablation in Appendix I shows that our NOV-aware LRP is essential for reliable concept attribution.
DISCUSSION
CAVE preserves NOVUM's faithfulness while providing implicit interpretability. Its geometrically- grounded concepts emerge through unsupervised clustering and are directly used for prediction. While this differs from explicitly interpretable models, e.g., CBMs and prototype networks, which enforce semantic visual grounding through supervision, all these approaches design, concept-based models. Thus, we compare CAVE against these baselines for assessing con- cept quality and predictive performance across explicit and implicit forms of interpretabilityy
faithful-by-

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(a) In-distribuutin
(b) Out-of-disribation (OOD)
[c] Top-2 sore gap distribution
CAVR (Ded) PoweE))
NOWTH PoeelE:
CAVS (Dun) TTeagSesD
CMVR (Dwed
SO0TM Teag Naath
CANT COOLLY
NOVESS (300
CWTT (0ar)) QuladkiPih 12
NOVESH Oodd
Pacsitii
Number Coucepts
Nunbor Coucepto
Figure 7: CAVE replace 1130 dense Gaussians in NOVUM with compact concept dictio- nary. yielding ~ 98% sparser representations that match or slightly exceed the performance of NOVUM especially in OOD settings. Both trained with 3D supervision for fair comparison. We report mean accuracy in (a), (b) across 10 random seeds, with shaded regions as 22.. (c) shows improved model prediction; more confident predictions indicate clearer class separation, which improves reliability (Hendrycks & Gimpel, 2017) and explanation confidence (Nauta et al., 2023b).
Input
NOV-aware LRP
Vanilla LRP
GradCAM
Snow
Train
40-60% Occ.
Chair
Figure 8: Our NOV-aware LRP correctly attributes concepts and yields localised explanations, under different OOD settings: snow and 40-60% occlusion. Colors indicate the top-5 class- wise concepts per row and are not comparable across rows. See full ablation in Appendix Fig. 12.
Our 3D-C metric requires reference object meshes to assess the spatial consistency of concepts. While this limits evaluation to datasets with reliable CAD models such as Pascal3D+ (Xiang et al., 2014) and ImageNet3D (Ma al., 2024), advances in large-scale object meshes (Deitke et al., 2023) and mesh generation from text (Siddiqui et al., 2024) or image (Yan et al., 2025) are making high- quality proxies increasingly accessible. We expect paired image-mesh benchmarks to become more common, which in turn enables wider practical use of 3D-C XAI evaluation.
While our experiments focus single-object settings, CAVE not inherently limited this regime. The method can be extended by first detecting object candidates and then applying our concept matching each detected region, following standard pipelines pose estimation and object-centric 3D understanding (Khirodkar et al., 2022). We consider this promising direction for future work. Our current formulation assumes a fixed canonical shape, which is effective for rigid and moderately varying categories but does not directly capture highly non-rigid classes such humans. We leave this for future work. Furthermore, our weak supervision relies on Orient-Anything (Wang et al., 2025b) for pose estimation, which, although effective, is not perfect across all object categories (cf. Fig. E3). Nevertheless, we expect the fast progress in foundation models to further strengthen this component. Finally, we discuss challenging failure cases in Appendix K.
CONCLUSION
We proposed CAVE, 3D-aware image classifier that introduces concept-based NOVs to jointly achieve OOD robustness and interpretability. while also removing the need for ground-truth 3D poses. This enables faithful. concept-based explanations while retaining strong task performance across OOD settings. We further complement existing XAI metrics with our novel 3D-C to measure concept consistency, relaxing prior assumptions alignment with pre-defined part annotations.
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ACKNOWLEDGEMENT
Adam Kortylewski acknowledges support via his Emmy Noether Research Group funded by the German Research Foundation (DFG) under Grant No. 468670075.
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Interpretable 3D Neural Object Volumes for Robust Conceptual Reasoning
Appendix
This supplement provides additional technical details, experimental setup, ablations, and qualitative results supporting work robust and interpretable 3D-aware classification with CAVE. We strongly encourage readers to review NOV-aware LRP in Section C, and its corresponding ablation in Section I which highlights the stability of our proposed LRP adaptation, well the additional randomly sampled qualitative examples from our method CAVE Section L.
(A) Class- and Nuisance-wise Analysis under OOD Settings
(B) On Implicit versus Explicit Interpretability
(C) Layer-wise Relevance Propagation for 3D-Aware Classifiers
Further Details on 3D Consistency of Concepts
Learning with Weak Supervision
3D-Aware Classification with NOVUM
(G) Additional Experimental Details
Ablation: Shape of Neural Object Volumes
Ablation: Attributing Concepts with NOV-aware LRP
Ablation: Concept Extraction on Neural Object Volumes
KK) Discussion of Failure Cases
LL) Additional Qualitative Examples
(M) The Use of Large Language Models (LLMss)
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A CLASS- AND NUISANCE-WISE ANALYSIS UNDER OOD SETTINGS
We analyse class- wise performance of CAVE (weak 3D supervision) under different occlusion levels (Sec. A.1) and OOD nuisances (Sec. A.2). We further analyse whether pose errors introduced by Orient Anything estimates affect our model performance in Sec. A.3.
A.1 CLASS- WASS ACCURACY AND 3D CONSISTENCY UNDER OCCLUSION
Overall, CAVE maintains strong class-wise accuracy and 3D consistency under mild occlusion (L1), with performance degrading gradually as occlusion increases. The drop most pronounced for classes such as Boat, Chair, and Train. A similar trend appears in the 3D-C scores.
Occlusion Level
Aeroplane
Bicycle
db
Boxt
Bonle
d
Das
Cur
Chair
A
Dining Table
Motochike
Sofa
Thm
G
TV Monite
Lo [058] (indiscitation)
99.67
99,96
99.26
99.85
98.48
99.72
91.78
99.53
98.79
99.57
95.90
100,00
(=0.03)
L1 [20
07% occluded)
96.78
98.20
92.41
98.06
86.32
97.99
55.58
96.48
94,85
98.32
76.58
99.55
94.8 0.12)
L2 140
07% accluded)
$3.51
90:44
73,50
93.88
2..38
87.63
71.49
85.08
$4,02
94.89
57.10
91.03
82.8 0.40)
L3 [60 90% occluded)
40.60
62.50
41.05
81.35
21.44
52.11
44.81
60.24
52.41
83.71
32.35
57.41
(2.7 0.96)
Table A1: Class-wise Accuracy on Pascal3D+ (in-distribution) and OccludedP3D+ (L1, L2, L3 occlusion). We report overall accuracy (not the average of class-wise accuracies) in the last column. See Fig. Al for wlass-wise statistical variance across seeds.
+
A
Accoplane
Bicycle
Botte
Bus
Dining Tuble
Mooothike
Soda
Train
TV Monitor
LA [195] lin disutbetioo)
0,220
0.235
0.174
0.694
IL343
0.299
0.430
0.456
0.248
0,561
0.385
0.799
0.404 EL 0.0014)
[10 a/% cochuded)
0.153
0.150
0.497
0.19
0.186
0152
0.336
0.241
0.681
0.287 (t 0.001))
6/ wabuuell
0.108
110
0.855
0.14
0.117
0,88
0.384
0.169
0.581
0:11 0.0915)
occluded)
0.288
0.186
0.118
0.0166)
Table A2: Class-wise 3D Consistency Scores on Pascal3D+ (LO, in-distribution) and Occlud- edP3D+ (L1, L,2, L3 occlusion). We report the average 3D-C scores as mean (#: std) and class wise mean 3D-C scores only for readability. We denote for classes that do not have consistent con- cepts. See Fig. A2 for class-wise statistical variance across seeds.
Accuracy (%)
60
40
No Docuaion
Occlusion
L2 Ocolusion
1.3 Occiusion
soroplane
boyole
boaal
bottle
Chetr
dninglabble
molorblia
Buda
Irai
hymoptor
Class
Figure Al: Class-wise accuracy on Pascal3D+ (LO, in-distribution) and OccludedP3D+ (L1,
L2, L3 occlusion) across 10 random seeds. For precise values, refer Tab. A1.
A.2 OOD ATTRIBUTE (NUISANCE)- ACCURACY AND 3D CONSISTENCY
We show class-wise and attribute (OOD nuisance)- performance of our CAVE with weak 3D supervision on OOD-CV dataset (Zhao et al., 2022). Across OOD attributes, we observe that pose is the most challenging nuisance factor, leading to the largest drop in both accuracy and 3D-C across classes. Weather is the second most difficult attribute, likely due to reduced visibility and contrast in rainy or foggy conditions, as we have seen in qualitative examples in Fig. 2. In contrast, context, shape, and texture shifts result in comparatively moderate changes, with performance remaining relatively stable across most classes. These trends hold consistently across random seeds and are reflected in both accuracy and 3D consistency metrics.
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Consistency Comparison
Oocuution FOLL,NGL
FGL2 26122
FOLD DCL3
6.C
3D Cordistency
0.4
smoppere
Heyde
bodk
deongaatee
Lowo
Class
Figure A2: Class-wise 3D-C on Pascal3D+ (LO, in-distribution) and OccludedP3D+ (L1, L2, L3 occlusion) across 10 random seeds. For precise values, refer Tab. A2.
OOD Attribute
Context
Pose
Shape
Texture
Weather
Accuracy (%, 82.95 (= 0.20)
72.77 (# 0.77)
81.22 (#0.65)
83.27 (#: 0.61)
77.61 (# 0.39)
80.3 (#: 0.27)
31-C 0.236 0.006)
0.227 0.018)
0.239 0.004)
0.238 0.004)
0.234 0.009)
0.235 (+ 0.002)
Table A3: Attribute-wise performance, both accuracy and 3D-C across 10 random seeds, where context, pose, shape, texture, and weather constitute 25%, 8%, 15%, 22%, and 30% of the OOD-CV dataset. The last column reports the overall score computed over all attributes. We further break down the scores class wise in Tab. A4 & Tab. A5.
000 Artihen
Amcgllane
Begale
Cle
Divng Tibee
Monsikke
Thxe
all
$2.55 cs 0.20
$7.50
1.70
16.37
19 2551
91
117
3,17
15 m00
#338:1 0.006
15
59-911 1866
Stags:
13.8811
0,37)
M0.89 :2 145)
23 1 1.61
90
2 D0
65.33
1400
7117 c2 1.20
02.33 2.99
23,00c2 14
$5,07
9445
63.33
1,57)
81 12
Weather
$1.01 (- 0.8))
65 1.7
41 K3:0 1.5)
(533 555
14.20
130
(1 m000)
41 11 066
21 9100
$4.31 (- 1.46
0 0.333
Table A4: Attribute-wise accuracy per class of OOD-CV dataset averaged across 10 random seeds. We report the accuracy for each Pascal3D+ class under each OOD attribute (context, pose, shape, texture, weather), averaged across seeds. For each OOD attribute, we additionally report the overall accuracy computed over the union of all classes (rather than averaging class-wise accuracies), along with its statistical variance across seeds (last column).
OOD Attribute
Acroplane
Bicycle
Boat
Rus
Car
Chair
Dining Table
Motorbike
Sofa
Train
avg
Context
0,152
0.159
0.129
0.235
0.164
0.239
0.394
0.175
0.401
0.309
0.236
0.006)
Pose
0.155
0.164
0.127
0.247
0.169
0.212
0.375
0.169
0.338
0.307
0.227
0.018)
Shape
0.157
0,162
0.131
0.246
0.148
0.242
0.392
0.176
0.422
0,310
0.239 (2: 0.004)
Texture
0.173
0.136
0.235
0.163
0.235
0.174
0.416
0.238 0.004)
Weather
0.153
0.156
0.131
0.228
0.156
0.229
0.411
0.176
0.387
0.305
0.234 (4 0.009)
Table A5: Attribute 3D-C (f) scores per class averaged across 10 random seeds. We report mean 3D-C attribute scores for each Pascal3D+ class and OOD factor: context, pose, shape, texture, and weather. For class-wise attribute-wise statistical variance, refer Fig. A3. We further report average score across classes for each attribute along with its statistical variance across seeds (last column).
A.3 CLASS- WISE SENSITIVITY TO POSE ESTIMATION ERROR
We further examine class-wise accuracy and 3D-C to training pose estimation error in Fig. A4. We find that accuracy does not strongly degrade for classes with substantial pose ambiguity (e.g., Dining Table, Boat with azimuth error > 20%). In contrast, 3D-C exhibits mild downward trend as azimuth error increases, which is expected because 3D consistency directly measures geometric alignment. We hypothesise that, since CAVE is trained Orient Anything's estimated poses, it in- herits symmetric ambiguities present in those estimates. At inference time, symmetric objects (c.g., left-right symmetric boat) still activate the correct class concepts even if the pose is mirrore;;
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Consistonry Numence Type Aaress Olgeet Closses
230
330
230
170
360
339
2.13
111
Figure A3: Class-wise 3D-C for each OOD aftribute in OOD-CV dataset across 10 random seeds. For precise values, refer Tab. A5.
concept trained to fire on the left may instead fire on the right, without affecting the final classifi- cation. This symmetry-inen -induced "flip" effect naturally explains why classification accuracy remains stable while 3D-C scores decrease for classes with higher pose error.
Metric
Acroplanc
Bicycle
Beat
Bottle
Bus
Car
Chair
Dining Table
Motorbike
Sofa
Train
TV Monitor
Azimuth error (*)
10.14
12.92
26.94
6.86
7.25
6.71
10.09
20.15
12.03
8.58
8.46
9.53
Table A6: Class-wise Mean Azimuth Pose Error (in degrees 9) between Orient-Anything predic-
tions and ground-truth pose Pascal3D+.
Class wise Accuracy vs. Training Pose Error (Azimuth)
Class-wise 3D-C vs. Training Pase Error (Azimuth)
oeducio
90
Accurery
60
Pepb
LB ocduaion
02
30
LL ocdusion
oedusion
20
7.3
10.0
12.5
15.0
17.5
20.0
225
25.0
27.
7.5
10.0
12.5
15.0
17.
20.0
22.5
25.0
27.5
Moan Aoimat Ertor (dagress)
Moan Arrmuth Entor (degresa)
Figure A4: Class-wise accuracy (left) and 3D-C (right) as function of training pose errors (azimuth) in degree (*) across occlusion levels. The icons and their corresponding class names are defined in Tab. A6.
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B ON IMPLICIT VERSUS EXPLICIT INTERPRETABILITY
Interpretability methods differ not only in whether they provide post-hoc explanations or are faithful- by-design, but also in how the underlying concepts acquire meaning. Two complementary paradigms have emerged in the literature.
Explicit interpretability. Models in this category impose architectural or training-time constraints that bind internal units directly human-understane understandable notions. CBMs (Koh et al., 2020; Oikari- nen et al., 2023) explicitly supervise units to correspond to semantic concepts such as object at- tributes or part labels. Prototype-based networks (e.g.. ProtoPNet (Chen et al., 2019) and its vari- ants ( (Wang et al., 2021; Nauta et al., 2023a; Wang et al., 2025a)) explicitly ground units by enforcing a pro layer and projecting prototypes onto representative input patches, yielding "this looks like that" explanations. In both cases, the interpretability is explicit because the model is guided toward semantic or visually grounded concepts during training. These approaches are therefore faithful- -auuul-y--eee by-denign and offer direct, easily inspectable explanations.
Implicit interpretability. In contrast, implicitly interpretable approaches not impose semantic supervision or dedicated prototype objectives. Instead, they rely on structure that emerges from the model's learned representation. Post-hoc concept discovery methods such as CRAFT (Fel et al., 2023b), ICE (Zhang al., 2021), MCD (Vielhaben et al., 2023), and PCX (Dreyer et al., 2024) ex- tract interpretable structure from trained models by clustering or factorising latent activations. These methods provide implicit interpretability but not faithful, as their concepts do not participate in the model's forward computation.
CAVE occupies a distinct position within this paradigm: although its concepts are obtained im- plicitly through unsupervised clustering rather than semantic or prototype supervision, these units are geometrically grounded and integrated directly into the model's decision pathway. This yields faithfulness -ey-ssngg while still achieving interpretability implicitly from the geometric and fea- ture structure of the NOV representation. The resulting region-level concepts differ from the atomic Gaussian features in NOVUM (Jesslen et al., 2024) by providing coarser, more coherent, and casier-to-inspect basis for prediction that can be visualised post-hoc with adapted LRP. Im- portantly, each CAVE centroid (concept) is a linear combination of NOVUM's Gaussian features and therefore lies within the span of the original predictive units. CAVE's concept dictionary thus remains in the same predictive subspace while offering a more compact and interpretable represen- tation, preserving both accuracy and faithfulness.
To contextualise CAVE's interpretability within the litera- ture, we draw Molnar's taxonomy of intrinsic (inherent) interpretability. Molnar highlights that models can be inherently interpretable even when they "mix both interpretability by design and post-hoc interpretability", with his examples being models whose structure makes their computa- tion transparent and complexity appropriately constrained, even individual components require post-hoc visualisation be inspected (Molnar, 2025). CAVE thus fits the same paradigm of in- herent interpretability: its prediction is transparent by design, decomposing exactly over small dictionary of region-level concepts derived from Gaussian features, while our adapted LRP used for post-hoc concept visualisation.
Inherent interpretability of CAVE.
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C LAYER-WISE RELEVANCE PROPAGATION FOR 3D- 3D-AWARE CLASSIHEESS
As mentioned Section 4.1, layer- relevance propagation (LRP) defined for standard architec- tures unfaithfully leaks relevances when attributing NOV-based concepts to image pixels. To enable tracing relevance from the model's prediction backward through the concept-based NOVs H. to the input image (Bach et al., 2015; Otsuki et al., 2024), we extend LRP to our 3D-aware setting with volumetric object representation. In doing so, we also ensure that the key conservation property of LRP is preserved, i..., total relevance remains constant throughout the network (Otsuki al., 2024).
In the following, network (cf. Sec. C.I), and formulate NOV-aware LRP for NOVUM and CAVE-like architectures (cf. Fig. CI, Sec. C.2). Specifically, this tailored two layers: (i) upsampling by concatenation, and (ii) volume concept matching, that do not exist in standard architectures. We further show how to estimate concept-wisg importance scores and visualise concepts in Section C.3.
briefly explain vanilla LRP with r-lu that is defined for standard feedforward
C.1 VANILLA LRP WITH RULEE
Standard LRP with c-rule propagates relevances backward through network layers I + 1 to layer I:
R₂ = E j Ex arwyy + sign R2
0gW0i
(C.1)
where a; is the activation of neuron in layer 1, wa is the weight connecting neuron i in layer to neuron j in layer / + 1, R2 is the relevance of neuron j and R; the relevance propagate back to neuron i. Here the - rule is introduce to dampen relevance when the denominator gets arbitrarily small (Springenberg meaning:
al., 2015). An important property of LRP is its relevance conservation,
R
(C.2)
which is often violated if relevances are not attributed faithfully through the network.
C.2 LRP WITH CONSERVATION FOR CAVE
As described, vanilla LRP does not handle non-standard operation such as upsampling by con- catenation (no weight matrix defines a simple mapping from input to output channels), or concept matching via NOVs, which introduces structured multiplicative interactions between image features and NOV-based concepts. We thus formulate the LRP redistribution rule for these layers.
(i) Upsampling by concatenation. Similar to NOVUM (Jesslen et al., 2024), the basic CAVE con- tains feature extractor which consists of ResNet-50 backbone followed by three upsampling layers with concatenation. In this design, each upsampling layer combines feature maps from ear- lier layers, preserving fine-grained details important for 3D-aware classification. Let us consider an upsampling layer U, which concatenates in the channel dimension feature maps Ag E R H1 xW xC2 and A.ti
R M2 x W.2 xCas from two concecseee layers. A++1 is padded to A E R x
to maintain spatial consistency. We denote this concatenation operation as Au Ag + A Let us further denote RG, Ro, and Ro4t as the relevance scores at the upsampling layer and two non- consecutive layers, respectively. Byyt is the padded relevance of Ru+t. By conservation property, should hold that RG R. + Ry4
We define relevance- preseervineeeeiiiggge.. splitting follows:
Bout Ryl: H1: W1,: C2), Roti Rot 1(A+1))
R, RH 2H,, W 2W,, (CI Oz)]
where 1()) is the indicator function that is 1 for original non -on-dddded elements in Aut and 0 other- wise. After three upsampling layers, we obtain our feature map F, for 3D-aware concept matching.
(ii) Volume concept matching. For the concept matching (F H)) between NOVs-based concepts H. and image features F, E R #xxxX xC let the output be $œ E R2 #xW We further denote R&p #x as the relevance for the feature matching layer, and Ry. E R XXXXC as the relevance the feature map Fr. To ensure spatial consistency, relevance score r; Ro is first directly mapped to
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Ry
Ry = Bi + Ri
U
Aa
Avtl
Ac,
Avit
C1
C2
Re+
Relevance splitting at Upsampling layer U
TC
F
x
R4
Relevance splitting at Matching layer O
Figure CI: NOV-aware relevance propagation CAVE. Top: At upsampling layer U, feature maps A, and A,-1 from non-consecutive layers are concatenated along channel dimension after padding for consistency. Relevance
Ry is split into R2 and R where R,41 is padded Rv+1. Bottom: We ensure spatial consistency by mapping relevance Rs at matching layer to corre- sponding feature fa Fa, then distributing channel-wise with NOV-weighted feature importance.
the corresponding feature fi Fz, and then further distributed channel-wise for each channel (cf.
Fig. C1). We get
C
C
IPPatial (1) = (1) = =
Σ
r4 Σ o H,H
J=1
1=1
(HOH)))) Elf & H2,
RP (i,c) Rspatial
where Hy, denotes the matching NOV-based concept for f. and c denotes element- wise multiplica- tion. integrate our formulation with LRP with conservation for ResNet-50 (Otsuki et al., 2024). In Section I, we provide the full comparisons between our NOV-aware LRP and other common attribution methods, including vanilla LRP.
C.3 EXPLANATIONS THROUGH VOLUME ALIGNMENT
Concept Importance through NOVs. Our next goal is to estimate the importance of all class-wise concepts in H using the NOV-aware LRP attributions. The intuition behind this is straightforward: starting from the model's softmax output, we trace back relevance each concept. The concept importance score is then determined using its x% quantile (e.g.. 90th percentile) across the training dataset capture the most representative high-relevance values while being robust to outliers. We denote the matching NOV-based concept in H for the feature map Fz as FF.-H. We compute the relevance for a concept (,))) H of class y by aggregating the relevance scores, denoted Rgs at all spatial locations where AF hyy (i) Formally, it is defined as:
R
Σ i
Rg 1 - "xx==x(()==
Concept visualisation. We visualise class-wise NOV concepts (. H by redistributing their rel- evance scores & (Sec. C.2) to pixel space and highlighting locations with positive contributions.
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D FURTHER DETAILS ON 3D CONSISTENCY OF CONCEPTS
As introduced in Section 5, our 3D consistency (3D-C) metric evaluates whether a concept remains consistent across test images of the same class. Unlike prior metrics (Huang al., 2023; Behzadi- Khormouji & Oramas, 2023; Huang et al., 2024), our 3D-C removes the need for part annotations and avoids assuming that concepts must align with human-defined parts, an assumption often not enforced explicitly during training. Instead, 3D-C complements existing measures such as spatial localisation and object coverage by leveraging object geometry to project concept attributions onto common 3D space (cf. Fig D1). In this section, we further describe 3D-C visualisation details.
Ours
NOVUM + ICE
NOVUM CRAFT
LF-CBM
ProtoPNet
TesNet
Figure DI: CAVE (Ours) shows more consistent concepts compared to both post-hoc and ad- hoc methods. Here, show top-5 most important (left to right, color-coded) concepts of class Bicycle for each method. CAVE visually shows better concept consistency in comparision to strong baselines (see also quantitative evaluation in Tab. 1).
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Object mesh. For each object class y, we load the canonical CAD mesh available in the datasets such as Pascal3D+ (Xiang et al., 2014) and ImageNet3D (Ma et al., 2024). Since these meshes fol- low CAD-centric coordinate convention that is inconsistent with the camera system of PyTorch3D, we apply a pre-processing step to re-align the axes, i.e.:
I Y/
CAD
Rendering, Rendering is performed with PyTorch31 We use image canvas of 640 x 800, and adjust camera intrinsics such that focal lengths are scaled to preserve field of view, and the principal point is placed at the image center. Addtionally, adopt spherical camera radius 15, elevation 30,, and azimuth -400 Rasterisation is done with a single face per pixel and no blur radius.
Concept attribution projections onto object mesh. Concept attributions are then projected onto the mesh. For each concept h, we use its positive attributions A (ax, h) defined as:
A+ h) max (0, h))
to highlight regions that contribute to this concept h. We assign these values as per-face textures on the CAD mesh and render with PyTorc33,, where barycentric interpolation distributes per-face attributions to pixels, yielding dense per-pixel attribution map.
3D-C visualisation. For visualisation, we first render a neutral base mesh to provide geometric context and occlusion boundaries. Positive attributions A+ h)) for concept f then overlaid as heatmap on this render, given the pixel-to-face face mapping from the projection step. To characterise the overall spatial footprint of the concept h, we aggregate attributions across all test images x X, of class y, i.e.:
At (h)
Σ (x,,h) =EX,
followed by min-max normalisation [0, 1] for the final visualisation. This naturally provides direct visual illustration to the 3D-C metric scores, showing concept consistency across instances.
Limitations and scope. While our 3D-C metric relies on class-level CAD meshes and face-level attribution aggregation, which may smooth out very fine-grained details, this design ensures scala- bility across large datasets and consistency of evaluation. By not enforcing alignment with human- annotated parts, 3D-C sidesteps annotation biases and instead directly reflects the model's own con- cept structure. Finally, canonical meshes do not capture all intra-class shape variations. Yet, they provide stable reference geometry that enables meaningful comparisons of concept consistency across object instances.
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E LEARNING WITH WEAK SUPERVISION
Recent advance in object orientation estimation, such as Orient-Antthin (Wang et al., 2025b), allows to relax the constraints pose annotations during training 3D-aware classifiers. We study how accurate Orient-Anything estimated poses are compared to ground-truth poses Pas- cal3D+ (Xiang al., 2014) and ImageNet3D (Ma et al., 2024) in Tab. El. With the tolerance X = 60%. Orient-Anything poses achieves near-perfect accuracy on polar and rotation estimation on both Pascal3D+ and ImageNet3D. For azimuth estimation, Orient-Anything performs better Pascal3D+ (~> 96%) while struggles on larger-scale dataset like ImageNet3D (~ 72%). A stricter tolerance thresholds introduce performance drops both datasets. Our inspection shows that fail- ures of Orient-Anything in predicting object pose often occur with symmetric objects such as tables and boats, where correct orientation is often ambiguous. See also Fig. E2 and Fig. E3 for qualitative visualisations.
Azimuth Estimation
Polar Estimation 1
Rotation Estimation
Class Label
(3)
(g"
10% 4T
(0)
(0)
10
60%(3)
()"
10 18
Pascal3D+
96.70
93.92
71.58
99.77
98.82
86.25
99.57
99.14
93,09
ImageNet3D
72.32
48.06
27.63
94.69
79.92
51.31
96.92
95.10
90.11
Table E1: Accuracy (%, 1) of zero-shot orientation estimation by Orient-Antthing (Wang et al., 2025b) training images of Pascal3D+ and ImageNet3D. Accuracy is reported within different tolerances of + with X {60?,300 100} (i.e., { /3, x/6, 7/18} radians).
Atimuth
Polor
Rotation
Contolence
0.6
0.2
Figure El: Prediction Confidence on Pascal3D+ of Orient-Anything (Wang et al., 2025b) across Azimuth, Polar and Rotation with respect to different tolerences of = with X {60,,30% 10º} (i.e., (T/3,n n /6, x x/18} radians). Orient- Anyth-nn produces consistently high- confidence predictions across both correctly and incorrectly classified samples.
Orient- Chient-Anythigg poses can be treated as pseudo ground-truth enabling weakly supervised training of CAVE without requiring manual pose annotations. Importantly, CAVE maintains competitive performance across all datasets, even under weaker supervision (see Tab. E2), while being substan- tially more parameter-effcient by representing each class with only D 20 concepts (roughly 98%
fewer than NOVUM's 1 130 Gaussians per class).
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Input Image
Ground-truth
Figure E2: Qualitative visualisation of accurate pose predictions (azimuth error < 109) by Orient-Anything (Wang et al., 2025b).
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Input Image
Ground-truth
Figure E3: Qualitative visualisation of inaccurate pose predictions (azimuth error 60%) by Orient-Anything (Wang et al., 2025b).
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Ground-truth 3D Pose
Orient-Anything 3D Pose
Models
P3D+
IN-3D Occ-P3D+
OOD-CV
P3D+
IN-3D) Occ-P3D+
OOD-CV
NOVUM
99.5
88.3
81.7
81.3
98.4
85.7
77.3
79.7
CAVE (ours)
99.4
88.5
81.5
84.0
99.0
84.7
77.4
80.4
Table E2: Accuracy (%, ?) of NOVUM (Jesslen al., 2024) and CAVE (ours) under full super- vision (ground-truth pose) and less supervision (generated pose via Orient-Anything (Wang et al., 2025b)). Results are reported on two in-distribution datasets Pascal3D+ (P3D+) and ImageNet31 (IN-3D), and two OOD datasets OccludedP3DD Occ-P3D+) and OOD-CV. Best scores are in bold. CAVE uses = 20 concepts/class, roughly 98% sparser than NOVUM (1130 Gaussians/class).
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F 3D-AWARE CLASSIHICATION WITH NOVUM
Training, NOVUM (Jesslen et al., 2024) is trained using feature-extractor backbone such as ResNet-50 and, for each class, a neural object volume (NOV) composed of 3D Gaussian primitives that emit feature vectors, as defined in Section 3. Full details of the training pipeline can be found in the original paper, but we provide here an overview of the different objectives that come into play during the training of NOVUM. During training, three main objectives are used:
Intra-object discriminative loss: Gaussians I: E Gy. also can be written as 93 be con- sistent with the main paper, of class NOV are trained to produce distinguishable features, thus different object regions are represented by different primitives.
Discriminative feature loss across classes: features produced by Gaussians of one class y. i.., 9m Gg. are encouraged to be distinct from those of other classes y.
the model is trained to separate object features ft E Fg from background features B, ensuring focus on object-specific regions.
Background contrastive loss:
Formally, we define the constrastive learning
к Ok log
[(G
(F.1)
Afx-100 + Wg
C + Wg
Σ
91 EGy 9I
A.EB
gm Egg
where 0k E {0,1} indicates the Gaussian visibility, R. is a concentration hyperparameter which determines the spread of the von von-Mieses- Fisher distribution of the Gaussians Js, Wg and wi indicate the probability that an image feature Sa E Fg corresponds to the background features B or Gaussians of class y. and N₂x {g. || Mr ll < 5, k * r) is the neighborhood of a Gaussian 9k with mean μa defined within a radius 8. Furthermore, fR denotes the extracted feature fi that Gaussian go projects to.
Importantly, all these losses require 3D pose supervision, which is provided by the dataset. Since each Gaussian primitive must be projected from 3D to the 2D image plane, the knowledge of the object pose is necessary. We relax this constraint in our CAVE with weak supervision from Orient- Anything ( (Wang et al., 2025b) estimated pose, and find that replacing ground-truth poses with noisy pseudo ground -rouh still yields strong performance in in-distribution and OOD settings (cf. Sec. E). Additionally, note that during training, the intra-object discriminative loss encourages nearby Gaussians to remain close in feature space while pushing apart those that are spatially distant. This reduces the influence of their spatial arrangement NOVUM demonstrates that replacing the underlying cuboid shape with a sphere, an ellipsoid or prototype CAD has minimal effect on model accuracy (cf. Appendix Tab. HI).
the learned representation. To support this,
Inference. At inference time, NOVUM classifies images by matching backbone features against the dense set of Gaussian features learned for each class. Each image feature compared to the ~ 1130 Gaussians per class, and the class score is obtained by aggregating the maximum similarity responses across spatial locations. As shown in Fig. 7, this dense matching yields only a thin decision margin, making predictions less robust and, more importantly, difficult to interpret. In contrast, our approach drastically reduces the number of Gaussians, producing clearer decision boundaries and enabling a more transparent understanding of how predictions arise.
Visualisation of NOVUM's feature matching. Given NOVUM's explicit volumetric object rep- resentations, i.e., NOVs, the visualisation of its feature matching between the learned Gaussian features and image features may give some insights into which parts of the images contribute the most to the classification decision (cf. Fig. 3). Nevertheless, its classification relies on thousands of Gaussian matches do align with semantic parts or human-understandable concepts.
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G ADDITIONAL EXPERIMENTAL DETAILS
In this section, we provide a comprehensive review of our experimental setting to ensure repro- ducibility for future research. We will release the codebase and relevant checkpoints upon publica- tion. We first describe the datasets (Sec. G.1) and interpretability metrics G.2 in our experiments. Finally, we detail training hyperparameters used our CAVE and baselines in Section G.3.
G.1 DATASETS
We follow the setup in NOVUM (Jesslen et al., 2024), which evaluates on three datasets Pas- cal3D+ (Xiang et al., 2014), OccludedP3D+ (Wang al., 2020) and OOD-CV (Zhao et al., 2022), and extend this setting to include the large-scale ImageNet33D (Ma et al., 2024). We further evaluate concept interpretability on Pascal-Part (Chen et al., 2014).
Pascal3D+. The Pascal3D+ dataset (Xiang et al., 2014) is a common benchmark for 3D object understanding. It augments 12 object class from the PASCAL VOC detection dataset (Everingham et al., 2010) with 3D annotations, and further includes images from ImageNet (Deng et al., 2009) for these categories. In total, Pascal3D+ consists of roughly 30000 images, with 8505 Pascal images and 22394 ImageNet images. Each class consists of about 3000 images on average, covering wide range of viewpoints and intra-class shape variations.
ImageNet3D. The ImageNet3D dataset (Ma et al., 2024) is large-scale dataset of natural images that extends the ImageNet dataset Deng et al. (2009) with pose annotations. It contains 200 diverse object classes, and consists of more than 86000 images in total, Only 189 object classes are currently available in ImageNet3ID with sufficient annotation quality (Ma et al., 2024).
OclcudedP3D+. The OccludedP3D+ dataset (Wang et al., 2020) is test benchmark that builds upon Pascal3D+ (Xiang et al., 2014) and evaluates OOD robustness against three different lev- els of simulated occlusion, ranging from mild (20-40%) to heavy (60-80%) occlusion. Similar to Pascal3D+ (Wang et al., 2020), this dataset contains 12 rigid object classes. Respectively, Oc- cludedP3D+ consists of more than 10400 images for L1 (20-40%) occlusion, 10200 images for L2 (40-60%) occlusion and 9900 images for L.3 (60-80% occlusion.
int-of-Distribution-CCV (OOD-CV). The OOD-CV dataset (Zhao et al., 2022) is test benchmark that introduces OOD examples for 10 different object classes. In specific, it has diverse real-world OOD nuisance factors including shape, 3D pose, lexture, context and weather. Overall, the OOD- CV consists of 2632 images with these aforementioned OOD nuisances collected from the internet and additionally 2133 test images from Pascal3D+ (Xiang et al., 2014).
Pascal-Part. The Pascal-Part dataset (Chen et al., 2014) introduces additional aaman--nnotated part labels for the PASCAL VOC 2010 (Everingham et al., 2010) dataset. It covers 20 object classes, consisting of 10103 training and validation images and 9637 test images. Additionally, provides silhouette annotations for classes without consistent parts such as Boat. We filter the dataset to include 12 object classes in Pascal3D+ and cross-reference them to identify test images that also appear in Pascal3D+. We use this dataset to evaluate two metrics introduced by prior works, namely spatial localisation and object coverage, that will be described formally in Section G.2 below.
G.2 METRICS
In the following, we further describe interpretability metrics used in our evaluation.
Model faithfulness evaluates whether a concept truly reflects what the model uses to make a pre- diction (Rudin, 2019; Böhle et al., 2022). By design, faithful, while post-hoe methods, which only approximate model computations, are not. Ensuring model faithfulness is important, since it determines whether an explanation can be trusted, for ex- ample, in safety-critical and high-stake downstream applications.
models are model-
Spatial localisation evaluates whether an explanation of a concept is spatially well-localised within ground-trui object part (Huang al., 2023; Sahzadi-Khormoujjj & Oramas, 2023; Schulz et al., 2020). Localisation can be measured by Intersection-over Union (IoU) between concept explanation and semantic part annotations, but this does not differentiate between pixels with varying attribution
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strengths, treating all contributing pixels equally. Therefore, use IoU weighted with attributions, defined similarly to Dice-Sørensen coefficient that has been previously used in XAI evaluation (He et al., 2023). Specifically, given an input image z, denote the attribution of a concept h at each pixel location (i as (i, Then, the spatial localisation score of concept h with respect to part by in image x: is computed as:
SL), Eis 4 (1,5) 1x(1.)) + (1(1))) (x(1.)
(G.1)
((.5) + Ei, lx(i.))
where (1, is the positive attribution given at pixel (i.j), and score (T.,.(r)) [0, with higher being better. A concept h with a good spatial localisation not only has high attributions in ground-truth region by but also covers it well. As described, this metric requires human-annotated parts and will be evaluated on Pascal-Part (Chen et al., 2014). For each image and each concept, we identify the ground-truth part that the concept is most aligned with and compute the spatial localisation score with respect to that part. The spatial localisation for concept in image is thus defined as:
(T) max (T.,
These per-image scores for concept h are then averaged across all test images of the same class to obtain a concept-level localisation score. These concept-level scores are then averaged per class. The dataset-level score is then obtained by averaging these per-class scores, and reported in Tab.
Object coverage measures the extent of concept comprehensiveness, i.e., how well discovered con- cepts cover the object (Zhu et al., 2025). This is especially crucial in case of occlusion, where a well-covered set of concepts improves robustness parts. We first normalise the attributions such that the total attribution across all concepts for a given input image x sums to 1. This means that if the union of all concepts perfectly collides with the ground-truth object mask, the coverage score is 1. This also ensures fair and consistent compari- across methods. The normalisation is computed follows:
it can still identify other visible, unoccluded
A (i.))
(1,5)) Σn Eig A (i.5)
(G.2)
For an input image æ, we define the object coverage score as
CoV (x) = Σ>>
Σ
A (1,
phoollojject mark (i,
(G.3)
Naturally, Covobjear(:)) E J0, for both cases, with a higher score means better coverage, and thus a more comprehensive set of concepts. This metric also requires ground-truth object masks, and is here evaluated on Pascal-Part (Chen et al., 2014). Each test image yields an object-coverage score. We average these scores over all images of a class obtain a class-level value, and then average the class-level values across all classes to obtain the dataset-level score reported in Tab. 1.
3D consistency (3D-C). We propose the 3D-C metric to complement existing evaluation metrics that relies heavily on pre-defined part labels. We describe this metric in detail in Section D. Our 3D-C allows for evaluation across 4 datasets: Pascal3D+ (Xiang et al., 2014), ImageNet3D (Ma al., 2024), OccludedP3D+ (Wang al., 2020), and OOD-CV (Zhao et al., 2022).
G.3 IMPLEMENTATION DETAILS
Our experimental setting requires training our CAVE as well as baseline methods on two datasets: Pascal3D+ (Xiang et al., 2014) and ImageNet3D (Ma et al., 2024). Our evaluation on the afore- mentioned metrics in Section G.2 is then done on five datasets: Pascal3D+ (Xiang et al., 2014), ImageNet3D (Ma et al., 2024), and two OOD datasets Occluded-P3D+ (Wang et al., 2020) and OOD-CV (Zhao al., 2022), and part-annotated Pascal-Pan (Chen et al., 2014).
In the following, we detail the training setup for our CAVE as well as for the baselines. For a fair comparision, our CAVE and all baselines use ResNet-50 backbone. In NOVUM (Jesslen et al., 2024), the 5e backbone was extended with two upsampling layers by concatenation for NOV alignment. Our CAVE adopts the same architecture.
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Training Hyperparameter
Value
Input resolution
640 x 800
Backbone
ResNet-50
Training batch size
38
Total epochs
200
Learning rate
1 x 10-4
Learning rate decay
x0.2 every epochs 0.9
Momentum update of Gaussian features
Weight decay
1 x 10-1
Gradient accumulation
10 steps
Temperature T
0.07
Noise weight
0.005
Distance threshold
48
Number of background features for momentum update
Table G1: Training hyperparameters used in CAVE (Ours) and NOVUM (Jesslen et al., 2024).
CAVE (Ours). Our model training, similar to NOVUM (Jesslen et al., 2024), uses input images of size 640 x 800. The ResNet-50 backbone produces the output feature map Fz by downsampling the input spatial resolution by factor of 8. Training on Pascal3D+ takes approximately 24 hours, while training on ImageNet31) requires about 72 hours on a single NVIDIA H100 GPU. As mentioned in section 4, we ellipsoid as volumetric surface of Gaussian features, computing its vertices and faces based on parametric sampling where a mesh is returned with roughly 1000 vertices. We summarise our training hyperparamters
the Tab, GI. Once the model is trained, we filter out Gaussian features with low visibility (< 0.1 of training data), and apply K-Means clustering for concept extraction with 20 clusters per class (i.e., D 20 following notation Sec. 4).
Baselines. For baseline methods, follow the original implementation, training details, and con- cept visualisation provided by the authors:
1. For NOVUM (Jesslen et al., 2024), the training follows the same hyperparameters in Tab. GI. We obtained the model checkpoint for Pascal3D+ from the NOVUM's code- base (Jesslen et al., 2024), and trained NOVUM from scratch for ImageNet3D.
2. For post-hoc methods CRAFT (Fel et al., 2023b), ICE (Zhang et al., 2021), I), and PCX Dreyer et al. (2024), we used the exact setting provided in their codebases. We set the number of class-wise concepts to 20. For MCD-SSC, we used completeness threshold 0.9, which determines the extent to which the discovered set of concepts jointly cover model predic- tion. The concepts were extracted from NOVUM's activations for each method.
3. For LF-CBM (Oikarinen et al., 2023), we followed the codebase instructions to generate a concept set for each dataset from GPT-3 model, resulting 441 concepts for Pascal3D+ and 710 concepts for ImageNet3D. We trained a ResNet-50 label-free CBM using their hyperparameters: input resolution 224 x 224, learning rate 0.1, and batch size 512, CLIP model ViT-B/16, and interpretability cutoff 0.45. Unlike post-hoc approaches, where the number of concepts is fixed at 20, label-free CBM learns this number dynamically. For Pascal3D+, we observed 297 non-zero weights out of 5292, yielding roughly 5% sparsity. For ImageNet3D, we observed 4058 non-zero weights out of 128709, yiedling 3% sparsity.
4. For prototypical networks such as ProtoPNet (Chen et al., 2019) and TesNet (Wang et al., 2021), we used the same training hyperparameters from their codebases: input resolution 224 x 224, log as prototype activation function, with regular add-on layers. a training batch size of 80, and training push batch size of 75. The learning rates for features, add-on layers, and prototype vectors are set to le - 4. 3e 3. 3e 3 respectively. with a joint learning rate step size of 5. The projection (push) step was performed every 10 epochs. The network was trained for 200 epochs without a warm-up period or extensive data augmentation to ensure fairness across baselines.
5. For PeP-Net (Nauta et al., 2023a), we trained the network using the hyperparameter settings from its codebase, with input resolution 224 x 224. During pre-training, used batch size
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of 128 and trained for 10 epochs. For the main training phase, used a batch size of 64 and trained for 200 epochs. The learning rate was set to 0.05 with no weight decay.
We also find that post-hoc methods such Fel et al. (2023b) threshold their attributions to reduce noise in their concept visualisations. For a fair qualitative comparision, we apply the same 90%-th quantile threshold across basclines that requires it for concept visualisation. Our method CAVE does not require such thresholding, as its attributions are correctly propagated for each concept with our NOV-aware LRP input pixels.
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H ABLATION: SHAPE OF NEURAL OBJECT VOLUMES
For fair comparision, we use full 3D supervision, i.c., with ground-truth 3D poses, for both NOVUM (Jesslen et al., 2024) and CAVE (Ours) in this ablation across different shapes of the neural volumes, including simpler shapes in NOVUM such as cuboids and spheres, and more expressive shapes such as ellipsoid and prototype CADs.
At first glance, CAVE is able match roughly D = 20 class-wiss wise concepts, yielding 98% sparser representation compared to NOVUM's 1130 Gaussians per class (cf. Fig H1).
slightly exceeding NOVUM's performance with
PrecalSD+ (unlittribuii
ImageNettD (indistribution)
OOD-CV ausenness
Accuray (15)
06.1
80-
96.
85-
80
72-
10
20
70
10
14
20
30
50
Oxcltded
[LL occ. 20 4099)
OcclndedP3D
[12 oce. 40 60%)
OceladedPPD (L3 cos. 60 SCR))
07.0
08.0
A0oura (51
06.8
780
10.0
82-
Consappto per
pem
Vamber Comoeppt (D) pur
NOVUM (boadime)
CANE (zubood))
CAV' (ellipeed))
CAVE Probotyne CAD)
CAVD (spherc)
Figure H1: CAVE with ellipsoid NOVs matches or slightly exceeding NOVUM in most cases with only D 20 concepts per class, compared to NOVUM with roughly 1130 Gaussians class. Compared to other shapes, ellipsoid NOVs give an advantage large-scale dataset ImageNet3I., heavy occlusion in OccludedP3D+ and OOD-CV with challenging nuisances.
Dataset
P3D+
ImageNet3D
Occluded P3D+
OOD-CV
Occlusion
1.0 (0%)
1.0 (0%)
(20
40%)
1.2 (40 60%)
1.3 (60 80%)
Nuisances
Sphere
99.2
85.8
96.7
86.3
57.9
81.6
Ellipsoid
99.4
88.6
97.0
87.5
58.9
82.4
Prototype CAD
99.5
87.7
97.3
58.6
83.3
Cuboid (default)
99.5
88.3
97.2
88.6
59.2
81.3
Table HI: Accuracy (%, 1) of 3D-aware classifier NOVUM on two in-distribution dataets Pas- cal3D+ (P3D+) and ImageNet3D, and on two OOD datasets Occluded-P3DD and OOD-CV, evalu- ated across different neural volume shapes. Best and second best are highlighted.
Dataset
P3D+
ImageNer3D
Occluded P3D+
OOD-CV
Occlusion
LO (0%)
Lo (0%)
LI (20
40%)
L2
(40 60%)
L3 (60
80%)
Nuisances
Cuboid
99.4
88.2
86.6
54.7
82.2
Sphere
99.0
85.3
85.0
56.5
79.8
Prototype CAD
87.7
97.1
59.0
83.5
Ellipsoid (default)
99.4
88.5
97.3
87.8
59.3
84.0
Table H2: Accuracy (%, 1) of CAVE (ours) with D = 20 class-wise concepts on two in ii-distribution dataets Pascal3D+ (P3D+) and ImageNet3D, and on two OOD datasets Occluded-Pai -PDD+ and OOD- CV, evaluated across different neural volume shapes. Best and second best are highlighted.
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Coverage
Shape
IoU f
Spatial Localisation t
3D-C1
U Parts
Object
Cuboid
0.150
0.264
0.368
0.873
0.402
Sphere
0.148
0.263
0.367
0.870
0.394
Ellipsoid 0.156
0.277
0.368
0.865
0.417
Prototype CAD
0.169
0.305
0.378
0.874
0.426
Table H3: Interpretability evaluation of CAVE across different neural volume shapes with D 20 concepts per object category on Pascal-Parr with different benchmark metrics. In specific, Part loU, Spatial Localisation (weighted IoU with attributions), Global Coverage assessing both object coverage and union annotated parts, and our proposed metric 3D Consistency (3D-C) to assess spatial consistency of concepts across images. Best and second best highlighted.
In terms of performance, while there is no consistent gain in NOVUM with particular NOV shape (cf. Tab. HI), CAVE with more expressive shapes like ellipsoid and prototype CAD performs rela- tively better in heavy occlusion (OccludedP3D+ L3), and OOD-CV, improving roughly 2-3% point in OOD accuracy (ef. Tab H2). We hypothesise that since Gaussians are densely populated in NOVUM which are then used for classification, having more accurate shape approximation has limited effects. Whereas for CAVE, our concept-based NOV representation is approximately 98% sparser than NOVUM's 1 130 Gaussians per class, and thus the shape matters more in design.
Additionally, we evaluate how NOV shape influences CAVE's concept interpretability (cf. Tab. H3). Prototype CADs score highest across all metrics, consistent with their closer match to the underlying object geometry. Ellipsoids are only slightly worse yet require no CAD assets and are faster fit. Given this empirical trade-off between OOD accuracy and interpretability, we adopt ellipsoid NOVs CAVE, instead of using cuboids as prior work (Jesslen et al., 2024).
Taken together, these results show that CAVE delivers strong OOD accuracy with a highly sparse and compact concept-bane based representation across shapes, with more expressive shapes such as ellipsoids and prototype CADs are slightly better. Among the tested shapes, ellipsoid NOVs offer the best balance between interpretability and robustness, making them a scalable choice for CAVE, where 3Daaware classification both inherently interpretable and robust to distribution shifts.
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I ABLATION: ATTRIBUTING CONCEPTS WITH NOV-AWARE LRP
We provide here more comprehensive quantitative and qualitative evaluation of our proposed NOV- aware LRP, described in Sec. 4.1 & Sec. C, against common attribution methods for attributing concepts in 3D-aware architectures like CAVE. These include Vanilla LRP (Bach al., 2015), Guided Backpropagation (Springenberg et al., 2015), Smooth Gradients (Smilkov et al., 2017), GradCAM (Selvaraju et al., 2017), and Integrated Gradients (Sundararajan et al., 2017).
In a direct comparison to vanilla LRP (Bach al., 2015) that we base our method on, show that our NOV-aware LRP enables faithful attribution of concepts through the NOVs back to the input pixels, achieving near-perfect rel- evance conservation. In contrast, vanilla LRP unfaithfully leaks relevances, where relevance either lost or incorrectly redistributed dur- ing propagation (cf. Fig. II), Qualitatively in Fig. 12, we observe spurious relevances visi- bly appear in background regions occlusion masks in vanilla LRP. On the other hand, our NOV-aware LRP consistently produces sharp, spatially coherent attributions that remain well- aligned with the underlying object structure. This demonstrates not only the technical ben- efits of adapting LRP to 3D-aware classifiers with volumetric representations, but also the practical interpretability gains, where concepts are now more reliably traced back to the input im- age. Taken together, our results demonstrate the strong effect of NOV-aware LRP in improving the fidelity of attribution, i.e., by ensuring that relevance is conserved properly during propagation.
Relevance conservation error on Pascal3D+
perfect
1.0
Conservation Errror
0.6-
0.6
0.1
0.2
0.0
Vanilla
Figure I1: Violin plot on relevance conservation of Ours vs. Vanilla Layer-wise Relevance Propa- gation (LRP), where indicates perfect conserva- tion. Our NOV-aware LRP achieves near-perfect conservation compared to Vanilla LRP.
Localise, t Coverage f
3D Consistency 1
Attribution Methods
Pascal-Part
Pascal3D+
OccludedP3D+
Vanilla LRP (c-rule)
0.26
0.73
0.29
0.16
Guided Backprop.
0.25
0.61
0.32
0.19
CAVE
SmoothGrad
0.23
0.69
0.31
0.16
Grad-CAM
0.12
0.47
0.27
0.13
Integrated Gradients
0.19
0.57
0.35
0.19
NOV-aware LRP (Ours)
0.28
0.80
0.40
0.23
Table 11: Quantitative comparison of differrnt attribution methods for CAVE, evaluated on spatial localisation, object coverage, and 3D consistency
We further study the effectiveness of our NOV-aware LRP compared to common attribution methods (cf. Tab. 11). Ours produces concepts with higher spatial localisation, object coverage (i.e., concept comprchensiveness), and 3D consistent across in-distribution Pascal3D+ (Xiang et al., 2014) and OOD OccludedP3D+ (Wang et al., 2020). This means that our LRP reformulation allows us gen- erate not only highly localised but also semantically comprehensive visualisation of concepts, cover- ing the object well rather than focusing on few discriminative fragments (cf. Fig. 12). Furthermore, NOV-aware LRP maintains strong consistency across 3D views, outperforming all baselines on Pas- cal3D+ (0.40 vs. 0.35 from Integrated Gradients) and OccludedP3D+ (0.23 vs. 0.19 from Guided Backpropagation and Integrated Gradients). The gains are particularly pronounced under occlusion, where reliable attribution is more challenging.
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No Occ.
20-40% Occ.
40-60% Oce.
Fog
Snow
Thunderstorm
Imput
NOV-aware LRP
Vanilla LRP
GradCAM
SmoothGrad
Guider BP
IG
Bus
Bottle
Chair
Car
Train
Boat
Figure 12: Our NOV-aware LRP (second row) yields better-localised, more stable visualisation of top-5 concepts across both in-distribution and OOD settings, while vanilla LRP and other common attribution methods show scattered explanations on the image background masks. From left - right, the first input image comes from in-distribution Pascal3D+ (Xiang et al., 2014), the next two from OccludedP3ID+ (Wang al., 2020) with different levels of occlusion, and the last three from OOD-CV (Zhao et al., 2022).
occlusion
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J ABLATION: CONCEPT EXTRACTION ON NEURAL OBJECT VOLUMES (NOVS)
bottar
CD
Chair
diiiggable
mobers be
sods
roin
bmmontor
Figure J1: Representation spaces derived from neural object volumes (left) and activations of features (right) of all classes in Pascal3D+.
An advantage of an image classifier with NOVs is that enhances the separation of the representa- tion space, ensuring that Gaussian features from different classes remain well-distinguished (Jesslen al., 2024). Naturally, this is also the case for activations features within the same classifier (cf. Fig. J1), which then leads us to examine where concept extraction is most effective. Our CAVE framework extracts class-wiss concepts directly from neural object volumes G, whereas traditional methods rely on activations from training features. We explore whether G provides a more mean- ingful concept space by following three key steps:
1. extracting concepts using low-rank approximations (e.g., NMF). For fair comparison, we use NMF as our extraction method because it is known to effectively extract meaningful and interpretable concepts from activations (Fel et al., 2024). Note that NMF is not guaranteed be the optimal choice for neural volumes G.
2. projecting activations into the concept space, and
3. train K-means clustering model on training image activations and evaluate it on test acti- vations across different occlusion levels for concept separation.
A well-structured concept space should produce well-separated and compact clusters, which can be evaluated using the Silhouette Score and Davies-Bouldin Index (DBI). The Silhouette Score ranges from [-1, 1]. where 1 indicates optimal separation and values near 0 suggest overlapping clusters. In contrast, the Davies-Bouldin Index measures the ratio of intra-cluster dispersion to inter-cluster separation, with lower values indicating better-separated, more compact clusters. We also show 2D low-dimensional representations comparing the concept spaces of neural volumes and training activations across different classes in Fig. J2.
Occlusion
0
[20, 40]
[40, 60]
[60, 80]
NOVs G
0.343
0.333
0.335
0.338
Activations
0.034
0.040
0.037
0.033
Table J1: Silhouette scores (1) averaged across all classes in Pascal3D+, comparing concept spaces derived from neural object volumes 9 and traditional activations. Higher scores indicate more com- pact clusters, with values close to 1 representing well-structured concept spaces. Results are reported across different occlusion levels in
As we extract concepts from NOVs, there are different established approaches obtain the de- composition Gy 25 WyH.T specifically K-Means, Principal Component Analysis (PCA) and Non- negative Matrix Factorisation (NMF). We aim to strategically select the concept extraction method that encourages disentangled, part- bast- concepts while maintaining competitive performance and faithfulness. To do so, conduct small ablation and compare in terms of three key metries:
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Occlusion
0
[20, 40]
[40, 60]
(60, 80
NOVs g
1.154
1.155
1.162
1.137
Activations
2.365
2.348
2.306
2.318
Table J2: Davics-Bouldin Index (L) averaged across all classes in Pascal3D+, comparing concept spaces derived from neural object volumes G and traditional activations. Lower score means better cluster separation.
CareesS
Dining
Figure J2: t-SNE projection of concept embeddings in neural volume space (top) vs. activation space (bottom) for four classes in Pascal3D+. Concepts in neural volume space are more well- separated and compact compared to those extracted from activation space.
(i) accuracy, (ii) sparsity, and (iii) feature distribution distance (FDD). Here, sparsity is measured following the approach in Fel al. (2024), which quantifies how sparse the weight matrix W is. FDD measures the divergence between the original distribution of Gy and its new representation Hy, thereby quantifying how faithful the latter preserves the former. After evaluating these three metries, we select K-Means clustering as concept identification in CAVE.
Accuracy (% t)
Sparsity (1)
FDD (L)
K-Means
99.36
0.95
0.32
PCA
99.39
0.00
0.39
NMF
99.25
0.63
0.83
NOVUM 99.5
Table J3: Ablation on concept extraction methods. The concept extraction methods are applied on the neural volumes Gy E G in image classifier NOVUM with D 20 concepts. Each result is averaged across all classes from Pascal3D+.
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K DISCUSSION OF FAILURE CASES
While CAVE achieves significant improvement in both robustness and interpretability, some inherent
limitations of 3DD-aware classification remain.
First, CAVE is trained on object-centric images and orients its ellipsoid NOVs to the primary object to learn Gaussian features for concept dictionary extraction. This in turn allows for spatially consistent and localised explanations. In multi-object classification tasks where mul- tiple instances of the same objects are present, CAVE surprisingly can still identify concepts across objects, even though its training is not optimised for multi-object scenes. In some cases, however, CAVE identifies concepts on the central object and abstains from others (cf. Fig. K1). While this behavior is consistent with object-centric learning of 3D-aware classifiers, improving CAVE further in multi-object scenes would be interesting future direction.
Figure KI: CAVE identifies concept across mul- tiple objects (left) but occasionally misses (right).
Second, we study cases where CAVE fails to find spatially consistent concepts in most test images. For example, in class Boat t of ImageNet3D (Ma et al., 2024), the same concept only localises on the stern in some images, while both bow and stern in others. This can be attributed the fact that boats do not have a consistent set of parts across subcategories, as also observed in the Pascal-Part dataset (Chen et al., 2014), as well as because of object symmetries. In fact, when the two ends are visually similar, the concept generalises to hull ends, rather than only on slern (cf. Fig. K2).
Figure K2: For the same concept in the Boat class of ImageNet3D, CAVE detects only stern in some cases (first two columns), while both hull ends in others (last two columns).
We further investigated how OOD nuisances af- feet concept consistency. In in-distribution set- tings such as Pascal3D+ (Xiang et al., 2014) and ImageNet3D (Ma et al., 2024), CAVE's 3D-C scores of Bicycle are roughly 0.24. Un- der distribution shift OOD-CV (Zhao et al., 2022), the score drops to about 0.16, albeit still substantially higher than all baselines, which fail detect any consistent concepts. We in- vestigate examples where CAVE shows incon- sistency, and find that for example concept such as front wheel activates also on back wheel un- der strong perspective shift, or when the bicycle is severely deformed (cf. Fig. K3).
Figure K3: Under OOD factors, CAVE correctly detects front wheel (above) but can occasionally activates back wheel or other parts (below) under strong perspective shift object deformation.
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L
ADDITIONAL QUALITATIVE EXAMPLES
Underwater
Fog
Shape
Context
3D Consistency
OOD Input
NOVUM CRAFT
NOVUM
+MD (CD (L=.9)
NOVUM +IC
NOVUM + PCX
LF-CBM
ProtoPNet
TesNet
PIP-Net
Ours
Figure LI: CAVE (Ours) produces more spatially consistent and localised explanations for OOD images of class Motorbike compared to all baselines.
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Pose
Shape
Weather
Fire
3D Consistency
OOD Imput
NOVUM +CRA
NOVUM MMD CUDCUUA 99
F3C
LF-OBM
ProtoPNet
TesNet
PIP-Net
Ours
Figure L2: CAVE (Ours) produces more spatially consistent and localised explanations for OOD images of class Bus compared to all baselines.
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Shape
Pose
Underwater
Snow
3D Consistency
OOD Imput
NOVUM +CRAFT
NOVUM
(CC
NOW NOVUM +ICE
NOVUM PPC
LF-CBM
ProtoPNct
TesNet
PIP-Net
Ours
Figure L3: CAVE (Ours) produces more spatially consistent and localised explanations for OOD images of class Bicycle compared to all baselines.
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Fire
Night
Texture
Shape
3D Consistency
OOD Imput
NOVUM + +CRAFT
NOVUM
MCD
NOVEL +ICE
NOVUS AA4
LF-CBM
ProtoPNet
TesNet
PIP-Net
Ours
Figure L4: CAVE (Ours) produces more spatially consistent and localised explanations for OOD images of class Boat compared to all baselines.
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Shape
Texture
Context
Pose
3D Consistency
OOD Imput
NOVUM +CRAFT
NOVUM
MCD MCD ((=.9)
NOVUM +ICE
NOVUM PCX
LF-CBM
ProtoPNct
TesNet
PIP-Net
Ours
Figure L5: CAVE (Ours) produces more spatially consistent and localised explanations for OOD images of class Chair compared to all baselines.
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Wind Turbine
Lipstick
020999
Tank
Snow Mobile
Shaver
Figure L6: CAVE (Ours) detects consistent concepts across different ImageNet3D classes. For each class, the concept is sampled randomly, and the images associated with that concept are also sampled randomly, both with seed 42.
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Ambulance
Forklift
Hockey Stick
Millwheel
Washing Machine
Figure L7: CAVE (Ours) detects consistent concepts different ImageNet3D classes. For each class, the concept is sampled randomly, and the images associated with that concept are also sampled randomly, both with seed 42.
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Air Hammer
Crutch
Lightbulb
Jinrikisha
Satellite Dish
Figure L8: CAVE (Ours) detects consistent concepts different ImageNet3D classes. For each class, the concept is sampled randomly, and the images associated with that concept are also sampled randomly, both with seed 42.
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CAT
Cap
CAT
Camera
LAROGO
Hair Dryer
W E Powe tith
LABOCO
Mailbox
XPRESS
AIL
XPRESS
VAIL
Hacksaw
Figure L9: CAVE (Ours) detects consistent concepts across different ImageNet3D classes and refrains from detection when the concepts are not visible in the image. For each class, the con- cept is sampled randomly, and the images associated with that concept are also sampled randomly, both with seed 42.
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M THE USE OF LARGE LANGUAGE MODELS
All scientific contributions, including the proposed method, experimental design, results, and analy- ses are solely our own work. We made minimal use of large language model, specifically ChatGPT, only assist with the polishing of this paper, including:
formatting tables and figures in latex (strictly for presentation), and
refining sentence structure for clarity and conciseness
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Reviews:
[{"review_id": "PvesB0RxOV", "reviewer": "Reviewer_zP4N", "summary": "This work introduces CAVE, a robust, interpretable image classifier based on 3-D object representations. To visualize pixel importance, the authors also extend LRP for the proposed model. Finally, a new metric called 3D consistency is introduced to measure whether learned concepts consistently match with the same part of the underlying 3D volume. Experiments show that CAVE produces better localization, coverage, and consistency than prior methods while achieving strong accuracy. Notably, in the absence of 3D annotations CAVE outperforms all other methods.", "questions": "- How can it be said that standalone NOVUM is not faithful, but CAVE is? The only difference between the two as predictive models seems to be the number of concepts.\n- In the appendix, Spatial localisation is defined with respect to a single image-concept pair. How is this aggregated to a single value per model/dataset?\n- It may be worth comparing to [1]; this is an extension of ProtoPNet that, while not targeting robustness, learns distributional concepts in 2D space.\n\n[1] Wang, Chong, et al. \"Mixture of gaussian-distributed prototypes with generative modelling for interpretable and trustworthy image recognition.\" IEEE Transactions on Pattern Analysis and Machine Intelligence (2025).", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- The problem targeted by this paper is interesting and well motivated, while remaining reasonable in scope.\n- The figures throughout the work are clear and well made.\n- CAVE is, to my knowledge, the first model to combine neural object volumes with concept based explanations, providing a source of novelty.\n- The numerical results achieved by CAVE are strong compared to other robust only or interpretable only methods.", "weaknesses": "- It is unclear to me why CAVE can be considered inherently interpretable/faithful. Each classification is a function of the dot product between each image patch and some concept; this dot product is not bounded, and does not reflect a meaningful distance/similarity measure. Even if it did, these concepts do not seem to have any semantic meaning -- they are freely learned parameters. As such, it may be inappropriate to compare with only interpretable/explainable models. If I am missing something fundamental, clarification would be appreciated. This is my primary concern.\n- The clarity of this work suffers a bit from not being self-contained. In particular, it is unclear from this work how spatial location and distributional nature of NOV's actually matter. If a reader does not read NOVUM, each NOV simply seems like a free parameter vector in the embedding space of the backbone. Moreover, there are a couple minor issues with formalism that impact clarity:\n    - Line 314: $\\sum_{(i,j)} A^+(x, h) = 1$ <- i, j do not appear as indices inside the sum\n    - The function $\\Omega_y$ is never defined, including in the appendix", "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": "7RNIXSq30Y", "reviewer": "Reviewer_Kx36", "summary": "The author introduces a framework for interpretable and robust 3D-aware reasoning for image classification. The method is based on learning a sparse, interpretable dictionary of 3D object concepts and replaces dense 3D feature representations with these high level concepts. The approach is designed to enable model-faithful, localized, and consistent explanations for its predictions, even under OOD scenarios such as occlusion and context shifts. They use a recent method of Want et al (ICML 2025) for orientation estimation form 3D models. In addition, the paper proposes 3D Consistency (3D-C) metric that evaluates the spatial coherence of concepts using either ground-truth or estimated 3D meshes instead of human-defined parts. The paper presents an extensive experiment that benchmark their work against both post-hoc and inherently interpretable baselines, demonstrating advantages in robustness - interpretability trade offs, standard interpretability metrics, and classification accuracy on both in-distribution and OOD datasets.", "questions": "1. Can the authors provide statistical variance of the results?\n2. Can the authors present class-wise or attribute-wise breakdowns of accuracy/consistency, particularly in OOD or high-occlusion cases?\n3. How can practitioners apply CAVE in unconstrained settings where 3D geometry is sparse or diverse?\n4. Can the authors provide an accuracy and 3D Consistency as a function of pose error?", "limitations": "", "rating": 6, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. Simplicity – instead of selecting dense 3D feature representations, it uses a sparse high level concepts instead. \n2. Effectiveness - can operate both with and without ground-truth pose supervision leveraging Orient-Anything.\n3. High accuracy – the authors demonstrates that CAVE achieves high accuracy and OOD robustness with far fewer parameters than dense NOV-based methods", "weaknesses": "1. 3D-C projects concept attributions onto a class CAD mesh. But if you do not have meshes for a class or the mesh is a poor proxy, you cannot score consistently well. This limits evaluation outside these datasets.\n2. If the pose estimator struggles on certain data such as symmetric objects, CAVE accuracy and consistency will drop, making it a manageable weakness.\n3. The method is limited to single objects scenes.\n4. No reported stability across random seeds or concept count for K-Means.\n5. No confidence intervals in the charts. Hard to judge the noise level.\n6. Seems to be some missing refs and related work, such as: \na.\tXue, N., Tan, B., Xiao, Y. (2024): NEAT: Distilling 3D Wireframes from Neural Attraction Fields\nb.\tLiu, X., Zheng, C., Qian, M. (2024): Multi-View Attentive Contextualization for Multi-View 3D Object Detection\nc.\tXue, N., Wu, T., Bai, S. (2023): Holistically-Attracted Wireframe Parsing\nd.\tTan, B., Xue, N., Wu, T. (2023): NOPE-SAC: Neural One-Plane RANSAC for Sparse-View Planar 3D Reconstruction\ne.\tXiao, Y., Xue, N., Wu, T. (2023): Level-S$^2$fM: Structure from Motion on Neural Level Set of Implicit Surfaces\nf.\tGrainger, R., Paniagua, T., Song, X. (2023): PaCa-ViT: Learning Patch-to-Cluster Attention in Vision Transformers\ng.\tKashyap, P., Ravichandiran, P., Wang, L. (2023): Thermal Estimation for 3D-ICs Through Generative Networks\nh.\tSavadikar, C., Dai, M., Wu, T. (2023): Learning to Grow Artificial Hippocampi in Vision Transformers for Resilient Lifelong Learning", "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": "LJ9lDz6oJm", "reviewer": "Reviewer_GACT", "summary": "The paper is aim at finding a robust and explainable architecture for classification of images based on 3D representation of the object. The authors propose the CAVE method, which is aware of 3D representation of the object, and create an importance measure through it. The idea is to find the best correlation to a set of representations of given classes when generating the importance map. They also proposed LRP based method for faithfull attribution and 3D-C to evaluate stability.", "questions": "* In line 51-85: \"Notably, post-hoc methods... However such methods only approximate the model’s computations, and thus do not provide a faithful explanation\". Seems to me like a very general and not accurate statement. Why did you claim that they do not provide faithful explanation? for the extreme case - a pure gradient from output to input of the entire architecture should ideally measure the impact of each input element on the output. Seems like very faithful explanation. I think that it should be clarify or backed somehow with experiments or references to other papers showing something like this. \n* It is not clear in the preliminaries section whether the approach limited to embedders which produce feature vector for each pixel, since I think that most embedders squeeze the input information into much smaller dimension, ViT for example patchify the input. If it is the case, then it is a very profound limitation of your approach (or NOVUM you based on). If not - then I think that the notations of H and W are not clear.\n* Im not sure how do the concepts being selected in space? why is bus contains the roof and car not (in Fig 4)?\n* In many concept decomposition papers the sparsity is playing a vital role, the most basic example for this is the SAE (Sparse AutoEncoders). In several places in your paper you are trying to cinvince that sparsity is a good characteristic where it is almost trivial in concept decomposition.\n\nOverall I find the ideas of the paper very intuitive, so the results seems reasonable to me. The idea to combine 3d-aware representation with XAI is very important, and the modeling through ellipsoids and Gaussians seems reasonable. I think that the paper is good and worth publishing.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "* XAI is obviously one of the most challenging and important issues in nowadays AI era, in almost all fields, especially vision.\n* The approach which the authors provide seems novel to me, and the idea to decompose each image to 3D concepts makes a lot of sense to me, and make it reasonable that the faithfulness of  the explanation will be better.\n* The link between ellipsoid and Gaussianity, appear in almost all figures is super reasonable, and make things clearer and simpler. Evidence for the link of Gaussians and Ellipsoids, and how it is appear in CLIP you can find here [1].\n* Impressive experimental section with convincing examples.\n\n\nrefs:\n\n[1] Levi, Meir Yossef, and Guy Gilboa. \"The Double-Ellipsoid Geometry of CLIP\". ICML 25.", "weaknesses": "* One main concern is that this method is limited to rigid motion. Think of human body which can be transformed in a non-rigid motion then it is obvious that fixed set of dictionary representation cannot hold all variation of the body. So I find it as a limitation of the method.\n* the 3D-C method is heavily relying on given set of meshes, where in the wild it is not given and may be hard to obtain especially for edge cases of objects (especially object with non-rigid movement abilities). I believe that the authors should elaborate on what are the options for a practitioner when this set is absent, or when he is interested in unknown set of classes.\n\nMinor weaknesses:\n* in the main figure on the first page, the left part is very intuitive and understandable, the right plot is much less. I didnt understand what the dashed lines stands for, moreover, it is better to put units or some explanation on the axes. I can get that the Y axis is accuracy in between 0-100 but what is 0.1 in spatial localization means?\n* The citation of the CRAFT paper by Thomas Fel et. al is in German, replace it with the appropriate English one.", "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)