From Error Prediction to Causal Influence: Auditing SAE Features in Multiple-Choice QA

Aria Nourbakhsh; Adelaide Danilov; Oleksandr Marchenko Breneur; Salima Lamsiyah

cs.CLOct 27, 2026

From Error Prediction to Causal Influence: Auditing SAE Features in Multiple-Choice QA

Authors: Aria Nourbakhsh, Adelaide Danilov, Oleksandr Marchenko Breneur, Salima Lamsiyah

Organizations: Department of Computer Science (DCS), University of Luxembourg

Abstract

Sparse autoencoders (SAEs) can predict internal features associated with model errors, but association alone does not establish causal influence. We study this distinction in multiple-choice question answering, where answer preference can be measured by the logit margin between the correct answer and the competing choices. Across eight datasets, we analyze Gemma~3 1B and 4B with Gemma Scope SAEs. We propose a pipeline to filter out the features that have high correlation with format and content artifacts, such as prompt and answer permutation, and evaluate the remaining ones with causal feature interventions. Our results show that SAE activations contain predictive signals about wrongness and uncertainty across models and datasets. After filtering artifact-contaminated features, selected features for causal intervention at question and option spans produce larger absolute margin shifts and a higher wrong-to-correct rate than randomly selected features, indicating greater causal leverage. However, answer flips are rare, and we do not observe stable effect directions across meaning-preserving changes in prompt format and answer order. An adapted HalluSAE baseline produces larger final-token margin changes, but relies on substantially contaminated features and does not significantly improve correction rates. Therefore, the identified features reflect context-dependent answer competition rather than the mechanism of incorrect answer errors.

Figures & tables

Figure 1: Overview of the discovery and intervention pipeline. Behavioral measurements and SAE activations feed predictive, statistical, and artifact-aware screening. Contrastive DLA then prioritizes separate non-oracle and oracle candidates for feature interventions and baseline comparisons. Position codes are FP (final prompt token), Q (question span), O (option span), GR (generated reasoning), C (correct-choice text), and TW (top-wrong-choice text); C and TW are oracle spans.

Dataset	Source split	$N_{\mathrm{samples}}$	Choices
CommonSenseQA	train	4,000	5
TruthfulQA MC1	validation	817	2–13
HaluEval QA	data	4,000	2
Wiki-FACTOR	data	1,560	4
Med-HALT R-NOTA	dev	2,636	4
MMLU	validation	1,531	4

Table 1: Datasets, source splits, sample counts, and numbers of answer choices before prompt expansion.

Code	Token position	Role
FP	final prompt token	primary decision readout
Q	question/context span	non-oracle context
O	complete option block	non-oracle choices
GR	generated rationale	non-oracle generation
C	gold-choice text	oracle diagnostic
TW	top-wrong-choice text	oracle diagnostic

Table 2: Reported activation positions. Multi-token feature activations are aggregated by taking their maximum over the corresponding span.

Target	Metric	Test summary
WvC	AUROC / F1	.715 / .644
LMvHM	AUROC / F1	.739 / .711
WHC	AUROC / F1	.739 / .688
WLM	AUROC / F1	.706 / .805
Margin	$R^{2}$ / $r$	.117 / .357
Entropy	$R^{2}$ / $r$	.285 / .541

Table 3: FP test performance over 192 runs: eight datasets, eight model–layer–SAE configurations, and three response modes. Binary metrics are means; regression

R^{2}

and Pearson

r

are medians.

Pool	Ranked	Eligible	Selected	Mean $a_{f}$
Non-oracle	81,304	2,205	300	.712
Oracle C/TW	48,888	1,100	300	.724

Table 4: Validation-ranked feature selection over eight datasets. Ranked counts are aggregated feature units; eligible units pass all clean-candidate filters.

a_{f}

is artifact risk.

Set	Pos.	$N$	$U$	W2C	C2W	W2W	$\overline{\Delta m}$	$\overline{\|\Delta m\|}$	$\overline{\|\Delta p_{y}\|}$
Selected	FP	2,500	73	2	9	9	+.016	.154	.0031
Random	FP	9,950	320	18	22	19	+.007	.237	.0039
HalluSAE	FP	3,650	73	5	9	3	-.275	1.760	.0052
Selected	Q	21,110	425	16	17	8	+.002	.158	.0010
Random	Q	15,150	320	1	9	10	-.001	.135	.0011
Selected	O	20,170	415	19	19	23	-.005	.216	.0021

Table 5: Final test-set intervention outcomes.

N

counts feature–instance–intervention events and

U

counts run-specific feature tests; each feature–instance pair contributes five intervention events.

p_{y}

is the gold-letter probability. HalluSAE matches the selected FP candidate count within dataset–model–layer–width strata, but not the number of active instances. Oracle C/TW spans have no random-active counterpart.

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 2: Artifact risk versus unpenalized predictive evidence in the final eight-dataset feature-selection pools. Each hexagon counts model–layer–SAE-width–feature units; darker cells contain more units. Evidence is the sum of validation-quality-weighted coefficient-rank scores before artifact, density, overfit-gap, and position penalties. Orange circles mark the selected top 300, and the dashed line marks the artifact-risk gate. Because artifact risk is maximized and evidence is summed over contributing candidate-ranking records, this descriptive visualization is not used as a correlation test.

		1B		4B
Dataset	$N$	Acc.	WHC	Acc.	WHC
CommonSenseQA	796	.438	.519	.657	.325
TruthfulQA	175	.209	.735	.501	.485
HaluEval QA	833	.880	.114	.907	.092
Wiki-FACTOR	331	.453	.502	.499	.464
Med-HALT	534	.063	.866	.115	.833

Appendix

Table 6: Forced-letter test accuracy and wrong high-confidence rate over rendered prompt instances.

Abbrev.	Type	Target
WvC	Bin.	Wrong vs. correct answer
LMvHM	Bin.	$m_{i}\leq 0.5$ vs. $m_{i}\geq 2.0$ ; intermediate instances are excluded
WHC	Bin.	Wrong with $p_{i}(w_{i})\geq 0.70$ vs. correct with $p_{i}(y_{i})\geq 0.70$ or $m_{i}\geq 2.0$
WLM	Bin.	Wrong vs. correct among instances with $m_{i}\leq 0.5$
Margin	Reg.	Correct-vs.-top-wrong margin
Entropy	Reg.	Entropy over answer letters

Appendix

Table 7: Statistical-audit target definitions.

Pos.	WvC	LMvHM	WHC	WLM
FP	.715/.644	.739/.711	.739/.688	.706/.805
Q	.569/.522	.558/.572	.573/.553	.567/.779
O	.662/.591	.720/.687	.722/.662	.638/.821
GR	.740/.660	.749/.738	.782/.732	.784/.820
C	.746/.652	.836/.774	.839/.760	.645/.825
TW	.694/.617	.801/.750	.804/.735	.595/.800

Appendix

Table 8: Binary test performance by activation position. Each cell reports mean AUROC/F1 over the available runs.

Pos.	Margin $R^{2}$ / $r$	Entropy $R^{2}$ / $r$
FP	.117/.357	.285/.541
Q	-.138/.102	-.066/.176
O	.059/.353	.054/.302
GR	.104/.360	.106/.373
C	.239/.550	-.020/.189
TW	.185/.480	-.021/.196

Appendix

Table 9: Regression test performance by activation position. Each cell reports median

R^{2}

/Pearson

r

Dataset	Pos.	WvC	LMvHM	WHC	WLM
CSQA	FP	.652	.688	.670	.648
	Q	.539	.531	.530	.555
	O	.583	.655	.650	.601
	GR	.672	.727	.751	.719
	C	.735	.820	.823	.636
	TW	.646	.781	.787	.556

Appendix

Table 10: Mean test AUROC for the four binary audit models by dataset and activation position.

Dataset	Pos.	Margin	Entropy
CSQA	FP	.062	.369
	Q	-.140	-.017
	O	.006	.145
	GR	.105	.174
	C	.272	-.019
	TW	.178	.000

Appendix

Table 11: Median test

R^{2}

for margin and entropy regression by dataset and activation position.

Mode	Exact prefix
FL	You are a multiple-choice classifier. Reply with only the answer label.
RF	You are a careful multiple-choice assistant. Reason briefly about the choices, then put the final answer in the requested exact format on the last line.
LTR	You are a careful multiple-choice assistant. Start with the answer letter, then explain your reasoning briefly.

Appendix

Table 12: Compact prompt construction for the three templates and three response modes. Template 3, the colon-labeled options block, was used in all Phase 0 runs alongside Templates 1 and 2. For datasets with fewer choices, the option lines and slash-separated label set are shortened accordingly.

Audit	Quantity	Result
Predictive	Dataset–model–width groups	32
	HalluSAE test AUROC / F1	.775 / .674
	Random-control test AUROC / F1	.761 / .659
Artifact	Nonzero feature–setting records	3,020
	Records above the $a_{f}=0.80$ gate	2,987 (98.9%)
	Unique nonzero feature units	711

Appendix

Table 13: Adapted HalluSAE predictive and artifact audit. Predictive metrics are means over the 32 groups; random-control metrics average ten repetitions per group. A unit is a model–layer–SAE-width–feature combination. Artifact categories refer to the forced-letter FP settings in which a unit has a nonzero classifier coefficient.

Set	Pos.	$U_{r}/U_{f}$	Pairs	W2C e/p	C2W e/p	W2W e/p	W2C%	C2W%	$\overline{\|\Delta m\|}$
Selected	FP	73/20	500	2/1	9/3	9/3	.159	.723	.154
Random	FP	320/311	1,990	18/10	22/9	19/9	.347	.462	.237
HalluSAE	FP	73/27	730	5/3	9/9	3/3	.332	.420	1.760
Selected	Q	425/55	4,222	16/6	17/6	8/6	.170	.145	.158
Random	Q	320/319	3,030	1/1	9/3	10/6	.013	.119	.135
Selected	O	415/55	4,034	19/8	19/10	23/12	.209	.172	.216

Appendix

Table 14: Event- and pair-level intervention outcomes.

U_{r}/U_{f}

gives run-specific and global model–layer–width–feature units. “e/p” gives intervention events and unique feature–instance pairs. W2C% is conditional on an initially wrong baseline answer; C2W% is conditional on an initially correct answer.

Metric	Selected FP	Random FP	HalluSAE FP	H–Selected $[95\%\ \mathrm{CI}]$	H–Random $[95\%\ \mathrm{CI}]$
Run-specific feature tests	73	320	73	–	–
Feature–instance pairs	500	1,990	730	–	–
Median activation frequency	.00133	.00131	.580	–	–
W2C rate (%)	.159	.347	.332	+.173 $[-.294,.745]$	-.015 $[-.458,.557]$
C2W rate (%)	.723	.462	.420	-.303 $[-1.489,.566]$	-.043 $[-.483,.412]$
$\overline{\|\Delta m\|}$	.154	.237	1.760	+1.606 $[1.327,1.902]$	+1.524 $[1.245,1.818]$

Appendix

Table 15: Matched-budget HalluSAE FP comparison. Outcome intervals use 10,000 bootstrap resamples of model–layer–width–feature units. HalluSAE and selected FP have the same feature-test budget within 42 strata; activation density and the number of active feature–instance pairs are not matched.

Metric	Selected Q/O	Random Q/O	Selected–random	Oracle C/TW
W2C rate (%)	.189 [.090, .308]	.058 [.021, .101]	+.132 [+.024, +.257]	.101 [.000, .307]
C2W rate (%)	.158 [.074, .253]	.089 [.014, .179]	+.069 [-.055, +.191]	.162 [.024, .330]
$\overline{\|\Delta m\|}$	.187 [.164, .212]	.146 [.136, .160]	+.041 [+.014, +.067]	.134 [.114, .154]
$\overline{\|\Delta p_{y}\|}$	.00152 [.00122, .00187]	.00133 [.00114, .00152]	+.00019 [-.00018, +.00059]	.00105 [.00085, .00130]

Appendix

Table 16: Point estimates and 95% percentile intervals from 5,000 bootstrap resamples of model–layer–width–feature units. The intervals describe variation across tested feature units; they are not row-level tests or randomization-based

p

-values.

Figure 3: Mean absolute margin shift under upward steering. Error bars are 95% feature-unit bootstrap intervals over matched pairs with

+1\sigma

+2\sigma

, and

+4\sigma

results.

Scope	Tokens S/R	Std. edit S/R	Raw diff.	Adjusted diff. [95% CI]
Q/O	33/34	11.49/14.19	.041	.021 $[-.006,.048]$
Q	32/35	11.62/14.39	.023	.008 $[-.001,.017]$
O	33/33	11.38/13.94	.058	.049 $[.014,.084]$

Appendix

Table 17: Selected–random difference in mean

|\Delta m|

before and after perturbation adjustment. Tokens and standardized latent-edit magnitude are medians for selected/random events. The feature-equal regression additionally adjusts for baseline margin and correctness, activation frequency, operation, dataset, and model configuration; intervals are clustered by feature and original question. Standardized latent magnitude excludes decoder norm.

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The wide-scale use of sparse autoencoders (SAEs) as interpretability tools is limited by inconsistent links between SAE features and model behavior. Features with clear activation descriptions may have weak or unexpected causal effects; steering can vary across prompts or oppose the intended direction; and activation-based feature selection can miss features that produce the desired output change. Prior work has studied feature geometry inside the model, where features are computed. We instead study the geometry of changes in model logits caused by feature interventions. We introduce Feature-Effect Geometry Analysis (FEGA), an unsupervised framework that removes the same active SAE feature across contexts and analyzes the resulting cloud of logit changes. Across SAE variants, consistent one-dimensional effects are rare: few features behave like reusable directions. To interpret this variation, we distinguish value-like features, tied to static information such as factual attributes, from pointer-like features, associated with context-dependent operations. Value-like features more often exhibit structured, low-dimensional effects, although these effects typically span several directions. Pointer-like features, by contrast, predominantly exhibit diffuse effects. Our results show that a feature can be interpretable and causally relevant without providing a stable direction for steering.

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