Correcting Attribution Patching with a Few Exact Measurements

Luyang Zhang; Minxing Zheng; Jialu Wang

cs.AIOct 19, 2026

Correcting Attribution Patching with a Few Exact Measurements

Authors: Luyang Zhang, Minxing Zheng, Jialu Wang

Organizations: Carnegie Mellon University · University of California, Santa Cruz

Abstract

Mechanistic interpretability asks which language model components matter for a behavior, and activation patching answers by changing one component's activation and measuring its effect, at a cost growing with components and prompts. Attribution patching estimates these effects from one gradient pass, but its estimates can be far off, and verifying each one restores the cost. Can the structure of these errors reduce this cost? We propose Guided-AP, which uses a few exact measurements to reveal attribution patching's errors and correct unmeasured estimates. On a single prompt, many components' errors share one sign, so a small exact sample yields one correction for the rest. Over many prompts of one task, components are misestimated similarly, so a few measured prompts show what to verify and how to correct each component's average effect. Our analysis shows that choosing what to verify needs error size, while correction also needs sign. On a single prompt, the correction lowers error by up to 26% across three behaviors at the compute of verifying the largest estimates and also on larger models. Over many prompts, learned corrections cut the error of average effects on factual completion by 75% to 79%, repaying their cost in long analyses.

Figures & tables

Figure 1: Guided-AP learns shared attribution errors. Within a prompt, a small exact sample corrects unmeasured estimates; across prompts, learned error profiles choose what to verify and correct remaining estimates and average effects. Final estimates are exact where verified and corrected elsewhere.

Figure 2: AtP errors on GPT-2. (a) The top four components ( $\blacktriangledown$ ) carry 80% of the test error. (b) Calibration versus test error for each component, with the top four highlighted. The two errors are strongly correlated and consistently biased away from zero.

Figure 3: Warm runtime and relative AP error for within-prompt Guided-AP and the baselines. Square size denotes the measurement budget

B

; hollow derivative markers denote larger MS-HVP and IG settings. Appendix D.3 gives the timing details.

Gemma-2-9B
Task	Groups	Lower MAE	Relative AP error	Warm time (s/layer)
IOI	100	17.4%	0.94%	2.08
Factual	100	26.2%	1.20%	1.30
SVA	100	19.9%	0.71%	1.25
Qwen3-14B
IOI	52	24.0%	1.34%	2.95

Table 1: Within-prompt Guided-AP accuracy and warm runtime. MAE reductions compare with runtime-matched verify-more. Groups is the number of evaluation prompts scored on all three tested MLP layers (Appendix D ).

Figure 4: Within-prompt Guided-AP ablations on Gemma-2-9B at 256 measurements: pilot size (left) and mean versus median (right). Values show MAE reductions versus verification alone. Cohorts: Appendix D.4 .

Task	Verify only	Verify + shift	Guided-AP
IOI	1.00	1.93	0.83
Factual	1.00	0.97	0.74
SVA	1.00	1.80	0.81

Table 2: Within-prompt Guided-AP controls on Gemma-2-9B at the same 256-measurement budget. MAE is relative to verification alone; lower is better.

Task	Method	Qwen3-8B		Qwen2.5-7B
		$B=16$	$B=128$	$B=16$	$B=128$
IOI	Guided-AP	12%	7%	$-$ 29%	12%
	ProbeCal	17%	19%	$-$ 39%	15%
Factual	Guided-AP	$-$ 20%	2%	$-$ 18%	$-$ 2%
	ProbeCal	$-$ 17%	31%	$-$ 5%	35%
SVA	Guided-AP	3%	4%	2%	3%

Table 3: Across-prompt MAE reductions relative to verify-more at matched projected total cost, calibration included, for 10,000 prompts. Bold and italic mark adjusted significant improvements and harms.

Figure 5: Dataset-average correction on the two models. Ratios are uncorrected over corrected MAE, with adjusted intervals; the dotted line denotes equality.

	Guided-AP		Verification to 1%
Task	Error	s/layer	Checks	s/layer
IOI	0.94%	2.08	2,416	16.37
Factual	1.20%	1.30	5,664	21.84
SVA	0.71%	1.25	32	0.43

Table 4: Warm cost at a 1% mean relative AP error target on Gemma-2-9B. Italic errors exceed the target; checks count magnitude-ranked AP measurements.

Figure 6: Scaling of the fixed budget. Left, SVA MAE reductions at matched cost with descriptive intervals. Right, measured 32B verification curves for factual completion and SVA (lines), within-prompt Guided-AP (stars), and verification at the same error (open circles), on the same complete groups; IOI: Appendix Table 6 .

Appendix figures & tables16 assets

Supplementary material from the paper’s appendix.

Appendix

			Guided-AP		Cheapest measured verification prefix: checks / s per layer
Model	Task	Groups	Error	s/layer	2% target	1% target	0.5% target
Gemma-2-9B	IOI	100	0.94%	2.08	0 / 0.27	2,416 / 16.37	8,128 / 54.16
Gemma-2-9B	Factual	100	1.20%	1.30	0 / 0.25	5,664 / 21.84	9,904 / 38.00
Gemma-2-9B	SVA	100	0.71%	1.25	0 / 0.25	32 / 0.43	5,472 / 20.25
Qwen3-14B	IOI	52	1.34%	2.95	16 / 0.76	8,016 / 73.12	12,608 / 114.56
Qwen3-14B	Factual	56	0.57%	1.67	0 / 0.42	0 / 0.42	2,144 / 10.29

Appendix

Table 5: Warm cost at all specified targets. Zero checks denotes ordinary AtP.

		Primary reference				FP64 reference
Task	Groups	Error	Guided-AP (s/layer)	Verify-more (s/layer)	Ratio	Error	Ratio
IOI	10	1.093%	6.52	91.16	14.0	1.110%	16.3
Factual	31	1.088%	3.54	51.95	14.7	1.099%	11.8
SVA	40	0.664%	3.55	21.06	5.9	0.658%	2.6

Appendix

Table 6: Post hoc 32B accuracy and warm runtime at Guided-AP ’s achieved error. Ratios divide verify-more time by Guided-AP time. FP64 rescoring keeps the estimates and measured runtimes fixed.

	IOI		Factual		SVA
Method	Error	Seconds	Error	Seconds	Error	Seconds
AtP	1.474%	0.29	1.828%	0.28	1.404%	0.29
Verify-more	1.292%	2.61	1.725%	1.29	0.909%	1.67
AtP* + AP	1.286%	3.46	1.721%	2.69	0.898%	2.62
No-pilot centering	1.320%	2.61	1.722%	1.29	0.942%	1.67
Selective HVP	1.321%	18.69	1.758%	18.70	1.029%	18.76

Appendix

Table 7: Measured comparator accuracy and warm seconds per layer on the complete Gemma comparator groups. Error is relative AP error. Parentheses identify MS-HVP steps or IG quadrature points.

Figure 7: Within-prompt Guided-AP ablations on Gemma-2-9B at 256 measurements. Panels (a) to (c) report MAE reductions relative to verification alone. Panel (d) shows factual absolute-error distributions before and after the common shift, scaled by the original root mean square error.

Model	Task	Groups	Guided-AP vs verification (%)	Guided-AP vs verification + shift (%)	FP64: Guided-AP vs verification + shift (%)
Gemma-9B	IOI	100	17.3 [14.7, 20.0]	57.2 [53.9, 60.1]	56.4 [53.0, 59.6]
Gemma-9B	Factual	100	26.2 [23.4, 28.9]	23.6 [17.4, 30.3]	22.9 [16.4, 30.0]
Gemma-9B	SVA	100	19.1 [16.7, 21.5]	55.1 [48.0, 61.8]	55.1 [47.9, 61.8]
Qwen3-14B	IOI	52	24.0 [19.2, 28.5]	45.8 [40.7, 50.3]	45.4 [40.1, 50.1]
Qwen3-14B	Factual	56	12.2 [9.6, 15.0]	75.9 [71.0, 79.3]	75.7 [70.7, 79.2]
Qwen3-14B	SVA	53	10.9 [7.9, 14.1]	75.3 [70.9, 78.8]	75.2 [70.8, 78.6]

Appendix

Table 8: Within-prompt Guided-AP MAE reductions at equal measurement counts. Intervals are descriptive paired-group 95% intervals. FP64 scoring keeps the deployed FP32 estimates fixed.

Task	Pilot	Stratified median	Uniform median	Stratified mean
IOI	16	16.7	16.5	7.0
IOI	32	17.6	17.5	8.2
IOI	64	17.3	17.3	5.0
IOI	128	15.3	15.3	5.9
Factual	16	24.2	24.1	23.9
Factual	32	25.6	25.7	25.3

Appendix

Table 9: Gemma Guided-AP pilot ablations with replayed samples. Entries give percent lower MAE than verification alone at 256 total measurements.

Task	Groups	$P=16$	$P=32$	$P=64$	$P=128$
IOI	20	17.0	18.2	18.0	15.8
Factual	20	25.4	26.7	27.3	27.1
SVA	20	19.4	20.2	20.1	18.5

Appendix

Table 10: Acquired pilot-size ablation on Gemma-2-9B. Entries are MAE reductions relative to verification alone, in percent, at 256 total measurements. The same complete groups enter each pilot size.

Task	$H_{U}$	$E_{U}$	$C_{\rm alloc}$	$C_{\rm count}$	Gain
IOI	19.76	0.72	1.74	$-$ 0.13	17.42
Factual	27.37	0.83	0.36	$-$ 0.02	26.21
SVA	21.07	0.82	1.36	$-$ 1.04	19.92

Appendix

Table 11: Theorem 1 ’s decomposition on Gemma, in percentage points of matched-baseline MAE. Negative count cost means fewer baseline checks.

Model	Task	Primary	Fixed	Refit
Gemma-9B	IOI	17.4	10.1	16.3
	Factual	26.2	23.4	25.4
	SVA	19.9	15.4	20.4
Qwen3-14B	IOI	24.0	21.0	24.5
	Factual	12.3	10.4	12.8
	SVA	10.9	4.1	9.5

Appendix

Table 12: Percent lower MAE under the primary reference and two FP64 sensitivity checks. Fixed estimates and FP64-acquired refits keep the budget match.

Model	Task	$N=1,024$	$N=4,096$	Full
Gemma-9B	IOI	22.7%	19.4%	17.4%
	Factual	27.8%	26.8%	26.2%
	SVA	22.6%	20.9%	19.9%
Qwen3-14B	IOI	27.4%	25.7%	24.0%
	Factual	16.2%	13.9%	12.3%
	SVA	19.2%	14.4%	10.9%

Appendix

Table 13: MAE reduction against runtime-matched verify-more at three predetermined component populations. Full populations are 14,336, 17,408, and 25,600 neurons for the three models.

Figure 8: Sketch-noise diagnostics. Left: median coupling across six model-task settings. Right: 41

N/R

means on Qwen3-8B IOI; dashed line denotes equality and red line the median. Points are dependent, not confidence intervals.

Model	Task	AP error $\rho$	Probe $\rho$	Top-16 kept
Qwen3	IOI	0.69	0.97	16 / 16
Qwen3	Factual	0.80	0.97	15 / 16
Qwen3	SVA	0.57	0.95	14 / 16
Qwen2.5	IOI	0.69	0.95	13 / 14
Qwen2.5	Factual	0.81	0.97	15 / 15
Qwen2.5	SVA	0.62	0.95	12 / 15

Appendix

Table 14: Stability between fixed calibration halves. AP error

\rho

uses heads measured in both halves (87 to 137 per setting); probe

\rho

uses all heads. Top-16 kept reports overlap for the Guided-AP / ProbeCal model fitted on all 50 calibration groups, scored on each half.

Model	Task	Guided-AP	ProbeCal	Heads	Coverage
		Error ratio		Guided-AP labels
Qwen3	IOI	0.95	1.49	121/1,152	10.5%
Qwen3	Factual	3.98	1.87	145/1,152	12.6%
Qwen3	SVA	1.23	1.14	265/1,152	23.0%
Qwen2.5	IOI	0.66	1.09	163/784	20.8%
Qwen2.5	Factual	4.78	1.86	141/784	18.0%

Appendix

Table 15: Dataset-average correction. Error ratio is uncorrected divided by corrected MAE. Bold and italic mark adjusted significant improvements and harms. Heads and coverage refer to Guided-AP calibration.

Figure 9: Across-prompt evaluation on Qwen3 IOI. Error against projected total cost at three analysis lengths, with markers for verification budgets and dotted curves for verify-more, followed by the dataset-mean correction ratios for all six cells with adjusted intervals.

Figure 10: Cost-error frontiers for three more cells at 100, 1,000, and 10,000 prompts. Conventions follow Figure 9 .

Figure 11: Cost-error frontiers for the remaining two cells. Conventions as in Figure 9 .

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