Causal Attribution via Activation Patching

Amirmohammad Izadi; Mohammadali Banayeeanzade; Alireza Mirrokni; Hosein Hasani; Mobin Bagherian; Faridoun Mehri; Mahdieh Soleymani Baghshah

cs.CVMar 13, 2026

Causal Attribution via Activation Patching

Authors: Amirmohammad Izadi, Mohammadali Banayeeanzade, Alireza Mirrokni, Hosein Hasani, Mobin Bagherian, Faridoun Mehri, Mahdieh Soleymani Baghshah

Organizations: Sharif University of Technology

Abstract

Attribution methods for Vision Transformers (ViTs) aim to identify image regions that influence model predictions, but producing faithful and well-localized attributions remains challenging. Existing attribution methods face several limitations, with gradient-based, relevance-propagation, and attention-based methods relying on local approximations, while perturbation or optimization-based methods intervene on inputs, tokens, or surrogates rather than internal patch representations. The key challenge is that class-relevant evidence is formed through interactions between patch tokens across layers; methods that operate only on input changes, attention weights, or backward relevance signals may therefore provide indirect proxies for patch importance rather than directly testing the predictive effect of contextualized patch representations. We propose Causal Attribution via Activation Patching (CAAP), which estimates the contribution of individual image patches to the ViT's prediction by directly intervening on internal activations rather than using learned masks or synthetic perturbation patterns. For each patch, CAAP inserts the corresponding source-image activations into a neutral target context over an intermediate range of layers and uses the resulting target-class score as the attribution signal. The resulting attribution map reflects the causal contribution of patch-associated internal representations on the model's prediction. The causal intervention serves as a principled measure of patch influence by capturing semantic evidence after initial representation formation, while avoiding late-layer global mixing that can reduce spatial specificity. Across multiple ViT backbones and standard metrics, CAAP consistently outperforms existing methods in various settings and produces more faithful and localized attributions.

Figures & tables

Figure 1: Overview of CAAP. Given a source image (top) and a blank target image (middle), we extract internal activations from the source image corresponding to a selected patch and a specified range of layers. These activations are injected into the target context to form a patched context (bottom), while all other activations remain unchanged. A forward pass on the patched sequence produces a class score for the CLS token (green), which measures the causal effect of the selected patch on the target prediction. Repeating this intervention for all patches yields a patch-level attribution.

h^{l}(c^{*})\leftarrow h^{l}(x_{0}),\hskip 8.50012pt\forall l\in\{1,\dots,L\}

Algorithm 1 CAAP: C ausal A ttribution via A ctivation P atching

	ViT-L/16 [ 1 ]			CLIP-L/14 [ 2 ]			DINOv2-L/14 [ 3 ]			DeiT3-L/16 [ 4 ]
Method	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$
RISE [ 17 ]	55.53 ±2.36	71.83 ±1.53	16.30 ±2.09	52.57 ±2.05	75.83 ±1.12	23.26 ±1.79	59.59 ±2.20	78.03 ±1.66	18.45 ±1.48	50.28 ±2.00	63.05 ±1.39	12.77 ±1.48
Grad-CAM [ 9 ]	48.99 ±1.22	70.40 ±1.08	21.40 ±1.17	46.74 ±1.14	73.19 ±0.85	26.46 ±1.07	49.36 ±1.20	76.01 ±1.11	26.65 ±1.00	31.81 ±0.89	62.18 ±0.93	30.37 ±0.80
Rollout [ 13 ]	67.69 ±1.06	56.11 ±1.24	-11.58 ±1.03	60.08 ±1.05	64.90 ±1.00	4.82 ±0.99	63.10 ±1.16	73.97 ±1.20	10.86 ±0.81	58.80 ±1.04	53.27 ±1.04	-5.54 ±0.86
T-Attr [ 10 ]	53.99 ±1.21	68.75 ±1.08	14.77 ±1.10	50.20 ±1.14	72.35 ±0.90	22.15 ±1.02	63.23 ±1.14	73.82 ±1.20	10.59 ±0.86	37.36 ±1.00	66.48 ±0.96	29.12 ±0.92
ViT-CX [ 22 ]	48.57 ±1.27	71.36 ±1.10	22.79 ±1.25	50.27 ±1.26	69.65 ±0.96	19.38 ±1.40	49.50 ±1.26	78.02 ±1.12	28.51 ±1.17	38.56 ±1.13	58.99 ±0.96	20.43 ±1.22

Table 1: Faithfulness quantitative results on ImageNet for ViT-L/16 [ 1 ] , CLIP-L/14 [ 2 ] , DINOv2-L/14 [ 3 ] , and DeiT3-L/16 [ 4 ] . Deletion (

\downarrow

), Insertion (

\uparrow

), and Ins

-

Del (

\uparrow

) are reported. Best is bold , second best is underlined in each column.

	ViT-L/16 [ 1 ]			CLIP-L/14 [ 2 ]			DINOv2-L/14 [ 3 ]			DeiT3-L/16 [ 4 ]
Method	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$
RISE [ 17 ]	41.92 ±2.15	71.04 ±2.24	40.62 ±4.34	43.12 ±2.13	72.75 ±2.20	39.84 ±4.33	37.32 ±2.25	69.62 ±2.19	30.47 ±4.07	40.28 ±2.19	69.79 ±2.28	35.94 ±4.24
Grad-CAM [ 9 ]	52.75 ±2.12	78.83 ±2.10	50.00 ±4.42	53.34 ±2.05	75.29 ±2.27	56.25 ±4.38	50.10 ±2.11	77.52 ±2.24	43.75 ±4.38	67.25 ±1.93	85.64 ±1.86	70.31 ±4.04
Rollout [ 13 ]	27.70 ±1.81	61.81 ±2.58	14.84 ±3.14	37.75 ±2.11	68.25 ±2.57	32.81 ±4.15	34.31 ±1.94	66.23 ±2.40	33.59 ±4.17	29.40 ±1.90	64.95 ±2.46	3.12 ±1.54
T-Attr [ 10 ]	38.74 ±1.91	72.64 ±2.41	20.31 ±3.56	51.00 ±1.70	75.27 ±2.35	40.62 ±4.34	40.23 ±2.32	72.22 ±2.16	36.72 ±4.26	60.90 ±1.71	81.13 ±1.99	34.38 ±4.20
ViT-CX [ 22 ]	56.35 ±2.05	78.97 ±2.22	53.12 ±4.41	49.89 ±2.42	73.12 ±2.37	50.78 ±4.42	47.76 ±2.10	72.29 ±2.50	45.31 ±4.40	57.88 ±2.30	77.61 ±2.48	52.34 ±4.41

Table 2: Localization quantitative results on ImageNet for ViT-L/16 [ 1 ] , CLIP-L/14 [ 2 ] , DINOv2-L/14 [ 3 ] , and DeiT3-L/16 [ 4 ] . AUPR 1 (

\uparrow

), AUPR 0 (

\uparrow

) and PG (

\uparrow

) are reported. Best is bold , second best is underlined in each column.

	Oxford-IIIT-Pet [ 33 ]			ImageNet-Hard [ 32 ]			Food-101 [ 34 ]
Method	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$
RISE [ 17 ]	62.15 ±1.25	85.08 ±0.57	22.92 ±1.23	11.69 ±0.78	34.82 ±1.29	23.13 ±1.15	46.82 ±1.35	70.80 ±0.82	23.98 ±1.16
Grad-CAM [ 9 ]	61.95 ±1.08	78.41 ±0.77	16.46 ±1.23	14.66 ±0.89	26.04 ±1.15	11.38 ±1.11	51.84 ±1.26	62.08 ±1.00	10.25 ±1.22
Rollout [ 13 ]	73.84 ±0.90	72.15 ±0.83	-1.69 ±1.03	22.61 ±1.07	17.91 ±0.91	-4.70 ±0.97	60.70 ±1.07	54.77 ±1.02	-5.93 ±0.92
T-Attr [ 10 ]	53.37 ±0.99	84.32 ±0.61	30.95 ±0.99	12.86 ±0.79	27.41 ±1.14	14.55 ±1.01	41.23 ±1.07	65.52 ±1.00	24.30 ±1.00
ViT-CX [ 22 ]	47.79 ±0.93	85.26 ±0.71	37.47 ±1.03	14.14 ±0.78	25.76 ±1.19	11.62 ±1.12	37.62 ±0.96	66.34 ±1.07	28.71 ±1.11

Table 3: Faithfulness quantitative results on Oxford-IIIT-Pet [ 33 ] , ImageNet-Hard [ 32 ] , and Food-101 [ 34 ] for ViT-B/16. Deletion (

\downarrow

), Insertion (

\uparrow

), and Ins

-

Del (

\uparrow

) are reported. Best is bold and second best is underlined in each column.

Figure 2: Qualitative attribution comparison between different methods for a representative ImageNet sample. CAAP produces more compact and well-localized attributions for the target class than the baselines. More single-object qualitative examples are provided in the Appendix B.3 (Fig. 13 – 42 ).

Figure 3: Qualitative attribution comparison between different methods for an image containing multiple objects. CAAP produces compact and class-specific attributions aligned with the queried object class. More multi-object qualitative examples are provided in Appendix B.3 (Fig. 43 – 52 ).

Panel of Figure 4 — Figure 4: Ablation studies of activation patching context characteristics on ImageNet using CLIP-L/14. (a) Effect of target blank type (Black, Blur Noisy, Mean, Noisy, White). (b) Effect of spatial support in the selection operator (No Padding, Radius-1 Box, Radius-2 Box, Radius-1 Manhattan). Faithfulness (Insertion, Deletion, Ins $-$ Del) and localization (PG, AUPR 1 , AUPR 0 ) are reported. Results on other ViT backbones are provided in Appendix D.1 .

Panel of Figure 5 — Figure 5: Layer analysis on ImageNet using CLIP-L/14. (a) Mean intra-object, inter-object, and object-to-background attention across layers. In early layers, intra-object attention increases and dominates, indicating strong object-level grouping. Around the middle layers, this gap reaches its peak. In later layers, intra-object attention decreases while object-to-background attention increases, reflecting growing extra-object contextualization and reduced spatial specificity. (b) Cumulative intervention depth sweep showing faithfulness metrics. Intermediate layers provide the best trade-off between object-level grouping and global contextual mixing.

Appendix figures & tables60 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 6 — Figure 6: Representative insertion curves on ImageNet for ViT-L/16, CLIP-L/14, DINOv2-L/14, and DeiT3-L/16. Higher curves indicate that the attribution method more effectively identifies regions that positively support the model prediction.

Panel of Figure 7 — Figure 7: Representative deletion curves on ImageNet for ViT-L/16, CLIP-L/14, DINOv2-L/14, and DeiT3-L/16. Lower curves indicate that the attribution method more accurately identifies regions whose removal causes a stronger drop in model confidence.

Figure 8: Radar-plot comparison of attribution performance over 10 representative ViT backbones. CAAP is compared against the four strongest baselines: MUTEX, TAM, Libra IxG+, and ViT-CX, across faithfulness and localization metrics. Higher values indicate better performance. CAAP shows the most consistently strong performance across backbones, supporting its effectiveness as a faithful and spatially precise method.

	ViT-B/16 [ 1 ]			Clip-B/16 [ 2 ]			DINOv2-B/14 [ 3 ]			DeiT3-B/16 [ 4 ]
Method	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$
RISE [ 17 ]	42.65 ±1.51	66.85 ±1.17	24.20 ±1.36	56.22 ±1.12	59.32 ±1.06	3.10 ±0.85	52.17 ±1.37	76.24 ±1.00	24.07 ±1.03	43.45 ±1.22	60.54 ±0.83	17.09 ±0.90
Grad-CAM [ 9 ]	43.92 ±1.41	59.07 ±1.25	15.15 ±1.40	55.21 ±1.21	52.68 ±1.04	-2.53 ±1.30	42.45 ±1.16	74.98 ±1.13	32.53 ±1.01	28.96 ±0.89	61.09 ±0.91	32.13 ±0.86
Rollout [ 13 ]	54.68 ±1.36	49.83 ±1.28	-4.85 ±1.27	51.65 ±1.12	56.68 ±1.09	5.03 ±1.16	52.01 ±1.16	71.06 ±1.18	19.05 ±0.97	46.78 ±1.03	53.76 ±0.98	6.98 ±0.94
T-Attr [ 10 ]	39.49 ±1.32	60.73 ±1.25	21.24 ±1.26	41.73 ±1.10	65.18 ±1.04	23.45 ±1.09	45.09 ±1.10	73.29 ±1.19	28.20 ±1.02	32.61 ±0.96	62.75 ±0.98	30.13 ±0.93
ViT-CX [ 22 ]	33.94 ±1.17	62.41 ±1.35	28.47 ±1.43	40.78 ±1.21	61.78 ±1.06	21.00 ±1.44	44.25 ±1.23	74.66 ±1.13	30.41 ±1.15	31.64 ±1.00	57.73 ±0.95	26.10 ±1.10

Appendix

Table 4: Faithfulness quantitative results on ImageNet for ViT-B/16 [ 1 ] , Clip-B/16 [ 2 ] , DINOv2-B/14 [ 3 ] , and DeiT3-B/16 [ 4 ] . Deletion (

\downarrow

), Insertion (

\uparrow

), and Ins

-

Del (

\uparrow

) are reported. Best is bold , second best is underlined in each column.

	ViT-B/16 [ 1 ]			Clip-B/16 [ 2 ]			DINOv2-B/14 [ 3 ]			DeiT3-B/16 [ 4 ]
Method	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$
RISE [ 17 ]	47.82 ±2.14	72.76 ±2.31	53.91 ±4.41	34.98 ±2.25	69.84 ±2.15	25.00 ±3.83	37.94 ±2.18	69.99 ±2.23	28.91 ±4.01	42.54 ±2.18	70.54 ±2.30	46.09 ±4.41
Grad-CAM [ 9 ]	46.29 ±2.37	73.78 ±2.23	45.31 ±4.40	34.26 ±2.36	66.35 ±2.26	22.66 ±3.70	37.07 ±2.31	72.09 ±2.08	46.09 ±4.41	66.84 ±2.08	86.85 ±1.78	66.41 ±4.17
Rollout [ 13 ]	31.62 ±1.83	65.91 ±2.65	14.84 ±3.14	39.24 ±1.95	68.69 ±2.66	28.91 ±4.01	33.34 ±2.05	67.76 ±2.30	36.72 ±4.26	32.41 ±1.77	67.86 ±2.64	11.72 ±2.84
T-Attr [ 10 ]	43.33 ±1.80	74.48 ±2.43	35.16 ±4.22	54.08 ±1.84	78.80 ±2.25	52.34 ±4.41	37.08 ±2.21	71.10 ±2.20	42.19 ±4.37	60.34 ±1.75	82.23 ±1.98	53.12 ±4.41
ViT-CX [ 22 ]	62.87 ±2.13	82.34 ±2.09	67.19 ±4.15	54.13 ±2.42	74.43 ±2.48	59.38 ±4.34	36.43 ±2.25	70.02 ±2.18	51.56 ±4.42	62.86 ±2.13	78.92 ±2.48	65.62 ±4.20

Appendix

Table 5: Localization quantitative results on ImageNet for ViT-B/16 [ 1 ] , Clip-B/16 [ 2 ] , DINOv2-B/14 [ 3 ] , and DeiT3-B/16 [ 4 ] . AUPR 1 (

\uparrow

), AUPR 0 (

\uparrow

) and PG (

\uparrow

) are reported. Best is bold , second best is underlined in each column.

	ViT-S/16 [ 1 ]			DINOv2-S/14 [ 3 ]			DeiT3-S/16 [ 4 ]
Method	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$
RISE [ 17 ]	35.38 ±1.31	63.68 ±1.12	28.29 ±1.19	39.25 ±1.30	71.03 ±1.02	31.78 ±1.05	39.65 ±1.45	68.01 ±1.21	28.36 ±1.23
Grad-CAM [ 9 ]	30.70 ±1.07	61.41 ±1.22	30.71 ±1.11	30.94 ±0.99	68.28 ±1.15	37.35 ±1.02	27.35 ±1.04	67.17 ±1.32	39.83 ±1.17
Rollout [ 13 ]	43.36 ±1.16	50.29 ±1.26	6.93 ±1.15	40.01 ±1.09	64.05 ±1.20	24.04 ±1.05	51.77 ±1.33	52.32 ±1.29	0.54 ±1.12
T-Attr [ 10 ]	30.23 ±1.04	60.06 ±1.24	29.83 ±1.10	34.39 ±1.01	66.21 ±1.20	31.82 ±1.04	33.29 ±1.18	65.70 ±1.34	32.41 ±1.14
ViT-CX [ 22 ]	28.84 ±1.01	61.42 ±1.27	32.58 ±1.22	33.44 ±1.09	66.93 ±1.17	33.49 ±1.17	33.98 ±1.22	63.77 ±1.38	29.79 ±1.36

Appendix

Table 6: Faithfulness quantitative results on ImageNet for ViT-S/16 [ 1 ] , DINOv2-S/14 [ 3 ] , and DeiT3-S/16 [ 4 ] . Deletion (

\downarrow

), Insertion (

\uparrow

), and Ins

-

Del (

\uparrow

) are reported. Best is bold , second best is underlined in each column.

	ViT-S/16 [ 1 ]			DINOv2-S/14 [ 3 ]			DeiT3-S/16 [ 4 ]
Method	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$
RISE [ 17 ]	47.43 ±2.05	72.46 ±2.30	50.78 ±4.42	42.35 ±2.07	70.93 ±2.36	41.41 ±4.35	47.43 ±2.15	72.66 ±2.31	49.22 ±4.42
Grad-CAM [ 9 ]	54.18 ±2.08	79.60 ±2.23	50.00 ±4.42	53.34 ±2.20	81.38 ±2.05	50.78 ±4.42	61.08 ±2.00	81.44 ±2.09	59.38 ±4.34
Rollout [ 13 ]	34.28 ±1.91	66.55 ±2.67	17.19 ±3.33	38.69 ±1.86	69.65 ±2.54	42.19 ±4.37	34.06 ±2.00	66.57 ±2.48	24.22 ±3.79
T-Attr [ 10 ]	44.47 ±1.68	76.60 ±2.39	18.75 ±3.45	49.48 ±2.07	76.20 ±2.31	43.75 ±4.38	55.54 ±1.85	75.75 ±2.19	62.50 ±4.28
ViT-CX [ 22 ]	59.01 ±2.16	80.91 ±2.24	53.91 ±4.41	53.98 ±2.16	75.50 ±2.53	59.38 ±4.34	56.21 ±2.16	78.51 ±2.28	54.69 ±4.40

Appendix

Table 7: Localization quantitative results on ImageNet for ViT-S/16 [ 1 ] , DINOv2-S/14 [ 3 ] , and DeiT3-S/16 [ 4 ] . AUPR 1 (

\uparrow

), AUPR 0 (

\uparrow

) and PG (

\uparrow

) are reported. Best is bold , second best is underlined in each column.

	CLIP-H/14 [ 2 ]			DINOv2-G/14 [ 3 ]			DeiT3-H/14 [ 4 ]
Method	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$
RISE [ 17 ]	45.28 ±1.74	63.61 ±0.93	18.33 ±1.58	64.41 ±2.81	81.11 ±1.88	16.70 ±1.59	63.56 ±2.34	55.43 ±2.25	-8.13 ±1.91
Grad-CAM [ 9 ]	43.90 ±1.63	54.91 ±1.28	11.01 ±1.64	58.01 ±1.86	79.67 ±1.67	21.65 ±1.54	35.53 ±1.58	64.04 ±1.43	28.51 ±1.31
Rollout [ 13 ]	44.64 ±1.46	54.02 ±1.35	9.37 ±1.45	69.34 ±1.79	76.50 ±1.76	7.16 ±1.10	63.67 ±1.48	52.83 ±1.62	-10.84 ±1.24
T-Attr [ 10 ]	41.07 ±1.58	57.55 ±1.27	16.48 ±1.58	53.01 ±1.99	81.48 ±1.55	28.47 ±1.64	40.30 ±1.70	67.09 ±1.45	26.78 ±1.51
CausalX [ 22 ]	39.61 ±1.67	56.52 ±1.34	16.91 ±2.00	56.65 ±2.07	81.24 ±1.55	24.59 ±1.74	41.69 ±1.82	60.09 ±1.51	18.40 ±1.80

Appendix

Table 8: Faithfulness quantitative results on ImageNet for CLIP-H/14 [ 2 ] , DINOv2-G/14 [ 3 ] , and DeiT3-H/14 [ 4 ] . Deletion (

\downarrow

), Insertion (

\uparrow

), and Ins

-

Del (

\uparrow

) are reported. Best is bold , second best is underlined in each column.

	CLIP-H/14 [ 2 ]			DINOv2-G/14 [ 3 ]			DeiT3-H/14 [ 4 ]
Method	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$
RISE [ 17 ]	47.27 ±3.03	71.21 ±3.39	51.85 ±6.80	32.43 ±4.27	68.07 ±4.43	25.00 ±8.84	34.94 ±4.43	68.90 ±4.55	50.00 ±10.21
Grad-CAM [ 9 ]	39.31 ±2.24	71.89 ±2.32	27.34 ±3.94	47.64 ±2.25	77.12 ±2.20	44.53 ±4.39	64.60 ±1.88	85.08 ±1.89	62.50 ±4.28
Rollout [ 13 ]	41.40 ±2.15	71.28 ±2.54	37.50 ±4.28	33.66 ±1.97	65.90 ±2.38	38.28 ±4.30	28.49 ±1.95	64.97 ±2.34	2.34 ±1.34
T-Attr [ 10 ]	43.87 ±1.76	73.82 ±2.44	33.59 ±4.17	52.91 ±1.79	76.06 ±2.46	46.88 ±4.41	54.06 ±1.63	80.76 ±2.06	28.91 ±4.01
CausalX [ 22 ]	51.98 ±2.32	75.55 ±2.35	58.59 ±4.35	45.94 ±2.37	71.65 ±2.38	41.41 ±4.35	52.49 ±2.40	76.23 ±2.26	50.78 ±4.42

Appendix

Table 9: Localization quantitative results on ImageNet for CLIP-H/14 [ 2 ] , DINOv2-G/14 [ 3 ] , and DeiT3-H/14 [ 4 ] . AUPR 1 (

\uparrow

), AUPR 0 (

\uparrow

), and PG (

\uparrow

) are reported. Best is bold , second best is underlined in each column.

	ViT-L/16 [ 1 ]		CLIP-L/14 [ 2 ]		DINOv2-L/14 [ 3 ]		DeiT3-L/16 [ 4 ]
Method	Ent $\downarrow$	Gini $\uparrow$	Ent $\downarrow$	Gini $\uparrow$	Ent $\downarrow$	Gini $\uparrow$	Ent $\downarrow$	Gini $\uparrow$
RISE [ 17 ]	97.93 ±0.04	24.58 ±0.24	98.03 ±0.03	24.80 ±0.18	98.35 ±0.03	22.65 ±0.18	98.02 ±0.04	24.02 ±0.23
Grad-CAM [ 9 ]	93.33 ±0.20	42.73 ±0.59	73.09 ±0.50	79.85 ±0.50	94.39 ±0.14	41.03 ±0.49	85.90 ±0.30	60.21 ±0.59
Rollout [ 13 ]	96.42 ±0.03	33.53 ±0.15	96.59 ±0.05	33.09 ±0.22	83.98 ±0.12	60.53 ±0.20	93.28 ±0.08	41.32 ±0.27
T-Attr [ 10 ]	88.93 ±0.12	53.99 ±0.30	89.15 ±0.41	55.24 ±0.88	95.89 ±0.12	32.75 ±0.37	81.01 ±0.31	69.68 ±0.42
ViT-CX [ 22 ]	97.14 ±0.07	27.79 ±0.44	97.63 ±0.07	25.87 ±0.43	97.31 ±0.05	28.51 ±0.32	95.90 ±0.10	33.95 ±0.44

Appendix

Table 10: Compactness quantitative results on ImageNet for ViT-L/16 [ 1 ] , CLIP-L/14 [ 2 ] , DINOv2-L/14 [ 3 ] , and DeiT3-L/16 [ 4 ] . Entropy (

\downarrow

) and Gini (

\uparrow

) are reported. Best is bold , second best is underlined in each column.

	ViT-L/16 [ 1 ]			CLIP-L/14 [ 2 ]			DINOv2-L/14 [ 3 ]			DeiT3-L/16 [ 4 ]
Method	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$
CAAP	43.61 ±2.73	71.10 ±2.61	27.50 ±2.71	34.20 ±2.21	74.92 ±2.01	40.73 ±2.15	43.48 ±2.76	79.05 ±2.50	35.57 ±2.16	28.93 ±1.84	65.79 ±2.06	36.86 ±1.82
E-CAAP	42.56 ±2.80	70.23 ±2.56	27.67 ±2.63	33.56 ±2.42	74.68 ±2.58	41.12 ±2.39	41.73 ±2.79	78.44 ±2.75	36.71 ±2.65	29.72 ±1.87	65.55 ±2.33	35.83 ±1.97

Appendix

Table 11: Faithfulness quantitative results for CAAP and Efficient-CAAP (E-CAAP) on ImageNet. Deletion (

\downarrow

), Insertion (

\uparrow

), and Ins

-

Del (

\uparrow

) are reported.

	ViT-L/16 [ 1 ]			CLIP-L/14 [ 2 ]			DINOv2-L/14 [ 3 ]			DeiT3-L/16 [ 4 ]
Method	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$
CAAP	62.29 ±3.70	80.83 ±3.75	77.78 ±8.00	64.30 ±3.68	84.44 ±3.29	74.07 ±8.43	53.04 ±3.88	74.96 ±4.52	37.04 ±9.29	73.53 ±3.10	87.19 ±3.17	85.19 ±6.84
E-CAAP	61.17 ±3.11	80.28 ±3.23	75.66 ±4.71	66.59 ±2.41	83.35 ±3.11	73.14 ±4.99	54.45 ±3.16	75.99 ±3.14	38.75 ±4.96	72.41 ±2.84	86.28 ±2.23	87.67 ±3.16

Appendix

Table 12: Localization quantitative results for CAAP and Efficient-CAAP (E-CAAP) on ImageNet. AUPR 1 (

\uparrow

), AUPR 0 (

\uparrow

), and PG (

\uparrow

) are reported.

Figure 9: Target blank ablation on ImageNet across four ViT backbones. The type of target blank patches is varied (Black, Blur, Noisy Mean, Noisy, White), and faithfulness (Insertion, Deletion, Ins

-

Del) and localization (PG, AUPR 1 , AUPR 0 ) are reported.

Figure 10: Selection operator ablation on ImageNet across four ViT backbones. The spatial support of the selection operator is varied by considering different neighborhood variants (No Padding, Radius-1 Box, Radius-2 Box, Radius-1 Manhattan), and faithfulness (Insertion, Deletion, Ins

-

Del) and localization (PG, AUPR 1 , AUPR 0 ) are reported.

Figure 11: Mean attention weights across layers for different region pairs: intra-object (blue), inter-object (orange), and object-to-background (green). In early layers, intra-object attention increases and dominates, indicating strong object-level grouping. Around the middle layers, this gap reaches its peak. In later layers, intra-object attention decreases while object-to-background attention increases, reflecting growing extra-object contextualization and reduced spatial specificity.

Figure 12: Intervention depth ablation on ImageNet using ViT backbones. For every cutoff point, we intervene on all transformer blocks from the initial layer up to that point and measure faithfulness metrics.

	ViT-L/16 [ 1 ]			CLIP-L/14 [ 2 ]			DINOv2-L/14 [ 3 ]			DeiT3-L/16 [ 4 ]
Method	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$
Input Insertion	55.63 ±1.24	69.51 ±1.19	10.63 ±1.01	43.86 ±1.10	75.33 ±0.87	14.93 ±0.83	49.79 ±1.20	79.41 ±1.11	19.59 ±0.79	33.33 ±0.92	64.50 ±0.97	22.16 ±0.75
Input Deletion	58.89 ±1.37	69.75 ±1.07	10.86 ±1.20	60.40 ±1.27	72.38 ±0.89	11.98 ±1.14	59.82 ±1.33	80.18 ±1.05	20.36 ±0.93	42.34 ±0.90	61.13 ±0.89	18.79 ±0.88
CAAP (Ours)	42.67 ±1.16	73.42 ±1.07	30.75 ±1.18	34.35 ±0.99	75.88 ±0.85	41.52 ±1.02	43.11 ±1.14	80.09 ±1.08	36.98 ±1.00	31.56 ±0.91	64.84 ±0.93	33.28 ±0.85

Appendix

Table 13: Faithfulness quantitative results for Input Insertion, Input Deletion, and CAAP on ImageNet. Deletion (

\downarrow

), Insertion (

\uparrow

), and Ins

-

Del (

\uparrow

) are reported. Best is bold , second best is underlined in each column.

	ViT-L/16 [ 1 ]			CLIP-L/14 [ 2 ]			DINOv2-L/14 [ 3 ]			DeiT3-L/16 [ 4 ]
Method	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$
Input Insertion	49.28 ±1.99	71.10 ±2.18	61.72 ±4.30	55.32 ±1.96	75.55 ±2.09	59.38 ±4.34	48.13 ±2.02	72.81 ±2.16	52.34 ±4.41	55.59 ±1.97	79.02 ±1.99	62.50 ±4.28
Input Deletion	40.82 ±2.07	67.53 ±2.23	46.09 ±4.41	40.44 ±2.10	66.01 ±2.18	58.59 ±4.35	39.05 ±2.09	67.45 ±2.27	45.31 ±4.40	47.51 ±2.50	80.74 ±1.69	57.81 ±4.37
CAAP (Ours)	63.40 ±2.01	83.40 ±1.99	73.44 ±3.90	66.42 ±1.78	84.86 ±1.89	74.22 ±3.87	52.76 ±1.86	76.68 ±2.17	41.41 ±4.35	71.21 ±1.86	86.93 ±1.85	82.81 ±3.33

Appendix

Table 14: Localization quantitative results for Input Insertion, Input Deletion, and CAAP on ImageNet. AUPR 1 (

\uparrow

), AUPR 0 (

\uparrow

) and PG (

\uparrow

) are reported. Best is bold , second best is underlined in each column.

	ResNet-18 [ 41 ]			ResNet-50 [ 41 ]			DenseNet-161 [ 42 ]			VGG-16 [ 43 ]
Method	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$	Del $\downarrow$	Ins $\uparrow$	Ins $-$ Del $\uparrow$
Input Insertion	16.05 ±0.67	38.75 ±1.20	22.70 ±1.13	15.65 ±0.64	49.11 ±1.28	33.46 ±1.25	20.83 ±0.78	52.87 ±1.34	32.04 ±1.26	14.60 ±0.62	41.01 ±1.22	26.41 ±1.14
Input Deletion	12.54 ±0.57	54.44 ±1.19	41.90 ±1.09	14.74 ±0.78	62.19 ±1.18	47.45 ±1.22	20.35 ±0.95	65.98 ±1.16	45.64 ±1.17	11.66 ±0.60	57.54 ±1.17	45.88 ±1.09
CAAP (Ours)	13.53 ±0.58	55.64 ±1.19	42.11 ±1.04	15.61 ±0.66	64.85 ±1.14	49.24 ±1.00	20.33 ±0.77	67.43 ±1.12	47.10 ±0.97	9.53 ±0.44	57.62 ±1.21	48.08 ±1.08

Appendix

Table 15: Faithfulness quantitative results for Input Insertion, Input Deletion, and CAAP on ResNet-18, ResNet-50, DenseNet-161, and VGG-16. Deletion (

\downarrow

), Insertion (

\uparrow

), and Ins

-

Del (

\uparrow

) are reported. Best is bold , second best is underlined in each column.

	ResNet-18 [ 41 ]			ResNet-50 [ 41 ]			DenseNet-161 [ 42 ]			VGG-16 [ 43 ]
Method	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$	AUPR 1 $\uparrow$	AUPR 0 $\uparrow$	PG $\uparrow$
Input Insertion	36.91 ±2.23	65.50 ±2.37	47.66 ±4.41	42.00 ±2.21	69.03 ±2.28	56.25 ±4.38	39.70 ±2.24	67.83 ±2.19	49.22 ±4.42	35.12 ±2.15	64.95 ±2.31	42.19 ±4.37
Input Deletion	50.49 ±2.20	72.09 ±2.31	60.94 ±4.31	49.40 ±2.08	69.96 ±2.35	64.06 ±4.24	49.54 ±2.14	71.87 ±2.25	62.50 ±4.28	51.61 ±2.23	73.62 ±2.32	64.84 ±4.22
CAAP (Ours)	61.10 ±2.18	84.68 ±1.80	69.53 ±4.07	59.32 ±2.07	84.55 ±1.82	64.84 ±4.22	62.85 ±2.22	84.72 ±1.85	75.78 ±3.79	55.82 ±2.07	79.39 ±2.10	62.50 ±4.28

Appendix

Table 16: Localization quantitative results for Input Insertion, Input Deletion, and CAAP on ResNet-18, ResNet-50, DenseNet-161, and VGG-16. AUPR 1 (

\uparrow

), AUPR 0 (

\uparrow

), and PG (

\uparrow

) are reported. Best is bold , second best is underlined in each column.

Figure 13: Visualization of single-object attribution maps produced by different methods across various models. The target object is an Granny smith .

Figure 14: Visualization of single-object attribution maps produced by different methods across various models. The target object is a Black swan .

Figure 15: Visualization of single-object attribution maps produced by different methods across various models. The target object is a Cheetah .

Figure 16: Visualization of single-object attribution maps produced by different methods across various models. The target object is a Sandbar .

Figure 17: Visualization of single-object attribution maps produced by different methods across various models. The target object is a Black grouse .

Figure 18: Visualization of single-object attribution maps produced by different methods across various models. The target object is a Goldfish .

Figure 19: Visualization of single-object attribution maps produced by different methods across various models. The target object is a Gyromitra .

Figure 20: Visualization of single-object attribution maps produced by different methods across various models. The target object is a Mousetrap .

Figure 21: Visualization of single-object attribution maps produced by different methods across various models. The target object is an Ear .

Figure 22: Visualization of single-object attribution maps produced by different methods across various models. The target object is a European fire salamander .

Figure 23: Visualization of single-object attribution maps produced by different methods across various models. The target object is a Tiger beetle .

Figure 24: Visualization of single-object attribution maps produced by different methods across various models. The target object is a Proboscis monkey .

Figure 25: Visualization of single-object attribution maps produced by different methods across various models. The target object is a White wolf .

Figure 26: Visualization of single-object attribution maps produced by different methods across various models. The target object is a Catamaran .

Figure 27: Visualization of single-object attribution maps produced by different methods across various models. The target object is a Lens cap .

Figure 28: Visualization of single-object attribution maps produced by different methods across various models. The target object is an Indigo bunting .

Figure 29: Visualization of single-object attribution maps produced by different methods across various models. The target object is a Cabbage butterfly .

Figure 30: Visualization of single-object attribution maps produced by different methods across various models. The target object is an Electric guitar .

Figure 31: Visualization of single-object attribution maps produced by different methods across various models. The target object is an Echidna .

Figure 32: Visualization of single-object attribution maps produced by different methods across various models. The target object is a Neck brace .

Figure 33: Visualization of single-object attribution maps produced by different methods across various models. The target object is an American alligator .

Figure 34: Visualization of single-object attribution maps produced by different methods across various models. The target object is an Eft .

Figure 35: Visualization of single-object attribution maps produced by different methods across various models. The target object is an American lobster .

Figure 36: Visualization of single-object attribution maps produced by different methods across various models. The target object is a Spotted salamander .

Figure 37: Visualization of single-object attribution maps produced by different methods across various models. The target object is a Cougar .

Figure 38: Visualization of single-object attribution maps produced by different methods across various models. The target object is a Lawn mower .

Figure 39: Visualization of single-object attribution maps produced by different methods across various models. The target object is an Albatross .

Figure 40: Visualization of single-object attribution maps produced by different methods across various models. The target object is a Trombone .

Figure 41: Visualization of single-object attribution maps produced by different methods across various models. The target object is a Junco .

Figure 42: Visualization of single-object attribution maps produced by different methods across various models. The target object is a Hermit crab .

Figure 43: Visualization of multi-object attribution maps produced by a selected set of strong methods. The target objects are a dolphin and a shark .

Figure 44: Visualization of multi-object attribution maps produced by a selected set of strong methods. The target objects are a pink flower and a blue butterfly .

Figure 45: Visualization of multi-object attribution maps produced by a selected set of strong methods. The target objects are a globe , a bed , and books .

Figure 46: Visualization of multi-object attribution maps produced by a selected set of strong methods. The target objects are a gnome , a unicycle , a clock , and a duck crossing sign .

Figure 47: Visualization of multi-object attribution maps produced by a selected set of strong methods. The target objects are a dog , shoes , and a camera .

Figure 48: Visualization of multi-object attribution maps produced by a selected set of strong methods. The target objects are a playground slide , a ponytail holder , and a red bag .

Figure 49: Visualization of multi-object attribution maps produced by a selected set of strong methods. The target objects are a panda , a clownfish , and hearts .

Figure 50: Visualization of multi-object attribution maps produced by a selected set of strong methods. The target objects are shoes and purple socks .

Figure 51: Visualization of multi-object attribution maps produced by a selected set of strong methods. The target objects are a laptop , a tray of food , and pillows .

Figure 52: Visualization of multi-object attribution maps produced by a selected set of strong methods. The target objects are a cat , an umbrella , a girl , and eyes .

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