What Do Visual-Head Discovery Scores Actually Find? Attention Source, Necessity, and Random-Control Pitfalls in Vision-Language Models

Md Abdul Kadir; Daniel Sonntag

cs.CVOct 9, 2026

What Do Visual-Head Discovery Scores Actually Find? Attention Source, Necessity, and Random-Control Pitfalls in Vision-Language Models

Authors: Md Abdul Kadir, Daniel Sonntag

Organizations: German Research Center for Artificial Intelligence (DFKI) Saarbrücken, Germany · Oldenburg University Oldenburg, Germany

Abstract

Attention heads that attend to image regions relevant to a question are increasingly used to steer, ground and interpret vision-language models (VLMs) and to reduce their hallucinations. They are mostly found by ranking heads with an attention- pattern score and validated by steering or masking them. We ask how the choices inside such a discovery score shape the heads it returns, and which of the two validations identifies them. On Qwen3-VL-8B-Instruct we vary the query type, the discovery corpus and the token positions whose attention is read (the attention source) in a full 2 x 3 x 2 design, and test all 12 head-sets for steerability (CERS: Contrastive Evidence-Region Steering score) and necessity (NCS: Necessity Con- trast Score) against layer-matched random head-sets. (1) The attention source and the query type reshape the selected heads far more than the corpus: changing the source keeps a median of 49 of the top-100 heads, the query 55 and the cor- pus 84, while two halves of the same data share 96-99. (2) Necessity follows the attention source: head-sets discovered from query-span attention are more nec- essary than last-token ones (difference 0.083, p=6 x 10^-10), and the two re- ferring + query-span sets lie 17-19 standard deviations above 250 layer-matched random sets (Holm-adjusted p=0.048). The referring + query-span effect re- plicates on several recent VLMs. (3) Steerability is not specific to the discovered heads: no discovered head-set steers better than its layer-matched random sets (rank p >= 0.14), and random sets drawn from the same or from any layer span the discovered sets' scores. Necessity therefore separates the discovery settings, while steering at this strength does not. We turn these findings into a protocol for reporting visual-head discoveries.

Figures & tables

Figure 1: Overview. (1) Discovery. Two query types (ordinal and referring; prompt shortened in the figure) $\times$ three attention sources (last prompt token, query-span tokens, generated answer tokens) $\times$ two corpora (comics, COCO) give 12 discovery scores. For each, we ask about one region $p$ of a six-panel strip, record how much attention every head sends to $p$ , and rank the heads; the head-set $S$ is the top-100 heads, and each $S$ is paired with layer-matched random controls. (2) Causal evaluation. Every $S$ and its controls get the same two tests. Steerability ( CERS , Eq. 3 ): steer $S$ onto the cell holding the correct answer ( $S{\to}c$ ) or a distractor’s cell ( $S{\to}d$ ) and compare $P(c)$ . Necessity ( $\mathrm{NCS}$ , Eq. ): mask $S$ ’s attention to all image tokens on a matched vs. mismatched ImageNet MCQ. The bars illustrate the related grid contrast $\mathrm{NCS}_{\mathrm{grid}}$ (Eq. 4 ): hide a distractor’s cell $\rho(d)$ or the answer’s cell $\rho(c)$ from $S$ ; $P(c)$ for $S$ and a random head-set on one real item.

Figure 2: Top-100 head overlap between all 12 discovery settings, Qwen3-VL-8B. The same query and attention source agree across corpora (e.g. cm-/co-ref-qsp share 85/100), while changing the attention source moves most of the set (cm-ord-last vs. cm-ref-qsp: 38/100; minimum 26/100).

Table 3

	CERS (steerability)				NCS (necessity)
	$S$	layer-matched random		any-layer random	$S$	layer-matched random
Setting	[95% CI]	mean [95% CI]	$p$	mean [95% CI]	[95% CI]	mean [95% CI]	$p$
cm-ord-last	$-$ .003 [ $-$ .033, .027]	$-$ .039 [ $-$ .147, .069]	.43	.268 [.171, .364]	$-$ .009 [ $-$ .021, .003]	$-$ .002 [ $-$ .003, .000]	1.0
cm-ord-out	.033 [.002, .064]	$-$ .079 [ $-$ .170, .011]	.24	$-$ .028 [ $-$ .140, .084]	.017 [ $-$ .010, .044]	.000 [ $-$ .002, .002]	.048
cm-ord-qsp	.139 [.111, .167]	.061 [ $-$ .023, .146]	.33	.158 [.018, .297]	.043 [.011, .075]	$-$ .004 [ $-$ .006, $-$ .001]	.048
cm-ref-last	$-$ .303 [ $-$ .341, $-$ .264]	.303 [.186, .420]	1.0	.136 [.005, .267]	.002 [ $-$ .029, .033]	.001 [ $-$ .001, .003]	.38

Table 3: All 12 settings, Qwen3-VL-8B, flat top-100 heads,

N{=}400

(cm/co = comics/COCO corpus; ord/ref = query; last/qsp/out = attention source).

S

: the discovered head-set, with a 95%

t

-interval over the 400 items. Random: mean over 20 random head-sets, either layer-matched or drawn from any layer, with a 95%

t

-interval of that mean over the draws.

p

= rank

p

S

among the individual layer-matched sets, whose spread is wider than the interval of their mean. ∗ 250 layer-matched random sets (Holm-adjusted

p{=}0.048

Figure 3: Table 3 at a glance: each discovered head-set (dot) against the mean

\pm

SD of its 20 layer-matched random sets (bar). On NCS the query-span and output-token sets lie outside their random bands, which sit at zero; on CERS every set falls inside or below a wide random band.

Setting	all rows	question/option rows	last row	NCS	CERS / random ( $p$ )
	flat top-100: NCS when masked at			top-3 heads per layer (108)
co-ref-qsp	$\mathbf{.126}$ [.086, .165]	$\mathbf{.140}$ [.100, .181]	.000 [ $-$ .003, .003]	$\mathbf{.046}$ [.013, .078]	.229 / .103 (.38)
co-ord-qsp	$\mathbf{.036}$ [.002, .070]	$\mathbf{.049}$ [.015, .083]	$-$ .001 [ $-$ .005, .002]	$\mathbf{.031}$ [ $-$ .004, .066]	.207 / $-$ .091 (.29)
co-ref-last	$-$ .002 [ $-$ .035, .032]	$-$ .001 [ $-$ .031, .028]	$-$ .003 [ $-$ .007, .001]	$\mathbf{.012}$ [ $-$ .020, .045]	.190 / .071 (.33)
co-ord-last	$-$ .002 [ $-$ .008, .004]	.002 [ $-$ .003, .006]	$-$ .001 [ $-$ .004, .002]	.005 [ $-$ .028, .038]	.458 / .195 (.24)

Table 5: Where and with which heads necessity acts (COCO,

N{=}400

; 95% CIs; bold: above all 20 layer-matched random sets, whose means lie within

0.003

of zero). Left: the flat top-100 set masked from the image at every row, only at the question and option rows, or only at the last row. Right: the top-3 heads of every layer instead of the flat top-100 (Appendix A.5 ).

	comics discovery		COCO discovery
Query + source	NCS [95% CI]	$p$	NCS [95% CI]	$p$
ord-last	.004 [ $-$ .001, .009]	.010	.001 [.000, .001]	.010
ord-out	.226 [.157, .294]	.010	.268 [.195, .340]	.010
ord-qsp	.194 [.129, .259]	.010	.222 [.154, .290]	.010
ref-last	.005 [ $-$ .004, .014]	.11	.007 [ $-$ .003, .016]	.050
ref-out	.247 [.176, .317]	.010	.181 [.117, .244]	.010

Table 6: Necessity as a region contrast on the leak-audited grid (

N{=}120

P(c)

with another cell hidden from

S

minus

P(c)

with the target cell hidden, so generic damage cancels within each item (maximum

0.716

p

: rank

p

against 100 layer-matched random sets, whose means lie within

0.002

of zero (floor

0.010

; Appendix A.8 ).

	NCS (necessity)				CERS (steerability)
	query span + output		last token		query span + output
Model	$S$	random	$S$	random	$S$	random
Qwen3-VL-4B	$.140$ – $.211$	$.006$ – $.032$	$.010$	$.002$	$-.015$ – $.154$	$-.041$ – $-.020$
Qwen3.5-9B	$.217$ – $.231$	$.025$ – $.043$	$.223$	$.060$	$-.034$ – $-.003$	$-.041$ – $.040$
Gemma-4-E4B	$.366$ – $.402$	$.070$ – $.097$	$.022$	$.035$	$-.005$ – $.007$	$-.026$ – $.038$
Ovis1.5-Llama3-8B	$.204$ – $.254$	$.005$ – $.023$	$.024$	$.004$	$.001$ – $.014$	$-.035$ – $-.001$

Table 8: Five further models, eight out-of-domain benchmarks (heads discovered anew per model, flat top-100; one layer-matched random draw per head-set). Ranges over the five query-span and output-token sets and over their random draws; last token: cm-ord-last (Appendix C.1 ).

Appendix figures & tables24 assets

Supplementary material from the paper’s appendix.

Appendix

	CERS		NCS
Setting	A	B	A	B
cm-ord-last	.43	.095	1.00	1.00
cm-ord-out	.24	.048	.048	.048
cm-ord-qsp	.33	.048	.048	.048
cm-ref-last	1.00	1.00	.38	.24
cm-ref-out	.62	.24	.048	.048

Appendix

Table 9: Rank

p

of each discovered head-set against 20 layer-matched (A) and 20 layer- and attention-matched (B) random head-sets (Qwen3-VL-8B, flat top-100,

N{=}400

). Scores are in Table 3 .

Setting	NCS	Control mean $\pm$ SD	$p$
cm-ref-qsp	$0.116$	$0.002\pm.007$	$.004$
co-ref-qsp	$0.126$	$-0.001\pm.007$	$.004$

Appendix

Table 10: The two referring + query-span settings against

R{=}250

layer-matched random head-sets (Qwen3-VL-8B, top-100,

N{=}400

): control mean

\pm

SD over the 250 draws and the rank

p

(floor

0.004

Setting	$P_{\text{mask}}$ matched	Matched drop	$P_{\text{mask}}$ mism.	Mism. drop	NCS
cm-ord-last	$0.996$	$-0.002$ [-0.005,0.001]	$0.212$	$0.005$ [-0.006,0.017]	$-0.007$ [-0.019,0.004]
cm-ord-out	$0.973$	$0.022$ [0.009,0.036]	$0.213$	$0.005$ [-0.019,0.028]	$0.017$ [-0.010,0.045]
cm-ord-qsp	$0.967$	$0.028$ [0.015,0.042]	$0.230$	$-0.013$ [-0.042,0.018]	$0.040$ [0.009,0.070]
cm-ref-last	$0.990$	$0.004$ [-0.000,0.010]	$0.217$	$0.000$ [-0.030,0.031]	$0.004$ [-0.027,0.034]
cm-ref-out	$0.963$	$0.032$ [0.017,0.048]	$0.216$	$0.002$ [-0.025,0.030]	$0.030$ [-0.001,0.059]
cm-ref-qsp	$0.885$	$0.110$ [0.083,0.135]	$0.220$	$-0.003$ [-0.034,0.029]	$0.113$ [0.074,0.153]

Appendix

Table 11: NCS split into its arms, all 12 settings (

N{=}400

, top-100).

P

renormalized over the four letters; drops are baseline minus masked.

95\%

percentile bootstrap intervals,

2{,}000

resamples.

Head-set	Heads	Matched drop	Mismatched drop	NCS	NCS-v2	Text-arm drop (text masked)
Discovered ( ref-qspan )	100	$0.112$	$-0.013$	$\mathbf{0.125}$	$\mathbf{0.112}$	$0.645$
Attention sinks	100	$0.002$	$-0.005$	$0.007$	$0.002$	$0.012$
Text-heavy heads	100	$0.002$	$-0.003$	$0.005$	$0.002$	$0.415$
Whole layers	96	$0.005$	$0.006$	$-0.001$	$0.005$	$0.232$
Random, 200 heads	200	$0.006$	$-0.014$	$0.020$	$0.006$	$0.718$
Random, 400 heads	400	$0.010$	$-0.015$	$0.025$	$0.010$	$0.776$

Appendix

Table 12: Generic-damage controls on co-ref-qsp (

N{=}400

). Matched and mismatched drops are the decrease in

P(\text{correct})

when the head-set’s image attention is masked; the last column is the decrease on the text-solvable arm when the head-set’s text attention is masked.

		flat top-100			top-3 per layer (108)
Setting	Masked rows	$S$ [95% CI]	random	$p$	$S$ [95% CI]	random	$p$
co-ref-qsp	all rows	.126 [.086, .165]	.000	.048	.046 [.013, .078]	.001	.048
	image rows	$-$ .001 [ $-$ .023, .020]	.002	.86	.010 [ $-$ .012, .033]	.000	.048
	question/option rows	.140 [.100, .181]	$-$ .004	.048	.056 [.025, .088]	$-$ .001	.048
	last row	.000 [ $-$ .003, .003]	.000	.67	$-$ .002 [ $-$ .006, .002]	.000	1.0
co-ord-qsp	all rows	.036 [.002, .070]	$-$ .002	.048	.031 [ $-$ .004, .066]	.003	.048

Appendix

Table 13: NCS when the image mask is applied only at one group of attention rows (COCO settings,

N{=}400

S

with 95%

t

-interval; random: mean of 20 random head-sets with the same per-layer counts;

p

: rank

p

(floor

0.048

	cm-ref-qsp			co-ref-qsp
$k$	$S$ [95% CI]	random	$p$	$S$ [95% CI]	random	$p$
20	.036 [.005, .066]	$-$ .002 $\pm$ .004	.048	.015 [ $-$ .011, .041]	$-$ .001 $\pm$ .004	.048
40	.045 [.014, .076]	$-$ .001 $\pm$ .003	.048	.026 [ $-$ .005, .056]	.000 $\pm$ .004	.048
60	.041	.001 $\pm$ .005	.048	.029	.000 $\pm$ .005	.048
100	.116 [.078, .155]	.002 $\pm$ .007	.004	.126 [.086, .165]	$-$ .001 $\pm$ .007	.004
140	.204 [.160, .249]	.002 $\pm$ .004	.048	.092	.001 $\pm$ .006	.048

Appendix

Table 14: NCS against head-set size (Qwen3-VL-8B,

N{=}400

S

with 95%

t

-interval where the per-example outputs are available; random: mean

\pm

SD of 20 layer-matched random sets (250 at

k{=}100

);

p

: rank

p

Figure 6: Top-

k

overlap between cm-ref-qsp and co-ref-qsp (Qwen3-VL-8B). Left: shared heads and each corpus’s unique heads (equal in count, not in identity). Right: overlap fraction (shared

/k

Comparison	Source	Shared / only	Shared	A-only	B-only
corpus (cm vs co), ordinal	query span	$91$ / $9$	$\mathbf{+0.036}$ (0.01)	$-0.001$ (0.61)	$+0.001$ (0.35)
corpus (cm vs co), ordinal	last token	$80$ / $20$	$-0.003$ (0.84)	$-0.003$ (0.84)	$+0.000$ (0.49)
query type (ord vs ref), comics	query span	$79$ / $21$	$\mathbf{+0.033}$ (0.015)	$+0.010$ (0.2)	$+0.005$ (0.14)
query type (ord vs ref), comics	last token	$35$ / $65$	$-0.001$ (0.67)	$-0.006$ (0.97)	$+0.005$ (0.37)
source (X vs out), COCO ordinal	query span	$71$ / $29$	$\mathbf{+0.029}$ (0.026)	$+0.011$ (0.19)	$-0.004$ (0.83)
source (X vs out), COCO ordinal	last token	$51$ / $49$	$-0.001$ (0.64)	$+0.000$ (0.42)	$+0.013$ (0.17)

Appendix

Table 15: NCS above the mean of 20 same-size layer-matched random controls (paired one-sided

p

in parentheses; bold

p<0.05

) for shared and setting-specific heads (Qwen3-VL-8B, top-100 per setting,

N{=}400

). “Shared / only” gives the head counts.

	NCS (region contrast)			CERS (symmetric)
Setting	$S$ [95% CI]	random	$p$	$S$ [95% CI]	random	$p$
cm-ord-last	.004 [ $-$ .001, .009]	.000 [.000, .000]	.010	$-$ .010 [ $-$ .052, .031]	$-$ .040 [ $-$ .078, $-$ .003]	.40
cm-ord-out	.226 [.157, .294]	$-$ .001 [ $-$ .001, .000]	.010	.027 [ $-$ .014, .068]	$-$ .102 [ $-$ .138, $-$ .066]	.21
cm-ord-qsp	.194 [.129, .259]	.000 [.000, .001]	.010	.141 [.106, .176]	.067 [.030, .104]	.37
cm-ref-last	.005 [ $-$ .004, .014]	.001 [.001, .002]	.11	$-$ .272 [ $-$ .325, $-$ .220]	.271 [.218, .325]	.99
cm-ref-out	.247 [.176, .317]	.001 [.000, .001]	.010	.057 [.026, .087]	.139 [.090, .187]	.64

Appendix

Table 16: Region-contrast NCS and symmetric CERS on the leak-audited grid (

N{=}120

items, Qwen3-VL-8B, flat top-100).

S

: discovered set, with a 95%

t

-interval over items; random: mean [95% CI] over 100 layer-matched random sets;

p

: rank

p

(floor

0.010

). The maximum attainable NCS is

0.716

	mean image-attention mass		$\rho$ (statistic, CERS ) over random sets
Setting	discovered	random	mean	median	min	max	SD
cm-ord-last	0.188	0.041 [0.032, 0.046]	$-$ .39	$-$ .54	$-$ .22	$-$ .20	$-$ .14
cm-ord-out	0.174	0.052 [0.045, 0.062]	$-$ .04	.12	$-$ .01	.28	.17
cm-ord-qsp	0.187	0.046 [0.040, 0.053]	$-$ .15	.02	$-$ .19	$-$ .10	$-$ .29
cm-ref-last	0.242	0.047 [0.040, 0.061]	.39	.11	.26	.37	.40
cm-ref-out	0.188	0.051 [0.043, 0.061]	$-$ .37	$-$ .40	$-$ .21	.01	$-$ .12

Appendix

Table 17: Image-attention mass of head-sets and its relation to CERS . Mass columns: mean over the set’s heads (random: mean [min, max] over 20 layer-matched sets).

\rho

: Spearman correlation between the mass statistic and CERS across the 20 random sets.

$\beta$	$S$	random	$S$	random	$S$	random	$S$	random
	cm-ref-qsp		co-ref-qsp		cm-ord-last		co-ord-last
1	.279	$-$ .026 [ $-$ .071, .009]	.176	.056 [ $-$ .021, .146]	.132	$-$ .040 [ $-$ .064, $-$ .017]	.032	.015 [ $-$ .013, .067]
3	.869	$-$ .103 [ $-$ .279, .029]	.789	.204 [ $-$ .059, .347]	.308	$-$ .134 [ $-$ .192, $-$ .071]	.027	.072 [ $-$ .076, .332]
10	.317	.004 [ $-$ .241, .221]	.396	.270 [.087, .558]	.092	$-$ .068 [ $-$ .200, .088]	.182	.175 [ $-$ .232, .461]
100	.266	$-$ .001 [ $-$ .214, .218]	.273	.226 [.081, .517]	.042	$-$ .040 [ $-$ .155, .095]	.206	.173 [ $-$ .224, .421]
$10^{4}$	.179	.031 [ $-$ .291, .291]	.172	.376 [.052, .841]	.018	$-$ .032 [ $-$ .192, .098]	.176	.161 [ $-$ .202, .463]

Appendix

Table 18: CERS against steering strength

\beta

(Qwen3-VL-8B, flat top-100,

N{=}200

): the discovered set

S

and the mean [min, max] of 5 layer-matched random sets.

\beta{=}30

and

10^{3}

lie between their neighbours and are omitted.

Setting (COCO)	Qwen3-VL-8B	Qwen3-VL-4B	Qwen2-VL-7B
ordinal + last token	$-0.002$ vs. $0.000$ ( $.86$ )	$0.006$ vs. $0.003$ ( $.14$ )	$-0.002$ vs. $0.001$ ( $1.00$ )
ordinal + query span	$\mathbf{0.036}$ vs. $-0.003$ ( $.048$ )	$-0.005$ vs. $0.005$ ( $.91$ )	$0.001$ vs. $0.002$ ( $.57$ )
referring + last token	$-0.002$ vs. $0.002$ ( $.76$ )	$-0.004$ vs. $0.004$ ( $.91$ )	$\mathbf{0.024}$ vs. $0.001$ ( $.048$ )
referring + query span	$\mathbf{0.125}$ vs. $0.000$ ( $.048$ )	$\mathbf{0.054}$ vs. $0.002$ ( $.048$ )	$\mathbf{0.029}$ vs. $0.002$ ( $.048$ )

Appendix

Table 19: Second-model check: NCS of the discovered head-set vs. the mean of 20 layer-matched random controls (rank

p

), COCO discovery, top-100 heads,

N{=}400

. Bold: above all 20 controls.

What changes	Pair	Shared heads	Ceiling	Fraction
corpus	cm-ord-last vs. co-ord-last	$81.2$ [ $80$ , $83$ ]	$98.4$	$0.82$
corpus	cm-ord-qsp vs. co-ord-qsp	$90.5$ [ $90$ , $91$ ]	$99.2$	$0.91$
corpus	cm-ref-last vs. co-ref-last	$83.8$ [ $81$ , $86$ ]	$96.6$	$0.87$
corpus	cm-ref-out vs. co-ref-out	$78.5$ [ $76$ , $80$ ]	$97.7$	$0.80$
corpus	cm-ref-qsp vs. co-ref-qsp	$83.8$ [ $82$ , $86$ ]	$97.8$	$0.86$
query type	cm-ord-last vs. cm-ref-last	$35.2$ [ $33$ , $37$ ]	$97.2$	$0.36$

Appendix

Table 20: Top-100 overlap between two discovery settings at

200

strips per half (mean [

2.5

97.5

percentile] over

200

half-splits), the geometric-mean noise ceiling of the two settings, and the overlap as a fraction of that ceiling.

Query + attention source	ord-last	ref-qspan	ref-out
ordinal + output tokens	$8$	$8$	$9$
referring + output tokens ( ref-out )	$5$	$7$	$\mathbf{13}$

Appendix

Table 21: Top-20 overlap with the native head-sets for the two crossover combinations not in Table 2 (

200

COCO strips, Qwen3-VL-8B). Bold: the combination’s own native set.

Figure 7: Top-100 overlap between the native ord-last, ref-qspan and ref-out sets and a uniform random draw of 100 heads, on eight further models (Gemma-4-E4B-it has ord-last scores only, so its other bars are marked N/A). Ord-last/ref-qspan overlap is

25

–

86

/100 across the seven scored models, ord-last/ref-out

25

–

89

/100, and ref-qspan/ref-out

40

–

92

/100; the random draw shares

3

–

76

/100 with ord-last and

1

–

78

/100 with ref-qspan.

Dataset	CERS oracle	CERS floor	NCS matched	NCS mismatched
MathVista	$0.885$	$0.275$	$0.870$	$\mathbf{0.730}$
CountBenchQA	$0.950$	$0.302$	$0.897$	$0.220$
CVBench	$\mathbf{0.632}$	$0.268$	$0.740$	$\mathbf{0.605}$
MMStar	$0.815$	$0.273$	$0.935$	$0.367$
SpatialRGPT	$\mathbf{0.282}$	$0.230$	$0.492$	$\mathbf{0.470}$
Spatial457	$\mathbf{0.573}$	$0.217$	$0.735$	$\mathbf{0.527}$

Appendix

Table 22: Out-of-domain baseline audit, Qwen3-VL-8B,

N{=}400

/dataset. Oracle: target cell named in the prompt (expect

\approx 1

). Floor: blank image (expect

0.25

). Matched/mismatched: NCS arms without intervention (expect

\approx 1

0.25

). Bold: outside the expected range.

Head-set	CERS [95% CI]	NCS [95% CI]
cm-ref-qsp	$\mathbf{0.288}$ [ $0.272$ , $0.304$ ]	$\mathbf{0.225}$ [ $0.188$ , $0.264$ ]
random	$-0.117$ [ $-0.135$ , $-0.100$ ]	$0.020$ [ $0.001$ , $0.039$ ]
co-ref-qsp	$0.092$ [ $0.078$ , $0.107$ ]	$0.211$ [ $0.175$ , $0.249$ ]
random	$0.009$ [ $-0.004$ , $0.021$ ]	$0.023$ [ $0.008$ , $0.037$ ]
co-ord-qsp	$0.271$ [ $0.257$ , $0.286$ ]	$0.161$ [ $0.127$ , $0.196$ ]
random	$-0.141$ [ $-0.158$ , $-0.124$ ]	$0.011$ [ $-0.003$ , $0.026$ ]

Appendix

Table 23: Out-of-domain CERS and NCS, pooled over the eight datasets, Qwen3-VL-8B (

N{=}1280

per head-set for CERS ,

563

pairs for NCS; flat top-100). Each discovered set is followed by its single layer-matched random draw. 95% intervals:

t

over items ( CERS ), bootstrap (NCS).

CERS
Setting	Qwen3-VL-4B	Qwen3.5-9B	Gemma-4-E4B	Ovis1.5-8B	InternVL3.5-14B
cm-ref-qsp	$.098$ ( $-.022$ )	$-.003$ ( $-.038$ )	$.001$ ( $.035$ )	$.011$ ( $-.026$ )	$.246$ ( $.135$ )
co-ref-qsp	$.070$ ( $-.041$ )	$-.017$ ( $-.041$ )	$-.005$ ( $.004$ )	$.013$ ( $-.003$ )	$.341$ ( $-.031$ )
co-ord-qsp	$.154$ ( $-.021$ )	$-.017$ ( $.040$ )	$.000$ ( $.038$ )	$.005$ ( $-.035$ )	$.228$ ( $.071$ )
cm-ord-qsp	$.090$ ( $-.041$ )	$-.034$ ( $.028$ )	$.007$ ( $-.026$ )	$.014$ ( $-.014$ )	$.288$ ( $.102$ )
co-ref-out	$-.015$ ( $-.020$ )	$-.024$ ( $.018$ )	$-.002$ ( $-.020$ )	$.001$ ( $-.001$ )	$.379$ ( $-.176$ )

Appendix

Table 24: Out-of-domain CERS / NCS of the discovered set, with its single layer-matched random draw in parentheses, five further models (flat top-100,

N{=}1280

CERS ,

563

NCS pairs).

Task	Family	What the model is shown and asked
CV-Bench_pointing	converted	Real photo; question about counting or relations; wrong answers overlaid on three copies of the same photo.
MMStar_pointing	converted	Same recipe, with MMStar’s multi-domain VQA items.
SpatialRGPT_pointing	converted	Real photo with two labeled regions and a spatial-relation question; distractor answers overlaid on copies.
Spatial457_pointing	converted	Four synthetic scene renders; the question refers to one scene’s objects; the correct cell is that scene.
CountBenchQA_pointing	converted	Real photo of counted objects; “how many X”; candidate counts as text options.
MathVista_pointing	converted	Four math diagrams; the correct item’s question and choices asked in text.

Appendix

Table 25: The 14 tasks of the pointing suite. Every task uses the same

2\times 2

CERS apparatus (Eq. 3 ); only how the four cells and four options are built differs.

Task	ord-last	Random	Gap
spatial457_pointing	$0.427$	$0.459$	$-0.033$
MathVista_pointing	$0.012$	$0.028$	$-0.016$
attribute_identification	$0.017$	$0.004$	$0.012$
general_causal_MathVista	$0.069$	$0.069$	$0.000$
CountBenchQA_pointing	$0.019$	$0.013$	$0.006$
general_causal_CVBench	$0.197$	$0.186$	$0.011$

Appendix

Table 26: CERS of the flat top-20 ord-last set and one layer-matched random draw, Qwen3-VL-8B,

N{=}80

per task. Bold: the three flagged tasks. The gap is computed from unrounded values.

Model	Baseline acc.	ord-last	ref-qspan	ref-out	Random
Qwen3-VL-2B	$0.492$	$\mathbf{0.161}$	$\mathbf{0.033}$	$\mathbf{0.022}$	$\mathbf{-0.041}$
Qwen3-VL-4B	$0.521$	$\mathbf{0.127}$	$\mathbf{0.189}$	$\mathbf{0.066}$	$\mathbf{-0.010}$
Qwen2-VL-7B	$0.487$	$\mathbf{0.066}$	$\mathbf{0.027}$	$\mathbf{0.025}$	$\mathbf{-0.056}$
Qwen3-VL-32B (4-bit)	$0.537$	$\mathbf{0.122}$	$\mathbf{0.168}$	$\mathbf{0.116}$	$\mathbf{-0.020}$
InternVL3.5-8B	$0.527$	$\mathbf{0.006}$	$\mathbf{0.019}$	$\mathbf{0.075}$	$\mathbf{0.003}$
InternVL3.5-14B (4-bit)	$0.483$	$\mathbf{0.102}$	$\mathbf{0.150}$	$\mathbf{0.159}$	$\mathbf{-0.054}$

Appendix

Table 27: Pointing-suite CERS on eight further models (all 14 tasks,

N{=}1120

per model, flat top-20, one random draw per model). Bold:

p<0.05

against zero (one-sample

t

-test).

Figure 8: CERS vs. NCS on real example images. Left: the $2\times 2$ MCQ grid with the correct cell (A, green) and a distractor cell (B, orange), steered via $\mathrm{do}(S,c)$ and $\mathrm{do}(S,d)$ . Right: the matched (target class visible, green) and mismatched (excluded class, orange) images used for NCS, with the attention mask indicated below each head-set box.

Result	Head-set	Evaluation data	$N$	$R$
Tables 1 , 20 (noise ceiling)	flat top-100	discovery strips, 200 half-splits	400	–
Tables 2 , 21 ; Fig. 7	top-20; top-100	200 COCO strips (discovery only)	200	–
Table 3 , Fig. 3 , Tables 9 , 11	flat top-100	ImageNet $2\times 2$ grid ( CERS ); ImageNet MCQ (NCS)	400	20 (250)
Table 4 , 14 , Fig. 5	flat top- $k$ , $k\in\{20..160\}$	ImageNet MCQ	400	20 (250)
Table 12	6 head-sets	ImageNet MCQ + text-solvable arm	400	–
Tables 5 , 13	flat top-100; $k_{\mathrm{per\_layer}}{=}3$	ImageNet MCQ ( CERS : grid)	400	20

Appendix

Table 28: Protocol per result, Qwen3-VL-8B-Instruct unless stated.

R

: random head-sets per discovered set.

Benchmark	Source content	Recipe
CountBenchQA	counting VQA	same-image overlay (near-miss count distractors)
CV-Bench	single-image MCQ perception	same-image overlay
MathVista	MCQ diagram reasoning	same-image overlay (overlaid answer-choice text)
MMStar	single-image MCQ perception	same-image overlay
Spatial457	spatial-relation VQA	image retrieval
SpatialRGPT-Bench	spatial-relation VQA	image retrieval

Appendix

Table 29: Source and conversion recipe of the seven converted benchmarks.

Attention Head Analysis

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Retrieval Heads Meet Vision: Uncovering How VLMs Locate and Extract Visual Information

Chanho Park, Daehyeon Choi, Jihyun Lee, Minhyuk Sung

KAIST · Independent Researcher

VLM Interpretability Vision-Language Retrieval Vision-Language Grounding

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Vision-language models (VLMs) can locate an image region referred to by a text prompt and route the corresponding visual evidence to the output, yet the internal mechanism behind this behavior is not understood. Inspired by retrieval heads in large language models, we ask whether VLMs contain an analogous mechanism for visual retrieval. We answer affirmatively by introducing Visual Retrieval Heads (VRHs), a small subset of attention heads (about 1.7-2.6%) that are causally responsible for grounding text descriptions to image regions. To find them, we recast existing head-scoring methods under a unified design space over query tokens, key aggregation, and cross-sample aggregation. We then show that scoring attention from output prediction tokens with a sum over the ground-truth referent region most reliably identifies causal heads. Across eleven VLMs and five referring-expression benchmarks, masking only the top 20 VRHs reduces grounding accuracy by up to 80 percentage points, while masking the same number of random heads has little effect. Beyond replicating the causal-sparse-universal triad established for text retrieval heads, VRHs exhibit several properties not previously reported: they generalize across visual reference tasks, remaining causal on attribute, spatial, counting, and visual-math benchmarks despite being discovered through bounding-box prediction; they are functionally specific, preserving output format while corrupting localization; and they are architecturally shared, transferring causally across VLMs that share an LLM backbone but differ in vision encoder, projector, and instruction tuning.

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