Kinematic Causal Attribution: Black-Box Explanations of Motion versus Geometry for 4D Point-Cloud Video Models

Zerui Wang

cs.CVOct 29, 2026

Kinematic Causal Attribution: Black-Box Explanations of Motion versus Geometry for 4D Point-Cloud Video Models

Authors: Zerui Wang

Abstract

4D perception models, which classify 3D point-cloud videos, are being built into robots, assistive monitoring and AR, yet before deploying one a practitioner cannot check which cue it relies on: how a body part moves, or what shape it has. 3D attribution is single-frame, video attribution is confined to RGB pixels, gradient maps need white-box access, attention is absent from state-space backbones, and point-level perturbations assume a point correspondence across frames that real depth and LiDAR data lack. We present Kinematic Causal Attribution (KCA), a black-box, interventional attribution method that queries only the model's outputs. Its freeze operator removes a region's motion while keeping its shape, and a shape-free proxy removes the shape while keeping the motion. Together they span a motion $\times$ geometry cube for every tracked region, whose order-symmetric Shapley decomposition is complete and whose interaction is measured rather than assumed away. The operators rewrite per-frame point sets, so they need no correspondences, and a context-averaged estimator handles structures that span several regions. We validate KCA on the official PSTNet, P4Transformer and Mamba4D trained on MSR-Action3D. The decisive test is an audit: two binary tasks are built from real clips whose classes differ only in the motion or only in the shape of the same arm, and the motion share of the arm's importance follows the defining cue on all three backbones (0.83 vs. 0.60 on P4Transformer, 0.86 vs. 0.30 on PSTNet, 0.92 vs. 0.61 on Mamba4D), a distinction no single attribution map can make. The split costs no faithfulness: the necessity maps have the lowest deletion AUC on P4Transformer and PSTNet, tie with the best baseline on Mamba4D, and lose their correlation with the trained model's once the weights are randomised. Skeleton ground truth, re-sampling stability and cost complete the validation.

Figures & tables

Figure 1: Kinematic Causal Attribution (KCA) attributes a 4D model’s decision to how each spacetime region moves ( $S_{\mathrm{mot}}$ , red) and to what shape it has ( $S_{\mathrm{geo}}$ , blue). It intervenes on the input and reads only the model’s output. The clip is a real MSR-Action3D test clip ( draw circle ) at four instants, explained for the official P4Transformer. The motion term is strongest on the drawing hand (weaker on the head and one foot), while geometry importance covers the upper body. Fig. 6 in the appendix shows two more actions on all three backbones, including one where the motion term falls on the torso. No attention, gradient or point correspondence is used, and the same code explains convolutional and attention-free state-space backbones (Sec. 4.3 ).

Panel of Figure 2 — Figure 2: Method overview. Regions are tracked through time as per-frame point sets , so no cross-frame point correspondence is needed. Each region carries two factors—its geometry $G$ and its motion $M$ —and four interventions realize the corners of the $(M,G)$ cube; every edge of the cube changes exactly one factor. A local or a context-averaged estimator turns the cube’s outputs into order-symmetric motion and geometry importance whose interaction is measured. Only outputs of $f$ are used, so the same pipeline explains convolutional, attention and state-space backbones.

Method	Del. $\downarrow$	Comp. $\uparrow$	Ins. $\uparrow^{\dagger}$	Suff. $\downarrow^{\dagger}$
Random (floor)	0.916 $\pm$ 0.14	0.003 $\pm$ 0.05	0.920 $\pm$ 0.14	0.041 $\pm$ 0.12
Geometry-edge (floor)	0.890 $\pm$ 0.19	0.011 $\pm$ 0.11	0.903 $\pm$ 0.16	0.103 $\pm$ 0.21
Motion-prior (floor)	0.505 $\pm$ 0.38	0.277 $\pm$ 0.33	0.860 $\pm$ 0.16	0.365 $\pm$ 0.22
Grad $\times$ Input	0.655 $\pm$ 0.28	0.086 $\pm$ 0.18	0.722 $\pm$ 0.25	0.332 $\pm$ 0.28
SmoothGrad [ Smilkov et al., 2017 ]	0.772 $\pm$ 0.24	0.031 $\pm$ 0.12	0.915 $\pm$ 0.14	0.083 $\pm$ 0.16
Integrated Grad. [ Sundararajan et al., 2017 ]	0.282 $\pm$ 0.26	0.347 $\pm$ 0.24	0.862 $\pm$ 0.17	0.129 $\pm$ 0.19

Table 1: Faithfulness on P4Transformer, MSR-Action3D test set (all 287 test clips; mean

\pm

std over clips). Del.: deletion AUC of the target-class probability; Comp.: comprehensiveness. Both remove the top-ranked points. Ins. and Suff. (

\dagger

) keep the top-ranked points, which rewards spatially scattered rankings on point clouds (a random subset preserves the whole body; see the random floor). Bold : best, underlined : second, floors excluded. ∗ : KCA significantly better than the strongest baseline after Bonferroni correction.

Figure 3: Deletion and insertion curves on P4Transformer (mean over the 287 clips of Tab. 1 ): target-class probability vs. fraction of points removed (left) or inserted (right), in 20 steps.

	PSTNet		P4Transformer		Mamba4D
Method	Del. $\downarrow$	EBPG $\uparrow$	Del. $\downarrow$	EBPG $\uparrow$	Del. $\downarrow$	EBPG $\uparrow$
Random (floor)	0.950	0.098	0.929	0.098	0.902	0.098
Integrated Grad. [ Sundararajan et al., 2017 ]	0.303	0.390	0.230	0.567	0.329	0.456
Region occlusion [ Zheng et al., 2019 ]	0.252	0.329	0.230	0.394	0.246	0.351
OccAM [ Schinagl et al., 2022 ]	0.845	0.098	0.865	0.098	0.778	0.098
Extremal Pert. [ Fong et al., 2019 ]	0.932	0.098	0.621	0.076	0.577	0.085

Table 2: Across backbones (the same 40 test clips, two per action, for every backbone; means over clips): deletion AUC and localisation of the moving ground truth (EBPG, on the clips with a complete skeleton;

S_{\mathrm{mot}}

for KCA). Attention methods are undefined on PSTNet and Mamba4D (n/a). Kendall’s

\tau

[ kendall1938 ] between the rankings by Del. of the 7 methods defined on all three backbones: PSTNet–P4Transf. 0.71, PSTNet–Mamba4D 0.81, P4Transf.–Mamba4D 0.71.

	$\to$ moving GT		$\to$ static	crossover: cue =
Method	PG $\uparrow$	EBPG $\uparrow$	PG $\uparrow$	motion	shape
Grad $\times$ Input	0.46	0.35	–	–	–
Integrated Grad. [ Sundararajan et al., 2017 ]	0.92	0.55	–	–	–
3D Grad-CAM [ Selvaraju et al., 2017 ]	0.19	0.10	–	–	–
Region occlusion [ Zheng et al., 2019 ]	0.40	0.40	–	–	–
OccAM [ Schinagl et al., 2022 ]	0.17	0.13	–	–	–

Table 3: Motion vs. geometry (P4Transformer). Left: localisation against the skeleton ground truth on the 275 clips of Tab. 1 with a complete skeleton (PG: Pointing Game;

S_{\mathrm{mot}}

against moving,

S_{\mathrm{geo}}

against static parts). Right: crossover (Sec. 4.4 , 40 test clips per task), motion share

S_{\mathrm{mot}}^{+}/(S_{\mathrm{mot}}^{+}+S_{\mathrm{geo}}^{+})

of the positive importance on the arm; single maps have no split (–).

Figure 4: Double dissociation: motion share on the cue structure when the class is defined by its motion (red) or by its shape (blue), local estimator. Controlled task: pooled over 3 seeds

\times

20 clips. Real crossover: 40 test clips per task and backbone, with 95% bootstrap intervals.

Appendix figures & tables13 assets

Supplementary material from the paper’s appendix.

Appendix

$X=\{P_{t}\}_{t=1}^{T}$	point-cloud video; $P_{t}\!\subset\!\mathbb{R}^{3}$ , sampled per frame
$f,\ \varphi(X){=}f(X)_{c}$	model; target logit of class $c$
$\mathcal{R}=\{\mathcal{R}_{t}\}_{t}$	a tracked region: its point set in each frame
$c_{t}(\mathcal{R})$	centroid of $\mathcal{R}_{t}$
$\mathrm{do}(\textsc{freeze},\mathcal{R})$	freeze: $\mathcal{R}$ static at its $t_{0}$ shape ( $M{=}0$ , $G{=}1$ )
$\mathrm{do}(\textsc{abl-geo},\mathcal{R})$	shape-free proxy moving along $c_{t}$ ( $M{=}1$ , $G{=}0$ )
$\mathrm{do}(\textsc{ablate},\mathcal{R})$	shape-free proxy static at $c_{t_{0}}$ ( $M{=}0$ , $G{=}0$ )

Appendix

Table 4: Notation.

	Assumption	Needed by
I	interventional validity (operators rewrite only $\mathcal{R}_{t}$ )	Props. 2 , 3 , 4
S	separability (measured by $\Delta_{\mathrm{int}}$ , not assumed)	Prop. 2 (marginal ACE only)
M	monotonicity & exogeneity	Prop. 3 (identification)

Appendix

Table 5: Assumptions and the results that require them.

$(0,0)$ corner, order	mot.	shape	Del. $\downarrow$
static proxy (default), symmetric	1.00	0.00	0.428
static proxy, motion-first	1.00	0.00	0.428
deletion, symmetric	0.92	0.49	0.419
deletion, motion-first	0.85	0.00	0.419
donor fill, symmetric	0.92	0.49	0.419
donor fill, motion-first	0.85	0.00	0.419

Appendix

Table 6: Controlled ablation (1 seed): the

(0,0)

corner and the order. Motion share within the odd cluster on the motion (mot.) and shape (shape) models; the decomposition is correct iff mot.

\approx 1

and shape

\approx 0

Result	Data	Model(s)	Record
Tab. 1 , 3 (left), 12 , 13 , 14 ; Fig. 3 , 1 , 6	all 287 test clips, 2048 points per frame; ground-truth metrics on the 275 with a complete skeleton	P4Transformer (Fig. 6 : all three)	benchmark, p4transformer/raw.jsonl
Tab. 2	the first two test clips per action (40)	all three	benchmark, one file per backbone
Tab. 3 (right), Fig. 4 , Appendix G	arm-moving videos: 163 train, 200 test; 40 test clips explained per task	one task model per task and backbone	crossover*/crossover.json
Tab. 11 , Fig. 5 ; displace probe	40 clips (sanity: the first 20)	P4Transformer	ablation/ablation.json
Tab. 8	the same 40 clips, 5 point samplings each	P4Transformer	stability/stability.jsonl
Tab. 10	as the crossover, 6 training seeds	P4Transformer task models	crossover*/crossover.json

Appendix

Table 7: The data, models and per-clip records behind each table and figure. All real-data results use the MSR-Action3D test subjects 6–10 and, except Tab. 9 , the full-scale models.

	one sampling		average of two samplings
Method	points	body parts	points	body parts
Random (floor)	0.00	$-$ 0.01	0.00	0.01
Motion-prior (floor)	0.66	0.99	0.73	0.99
Grad $\times$ Input	0.82	0.86	0.81	0.87
Integrated Grad. [ Sundararajan et al., 2017 ]	0.92	0.94	0.91	0.93
Region occlusion [ Zheng et al., 2019 ]	0.71	0.85	0.81	0.91

Appendix

Table 8: Stability under sensor re-sampling (P4Transformer, 40 test clips, 5 independent point samplings each). Spearman rank correlation between the map of sampling 0 and the map of another sampling transferred onto the points of sampling 0 (nearest neighbour per frame), averaged over samplings and clips. Body parts: each map averaged over the points of each of the 19 skeleton bones (one clip without a complete skeleton is left out). Average of two samplings: maps of samplings 0 and 1 averaged and compared with the average of samplings 2 and 3. Method randomness is fixed per clip, so only the point sampling changes.

Quantity	laptop	full scale
Test accuracy, P4Transformer (%)	90.6	89.2
Test accuracy, PSTNet (%)	87.5	88.9
Test accuracy, Mamba4D (%)	83.6	88.2
P4T Del.: KCA (context)	0.178	0.179
P4T Del.: region occlusion	0.219	0.233
P4T Del.: Integrated Gradients	0.268	0.282

Appendix

Table 9: Headline numbers at the two training scales (laptop: 100 P4Transformer clips; full scale: all 287; the other rows use the same clips at both scales. Del.: deletion AUC; crossover: motion share of the arm’s importance; randomised model: rank correlation with the trained model’s map once every block is re-initialised).

Seed	acc. % (mot. / shape)	share (mot. / shape)	gap 95% CI
0	80.5 / 83.5	0.83 / 0.60	[0.14, 0.32]
1 (not trained)	50.0 / 86.5	0.65 / 0.55	[ $-$ 0.02, 0.21]
2	67.8 / 88.8	0.73 / 0.57	[0.06, 0.26]
3	78.8 / 77.5	0.85 / 0.78	[ $-$ 0.02, 0.19]
4 (not trained)	50.0 / 72.2	0.60 / 0.81	[ $-$ 0.32, $-$ 0.08]
5 (not trained)	50.0 / 80.5	0.73 / 0.69	[ $-$ 0.05, 0.17]

Appendix

Table 10: P4Transformer crossover over training seeds (local estimator, 40 explained test clips per task). A seed counts only if both task models leave chance (accuracy

\geq 60\%

on the balanced binary test set); seed 0 is the one reported in the main text.

Variant	Del. $\downarrow$	$S_{\mathrm{mot}}$ EBPG $\uparrow$	mot. share	$\tfrac{\|\Delta_{\mathrm{int}}\|}{\|\mathcal{N}\|}$	passes	s
local, $m{=}6$	0.235	0.47	0.65	0.46	19	0.3
local, $m{=}12$ (default)	0.272	0.54	0.73	0.63	37	0.5
local, $m{=}24$	0.334	0.54	0.78	0.70	73	0.8
context, $m{=}6$	0.192	0.44	0.65	0.48	257	2.3
context, $m{=}12$ (default)	0.219	0.54	0.75	0.58	257	2.3
context, $m{=}24$	0.212	0.52	0.82	0.66	257	2.4

Appendix

Table 11: Ablation and cost (P4Transformer, 40 clips). EBPG and motion share on the moving ground truth;

|\Delta_{\mathrm{int}}|/|\mathcal{N}|

: mean interaction relative to necessity; forward passes and seconds per clip on one A100 GPU.

Method	Del. $\downarrow$	Comp. $\uparrow$	Ins. $\uparrow^{\dagger}$	Suff. $\downarrow^{\dagger}$	Sens- $n\uparrow$
Random (floor)	0.916 $\pm$ 0.14	0.003 $\pm$ 0.05	0.920 $\pm$ 0.14	0.041 $\pm$ 0.12	0.004 $\pm$ 0.17
Geometry-edge (floor)	0.890 $\pm$ 0.19	0.011 $\pm$ 0.11	0.903 $\pm$ 0.16	0.103 $\pm$ 0.21	0.000 $\pm$ 0.17
Motion-prior (floor)	0.505 $\pm$ 0.38	0.277 $\pm$ 0.33	0.860 $\pm$ 0.16	0.365 $\pm$ 0.22	0.000 $\pm$ 0.18
Grad $\times$ Input	0.655 $\pm$ 0.28	0.086 $\pm$ 0.18	0.722 $\pm$ 0.25	0.332 $\pm$ 0.28	0.028 $\pm$ 0.23
SmoothGrad [ Smilkov et al., 2017 ]	0.772 $\pm$ 0.24	0.031 $\pm$ 0.12	0.915 $\pm$ 0.14	0.083 $\pm$ 0.16	0.006 $\pm$ 0.18
Integrated Grad. [ Sundararajan et al., 2017 ]	0.282 $\pm$ 0.26	0.347 $\pm$ 0.24	0.862 $\pm$ 0.17	0.129 $\pm$ 0.19	0.046 $\pm$ 0.22

Appendix

Table 12: Full faithfulness table on P4Transformer, including Sensitivity-

n

(Pearson correlation between summed attribution and output drop over random 10% subsets; near zero for all methods, because random subsets barely change the output).

Method	s / clip
Random (floor)	0.00
Geometry-edge (floor)	0.14
Motion-prior (floor)	0.16
Grad $\times$ Input	0.06
SmoothGrad [ Smilkov et al., 2017 ]	1.53
Integrated Grad. [ Sundararajan et al., 2017 ]	1.93

Appendix

Table 13: Explanation cost per clip on one A100 GPU (P4Transformer, 24 frames

\times

2048 points; seconds, excluding metric evaluation).

Figure 5: Cascading model randomisation [ Adebayo et al., 2018 ] of P4Transformer, from the classification head down: rank correlation of the attribution map with the trained model’s.

Figure 6: $S_{\mathrm{mot}}$ (red) and $S_{\mathrm{geo}}$ (blue) on real MSR-Action3D test clips at three instants; rows: three actions ( draw circle , high arm wave , forward kick ) $\times$ the three backbones, same code.

Action	mot. share	Del. KCA	Del. occl.	acc. %
high arm wave	0.61	0.151	0.265	100
horizontal arm wave	0.61	0.062	0.090	100
hammer	0.63	0.074	0.075	7
hand catch	0.68	0.244	0.359	80
forward punch	0.63	0.193	0.232	92
high throw	0.65	0.103	0.101	86

Appendix

Table 14: Per action (P4Transformer, all test clips of each action): motion share

S_{\mathrm{mot}}^{+}/(S_{\mathrm{mot}}^{+}+S_{\mathrm{geo}}^{+})

of KCA (context) over the whole body, deletion AUC of KCA (context) and of region occlusion, and the model’s accuracy on these clips.

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