XSPLAIN: Interpretability for 3D Gaussian Splatting

• XSPLAIN is an ante-hoc, prototype-based interpretability framework for 3D Gaussian Splatting that delivers spatially coherent explanations without modifying classifier decision boundaries.
• It aggregates voxelized splat features and applies a channel-disentangling orthogonal transform to enable localized, 'this looks like that' reasoning.
• Its two-stage training strategy separates classification from interpretability, ensuring preserved accuracy and enhanced evidence grounding.

Searching arXiv for the primary paper and closely related context. arXiv search query: (Galus et al., 10 Feb 2026) XSPLAIN is an ante-hoc, prototype-based interpretability framework for supervised classification of 3D Gaussian Splatting (3DGS) instances that is designed to provide spatially localized, example-grounded explanations without changing the classifier’s decision boundaries (Galus et al., 10 Feb 2026). It addresses a specific interpretability problem in 3DGS: although 3DGS has become a compelling scene and object representation through anisotropic Gaussian primitives rendered with volumetric compositing, existing explanation strategies adapted from point clouds typically yield scattered saliency patterns that do not respect the volumetric coherence of Gaussian primitives. XSPLAIN instead builds explanations around voxelized aggregations of splat features, a channel-disentangling orthogonal transform, and channel-wise prototypes that support “this looks like that” reasoning while preserving classification fidelity by construction (Galus et al., 10 Feb 2026).

1. Problem setting and interpretability objective

3D Gaussian Splatting represents geometry as a set of anisotropic Gaussian primitives, each with position, scale, orientation, and opacity. In XSPLAIN, the target task is supervised classification of 3DGS instances using only geometry-related per-splat attributes, excluding color and view-dependent appearance (Galus et al., 10 Feb 2026). The framework is motivated by three challenges identified for interpretability in this setting.

First, point-cloud saliency is described as insufficient for 3DGS. Post-hoc saliency on unstructured points often produces scattered and noisy attributions; in the 3DGS case this is especially problematic because each primitive is a volumetric ellipsoid with opacity and oriented anisotropic radii. Point-level highlighting can therefore fail to correspond to coherent volumetric regions and may not reflect how the underlying radiance field is supported by splats (Galus et al., 10 Feb 2026).

Second, the method emphasizes the need for volumetric coherence. Explanations should align with the spatial aggregation level at which the classifier “sees” the object. For Gaussian primitives, the relevant explanatory unit is not an isolated point but a group of splats jointly covering a volume with consistent density and orientation. XSPLAIN operationalizes this by voxelizing normalized splat positions and aggregating features per voxel, thereby anchoring explanations to stable, spatially localized regions (Galus et al., 10 Feb 2026).

Third, XSPLAIN adopts ante-hoc interpretability rather than post-hoc attribution. In the formulation used by the paper, ante-hoc, prototype-based interpretability means that the model is designed and trained to be interpretable from the outset, and each explanation is grounded in representative training examples by comparing latent responses in localized regions of a test object to prototype responses from the training set. The paper characterizes this as intuitive “this looks like that” reasoning, with the additional requirement that the original decision function remain unchanged (Galus et al., 10 Feb 2026).

A central misconception addressed by the framework is that interpretability in geometric deep learning necessarily entails some degradation in predictive performance. XSPLAIN is explicitly designed so that explanations are not part of the prediction path, and the decision boundaries are strictly preserved after insertion of the interpretability layer (Galus et al., 10 Feb 2026). This distinguishes it from approaches in which prototype matching or saliency regularization can alter the classifier.

2. Representation of 3D Gaussian primitives and voxel-aggregated input processing

Each Gaussian primitive, or splat, is represented by geometric parameters comprising position $\mu_i \in \mathbb{R}^3$, anisotropic scales $s_i \in \mathbb{R}^3$, orientation $q_i \in \mathbb{R}^4$, and opacity $\alpha_i \in \mathbb{R}$. XSPLAIN uses the compact tuple

$$g_i = (x_i, s_i, q_i, \alpha_i) \in (\mathbb{R}^3, \mathbb{R}^3, \mathbb{R}^4, \mathbb{R}),$$

with $x_i \equiv \mu_i$, and excludes per-splat color in order to improve robustness and simplify inputs (Galus et al., 10 Feb 2026). When needed for analysis, the full covariance is written as

$$\Sigma_i = R(q_i)\,\mathrm{diag}(s_i \odot s_i)\,R(q_i)^T,$$

where $R(q_i) \in SO(3)$ is the rotation induced by the quaternion (Galus et al., 10 Feb 2026).

The conversion from raw 3DGS to network input begins by normalizing positions to a unit bounding box, yielding $\tilde{x}_i \in [0,1]^3$. Space is then partitioned into a uniform $G \times G \times G$ grid. The immutable voxel index is defined before any learned alignment:

$s_i \in \mathbb{R}^3$0

with per-axis clipping to $s_i \in \mathbb{R}^3$1 (Galus et al., 10 Feb 2026). The immutability of this index is a key architectural choice, because later explanations can be mapped directly back to the original spatial region without inverse alignment or de-warping.

A PointNet-style backbone computes per-splat features $s_i \in \mathbb{R}^3$2. These are aggregated within each voxel using channel-wise max pooling:

$s_i \in \mathbb{R}^3$3

The voxel features are then averaged to form a global representation

$s_i \in \mathbb{R}^3$4

and a linear classifier produces logits

$s_i \in \mathbb{R}^3$5

The predicted class is $s_i \in \mathbb{R}^3$6 (Galus et al., 10 Feb 2026).

The method supplements this pipeline with a density-aware voxel activation alignment term. Let $s_i \in \mathbb{R}^3$7 be the voxel activation magnitude and $s_i \in \mathbb{R}^3$8 the number of splats in voxel $s_i \in \mathbb{R}^3$9. XSPLAIN defines a soft attention distribution

$q_i \in \mathbb{R}^4$0

and a target density distribution

$q_i \in \mathbb{R}^4$1

with $q_i \in \mathbb{R}^4$2, then uses the KL penalty

$q_i \in \mathbb{R}^4$3

This regularizer promotes attention-density alignment and is intended to shift attention toward dense, coherent voxels rather than isolated outliers (Galus et al., 10 Feb 2026).

This architecture implies a specific explanatory ontology. A plausible implication is that XSPLAIN treats interpretability as a property of channel-voxel interactions rather than of individual splats. The explanatory primitive is therefore a localized volumetric activation pattern, not an isolated input attribute.

3. Backbone architecture and decision-boundary-preserving feature transformation

The backbone is a voxel-aggregated PointNet. Its input is a set of $q_i \in \mathbb{R}^4$4 splats described by $q_i \in \mathbb{R}^4$5, with per-splat raw features formed by concatenating $q_i \in \mathbb{R}^4$6 after normalization. The model uses two spatial transformer networks: one aligns input coordinates and the other aligns intermediate features. Shared 1D convolutions or MLPs then produce the per-splat features $q_i \in \mathbb{R}^4$7 (Galus et al., 10 Feb 2026).

XSPLAIN’s interpretability mechanism is inserted between voxel aggregation and global pooling. Let $q_i \in \mathbb{R}^4$8 be the stacked voxel feature matrix with columns $q_i \in \mathbb{R}^4$9. The method introduces an invertible orthogonal transformation $\alpha_i \in \mathbb{R}$0 satisfying $\alpha_i \in \mathbb{R}$1, and defines transformed voxel features

$\alpha_i \in \mathbb{R}$2

with columns $\alpha_i \in \mathbb{R}$3 (Galus et al., 10 Feb 2026). Pooling after transformation gives

$\alpha_i \in \mathbb{R}$4

The paper’s central formal property is exact preservation of decision boundaries. Given a linear classifier with weights $\alpha_i \in \mathbb{R}$5, XSPLAIN defines compensated weights

$\alpha_i \in \mathbb{R}$6

Then

$\alpha_i \in \mathbb{R}$7

so the logits and predicted class remain identical before and after the transformation (Galus et al., 10 Feb 2026). The paper therefore states that decision boundaries are strictly preserved. This guarantee depends on the linear head; the paper notes that with a non-linear head, $\alpha_i \in \mathbb{R}$8 could be inserted immediately before the final linear layer and the first following linear layer could be compensated instead (Galus et al., 10 Feb 2026).

The orthogonal matrix is parameterized through the exponential of a skew-symmetric matrix:

$\alpha_i \in \mathbb{R}$9

with unconstrained $$g_i = (x_i, s_i, q_i, \alpha_i) \in (\mathbb{R}^3, \mathbb{R}^3, \mathbb{R}^4, \mathbb{R}),$$0. Because $$g_i = (x_i, s_i, q_i, \alpha_i) \in (\mathbb{R}^3, \mathbb{R}^3, \mathbb{R}^4, \mathbb{R}),$$1, the resulting $$g_i = (x_i, s_i, q_i, \alpha_i) \in (\mathbb{R}^3, \mathbb{R}^3, \mathbb{R}^4, \mathbb{R}),$$2 is orthogonal and has determinant $$g_i = (x_i, s_i, q_i, \alpha_i) \in (\mathbb{R}^3, \mathbb{R}^3, \mathbb{R}^4, \mathbb{R}),$$3. Initialization with $$g_i = (x_i, s_i, q_i, \alpha_i) \in (\mathbb{R}^3, \mathbb{R}^3, \mathbb{R}^4, \mathbb{R}),$$4 yields $$g_i = (x_i, s_i, q_i, \alpha_i) \in (\mathbb{R}^3, \mathbb{R}^3, \mathbb{R}^4, \mathbb{R}),$$5, so training begins from the backbone’s native feature basis (Galus et al., 10 Feb 2026). No additional orthogonality penalty is required, since orthogonality is enforced exactly by construction.

In the framework’s internal logic, the role of $$g_i = (x_i, s_i, q_i, \alpha_i) \in (\mathbb{R}^3, \mathbb{R}^3, \mathbb{R}^4, \mathbb{R}),$$6 is not to alter the classifier’s behavior but to rotate the latent basis into channels that are more interpretable. The paper describes this as disentangling feature channels for interpretability while preserving the original decision boundaries (Galus et al., 10 Feb 2026). This suggests a separation between semantic restructuring of latent space and predictive computation: the classifier’s geometry is invariant, while the coordinate system in which channel responses are interpreted is optimized.

4. Prototype mechanism and localized “this looks like that” explanations

Prototypes are defined in the transformed latent space rather than in raw input space. Let $$g_i = (x_i, s_i, q_i, \alpha_i) \in (\mathbb{R}^3, \mathbb{R}^3, \mathbb{R}^4, \mathbb{R}),$$7 denote the transformed per-voxel feature map. For each channel $$g_i = (x_i, s_i, q_i, \alpha_i) \in (\mathbb{R}^3, \mathbb{R}^3, \mathbb{R}^4, \mathbb{R}),$$8, XSPLAIN defines a per-sample channel score

$$g_i = (x_i, s_i, q_i, \alpha_i) \in (\mathbb{R}^3, \mathbb{R}^3, \mathbb{R}^4, \mathbb{R}),$$9

The top-$x_i \equiv \mu_i$0 training samples with the largest $x_i \equiv \mu_i$1 values are stored as the prototype set

$x_i \equiv \mu_i$2

for that channel (Galus et al., 10 Feb 2026). Prototypes are therefore discovered by activation ranking, not by distance-based clustering, and they are explicitly not used to make predictions.

During explanation, XSPLAIN computes per-channel importance for the predicted class $x_i \equiv \mu_i$3 as

$x_i \equiv \mu_i$4

where $x_i \equiv \mu_i$5 are the compensated classifier weights. The top-$x_i \equiv \mu_i$6 channels with the largest importance values are selected, and their associated prototypes provide the explanatory evidence (Galus et al., 10 Feb 2026). Each prototype is a real training example that strongly activated the same feature channel, which grounds the explanation in representative data rather than synthetic abstraction.

Spatial localization is performed channel-wise. For an important channel $x_i \equiv \mu_i$7 in a test sample, XSPLAIN finds the maximally activated voxel

$x_i \equiv \mu_i$8

The explanation region is then the set of splats assigned to that voxel:

$x_i \equiv \mu_i$9

Because voxel indices were computed before learned transformations and never changed thereafter, rendering only $$\Sigma_i = R(q_i)\,\mathrm{diag}(s_i \odot s_i)\,R(q_i)^T,$$0 yields a coherent localized volumetric region that corresponds exactly to a region in the original object (Galus et al., 10 Feb 2026).

This explanatory design differs from prototype networks of the ProtoPNet type in three ways identified by the paper: it uses a 3DGS-specific pipeline with voxel aggregation for volumetric coherence; it relies on a global invertible orthogonal transformation that disentangles channels without changing decision boundaries; and its prototypes are discovered per-channel and per-voxel in latent space but are not part of the forward prediction path (Galus et al., 10 Feb 2026).

A concise summary of the explanatory logic can be organized as follows.

Component	Definition in XSPLAIN	Explanatory role
Channel prototype set	Top-$$\Sigma_i = R(q_i)\,\mathrm{diag}(s_i \odot s_i)\,R(q_i)^T,$$1 training samples by maximal channel activation $$\Sigma_i = R(q_i)\,\mathrm{diag}(s_i \odot s_i)\,R(q_i)^T,$$2	Provides representative training evidence
Important channel	Largest $$\Sigma_i = R(q_i)\,\mathrm{diag}(s_i \odot s_i)\,R(q_i)^T,$$3 for predicted class	Selects class-relevant latent semantics
Local region	Splats in voxel $$\Sigma_i = R(q_i)\,\mathrm{diag}(s_i \odot s_i)\,R(q_i)^T,$$4 with maximal channel response	Localizes evidence volumetrically

The phrase “this looks like that” is not a metaphor external to the method; it is the paper’s description of a retrieval-based explanatory relation between localized channel responses in the test sample and highly activating training examples in the same transformed channel (Galus et al., 10 Feb 2026).

5. Training procedure, objectives, and optimization strategy

XSPLAIN uses a two-stage training strategy. Stage 1 trains the backbone parameters $$\Sigma_i = R(q_i)\,\mathrm{diag}(s_i \odot s_i)\,R(q_i)^T,$$5—including the STNs, shared MLPs, and classifier weights—using cross-entropy plus density-aware regularization. The classification loss is

$$\Sigma_i = R(q_i)\,\mathrm{diag}(s_i \odot s_i)\,R(q_i)^T,$$6

The total Stage 1 objective is

$$\Sigma_i = R(q_i)\,\mathrm{diag}(s_i \odot s_i)\,R(q_i)^T,$$7

Only the backbone parameters are optimized in this stage (Galus et al., 10 Feb 2026).

Stage 2 freezes the trained backbone at $$\Sigma_i = R(q_i)\,\mathrm{diag}(s_i \odot s_i)\,R(q_i)^T,$$8, inserts the orthogonal transformation $$\Sigma_i = R(q_i)\,\mathrm{diag}(s_i \odot s_i)\,R(q_i)^T,$$9, and optimizes only the parameters $R(q_i) \in SO(3)$0 underlying $R(q_i) \in SO(3)$1. The training signal is a purity objective defined on dynamically updated prototypes. For a given sample and channel $R(q_i) \in SO(3)$2, let

$R(q_i) \in SO(3)$3

Purity is defined as

$R(q_i) \in SO(3)$4

where $R(q_i) \in SO(3)$5 is the vector of all channels in the maximally activated voxel (Galus et al., 10 Feb 2026). The purity loss is

$R(q_i) \in SO(3)$6

with $R(q_i) \in SO(3)$7 denoting a batch of sample-channel pairs drawn from the current prototype pool.

Prototype sets are updated dynamically across epochs using a schedule

$R(q_i) \in SO(3)$8

so that the number of retained prototypes per channel decreases over time to focus on more representative examples (Galus et al., 10 Feb 2026). After convergence, classifier compensation is applied by setting $R(q_i) \in SO(3)$9.

The paper reports that Stage 1 can be trained with Adam or a similar optimizer and early stopping on validation accuracy, while Stage 2 optimizes only $\tilde{x}_i \in [0,1]^3$0 with Adam. The ablation identifies $\tilde{x}_i \in [0,1]^3$1 and $\tilde{x}_i \in [0,1]^3$2 as a good balance; practical guidance also lists default feature dimension $\tilde{x}_i \in [0,1]^3$3 and recommends starting with $\tilde{x}_i \in [0,1]^3$4–$\tilde{x}_i \in [0,1]^3$5 and $\tilde{x}_i \in [0,1]^3$6–$\tilde{x}_i \in [0,1]^3$7 for new datasets (Galus et al., 10 Feb 2026).

The choice of a two-stage procedure is empirically motivated as well as conceptually aligned with the method’s decoupling principle. Jointly optimizing classification and purity led to substantial accuracy degradation, reported as down to $\tilde{x}_i \in [0,1]^3$8–$\tilde{x}_i \in [0,1]^3$9, whereas the decoupled design preserved the baseline accuracy exactly after compensation (Galus et al., 10 Feb 2026). This suggests that feature disentanglement for interpretability can interfere with discriminative learning if imposed too early or too directly.

6. Evaluation, empirical findings, and comparative context

The empirical study covers multiple classification settings. The datasets are: a converted 3DGS version of Toys4K using TRELLIS; subsets of ShapeSplat with labels; MACGS, described as an MVImageNet-GS subset of real-world Gaussian splat objects; and the 3D Real Car Toolkit, used qualitatively for fine-grained discrimination such as sedans versus SUVs (Galus et al., 10 Feb 2026).

The evaluation considers classification accuracy, deletion-based faithfulness, a user study, and ablations over training strategy, grid size $G \times G \times G$0, feature dimension $G \times G \times G$1, density regularization strength $G \times G \times G$2, and the effect of the orthogonal transform on prototype purity (Galus et al., 10 Feb 2026).

The principal quantitative findings reported by the paper are summarized below.

Evaluation aspect	Reported result	Interpretation in paper
Accuracy preservation	On ShapeSplat, baseline accuracy was $G \times G \times G$3 and XSPLAIN matched it exactly after compensation	Fidelity to backbone is preserved by construction
Deletion test	Removing top 5 most active voxels caused accuracy drops of $G \times G \times G$4 on Toys and $G \times G \times G$5 on MACGS	Highlighted voxels are predictive
Deletion test	Removing only the single most active voxel caused a $G \times G \times G$6 drop on MACGS	Top localized region carries significant evidence
User study	$G \times G \times G$7; participants selected XSPLAIN explanations $G \times G \times G$8 of the time as the best, significantly above baselines with $G \times G \times G$9	Explanations were preferred over adapted baselines
Training strategy	Joint optimization degraded accuracy to $s_i \in \mathbb{R}^3$00–$s_i \in \mathbb{R}^3$01	Supports the two-stage design

The deletion tests are used as a faithfulness proxy. The paper interprets accuracy degradation after removing top-activated voxels as evidence that the highlighted regions are genuinely predictive rather than cosmetically salient (Galus et al., 10 Feb 2026). The use of voxel removal rather than point deletion is consistent with the framework’s volumetric notion of coherence.

The user study compares XSPLAIN with adapted post-hoc baselines, specifically LIME and PointSHAP as named in the data. Participants selected XSPLAIN explanations as the best $s_i \in \mathbb{R}^3$02 of the time, significantly outperforming baselines with $s_i \in \mathbb{R}^3$03, and the study also reports higher confidence on at least one item, with a median shift of approximately one Likert level versus LIME (Galus et al., 10 Feb 2026). The paper interprets this as evidence that prototype-grounded, localized explanations are more persuasive than scattered per-point attributions.

In comparative context, XSPLAIN is positioned against three neighboring lines of work. Relative to saliency-based XAI for point clouds, it aims to avoid scattered, noise-sensitive attributions that ignore volumetric overlap. Relative to prior 3DGS interpretability, which the paper says has focused on generative disentanglement or single-view reconstruction, XSPLAIN addresses discriminative classification and supplies localized 3D evidence. Relative to prototype networks, it separates explanation from inference, so classification performance is provably unchanged after compensation (Galus et al., 10 Feb 2026).

A plausible implication is that XSPLAIN treats faithful explanation as a structural property of model design rather than a property of a post-hoc attribution map. In this reading, preservation of logits and localization via immutable voxel indices jointly define faithfulness in operational terms.

7. Computational profile, reproducibility, limitations, and future directions

The computational complexity is broken down explicitly in the paper. Backbone forward computation is $s_i \in \mathbb{R}^3$04 for shared MLPs, voxel max-pooling is $s_i \in \mathbb{R}^3$05 in practice, and average pooling is $s_i \in \mathbb{R}^3$06. Applying the orthogonal transform costs $s_i \in \mathbb{R}^3$07 per sample, and updating $s_i \in \mathbb{R}^3$08 requires computing $s_i \in \mathbb{R}^3$09 at cost $s_i \in \mathbb{R}^3$10 per optimizer step in Stage 2 (Galus et al., 10 Feb 2026). For the reported configuration with $s_i \in \mathbb{R}^3$11 and moderate $s_i \in \mathbb{R}^3$12 such as $s_i \in \mathbb{R}^3$13, the paper characterizes these costs as modest on modern GPUs.

Prototype bookkeeping requires scanning the training set to compute activation scores $s_i \in \mathbb{R}^3$14, with cost $s_i \in \mathbb{R}^3$15, so periodic updates and caching are recommended (Galus et al., 10 Feb 2026). The number of prototypes per channel, $s_i \in \mathbb{R}^3$16, affects coverage and retrieval or storage overhead but not classification accuracy, because prototypes are not on the forward path.

For reproduction, the paper provides source code at the stated repository and recommends preprocessing 3DGS objects into splat parameters $s_i \in \mathbb{R}^3$17, normalizing positions to $s_i \in \mathbb{R}^3$18, and precomputing voxel indices for a chosen grid resolution, with default $s_i \in \mathbb{R}^3$19. The suggested backbone is PointNet with two STNs and a shared MLP to $s_i \in \mathbb{R}^3$20 channels, defaulting to $s_i \in \mathbb{R}^3$21. Stage 1 uses the combined loss $s_i \in \mathbb{R}^3$22 with $s_i \in \mathbb{R}^3$23 and $s_i \in \mathbb{R}^3$24, while Stage 2 initializes $s_i \in \mathbb{R}^3$25 so that $s_i \in \mathbb{R}^3$26, freezes the backbone, and trains $s_i \in \mathbb{R}^3$27 using $s_i \in \mathbb{R}^3$28 with periodic prototype refreshes (Galus et al., 10 Feb 2026).

The hardware guidance states that a single modern GPU, exemplified by $s_i \in \mathbb{R}^3$29 GB VRAM, suffices for the reported settings. The main expensive operation is the matrix exponential, but the paper describes its cost as moderate for the feature sizes considered (Galus et al., 10 Feb 2026).

The reported limitations are several. Scaling to very large 3DGS scenes with millions of splats may require larger or hierarchical voxel grids, and the memory and time needed to build prototype pools can grow. The method is sensitive to voxelization choices: grids that are too fine produce sparse cells, while coarse grids blur parts. The matrix exponential introduces $s_i \in \mathbb{R}^3$30 overhead, which may become problematic for much larger channel dimensions. The current setup excludes color and view-dependent appearance. Finally, the method is presently limited to classification; the paper identifies segmentation, detection, part-level prototypes, scene-level explanations, alternative similarity metrics such as Mahalanobis or cosine distance, and counterfactual editing or robustness testing under perturbations and domain shift as future work (Galus et al., 10 Feb 2026).

These limitations define the present scope of XSPLAIN with some precision. It is a framework for attribute-aware interpretability of 3DGS object classification, grounded in geometry-only splat attributes, voxel-localized evidence, and prototype retrieval, with exact decision-boundary preservation under a linear classification head (Galus et al., 10 Feb 2026). Within that scope, it offers a specific resolution to a broader interpretability tension in geometric learning: explanations are made more semantic by rotating and purifying latent channels, but the classifier itself is kept fixed at the level of logits.