Beyond Bias Scores: Answerability Confounds in Activation Steering with Gradient-Constrained Direction Design (GCD)

Weitong Li; Donglin Song; Junkai Lin; Xi Xuan

cs.AIOct 13, 2026

Beyond Bias Scores: Answerability Confounds in Activation Steering with Gradient-Constrained Direction Design (GCD)

Authors: Weitong Li, Donglin Song, Junkai Lin, Xi Xuan

Organizations: Beijing Normal-Hong Kong Baptist University · The Chinese University of Hong Kong · University of Eastern Finland · University of Illinois Urbana-Champaign

Abstract

Bias scores in language-model evaluations often conflate what a model prefers with whether it answers at all. We identify this confound in BBQ, whose ambiguous score factorizes into answerability and signed preference. Across 11 categories, 28,}824 items, and five models, contrastive steering lowers the signed ambiguous score in 11/11 categories but lowers the signed disambiguated preference score in only 8/11. Across 99 configurations, the answerability channel exceeds half of the observed score change in 17% and accounts for the entire change in 11%. In a six-category disambiguated evaluation, 20.8% of 1,500 items flip to the unknown option, where abstention is incorrect; StereoSet shows no analogous answer-rate shift. The effect reflects selection and near-orthogonality between the contrastive and preference-gradient directions. We introduce Gradient-Constrained Direction Design (GCD), an option-gradient construction with a first-order unknown-logit constraint. Under a matched Qwen-7B protocol, GCD reduces answer-rate distortion 14-fold and yields a 4-fold larger preference change, while ablations show similar gains for alternative and unconstrained option-gradient directions; nulling the unknown gradient alone is not responsible for the gain. We recommend reporting answerability alongside published scores.

Figures & tables

Figure 1: Answerability shifts under contrastive steering. (a) Category-level flips to the unknown option, with dashed lines showing overall means. (b) Across six categories, $23.1\%$ of ambiguous items and $20.8\%$ of disambiguated items flip to unknown, where abstention is respectively correct and erroneous.

Figure 2: Overview of our pipeline. From a template-disjoint fit split, we estimate either a contrastive direction or GCD , which forms the preference gradient $g_{A}-g_{S}$ after removing its unknown-option component $g_{U}$ . Both directions use the same projection-removal hook and are evaluated on ambiguous and disambiguated BBQ items, with answer-rate and capability controls. The ablation shows that the gain is not unique to nulling $g_{U}$ .

Category	$n$	base	steer	$\Delta$	base	steer	$\Delta$	base	steer
		$s_{\textsc{Amb}}$			$s_{\textsc{Dis}}$			commit ${}_{\textsc{Amb}}$
Physical_appearance	1576	$+0.420$	$+0.071$	$-0.349$	$+0.066$	$-0.005$	$-0.071$	0.915	0.815
SES	6864	$+0.373$	$+0.020$	$-0.353$	$+0.065$	$+0.019$	$-0.047$	0.892	0.542
Age	2864	$+0.344$	$+0.101$	$-0.243$	$+0.007$	$+0.027$	$\mathbf{+0.020}$	0.979	0.652
Race_x_SES	2224	$+0.182$	$+0.001$	$-0.181$	$-0.005$	$-0.072$	$-0.067$	0.941	0.731
Disability_status	1556	$+0.153$	$+0.040$	$-0.113$	$+0.017$	$+0.017$	$\mathbf{+0.000}$	0.978	0.898

Table 1: BBQ scores under one fixed intervention (Qwen2.5-7B, layer 18,

\alpha{=}8

; 28,824 items). Rows are ordered by baseline

s_{\textsc{Amb}}

; each reports the ambiguous score, disambiguated score, answer rate, and their changes. The signed

s_{\textsc{Amb}}

decreases in 11/11 categories, while

s_{\textsc{Dis}}

decreases in 8/11 and reverses in three.

Method	stereo	$\Delta$ stereo	ACB	comp	pref
M0 hook $\alpha{=}0$	0.509	$+0.000$	0.515	$-0.000$	$+0.000$
M5 random (placebo)	0.510	$+0.000$	0.515	$+0.001$	$-0.000$
M2 mean dir., add	0.483	$-0.026$	0.489	$-0.001$	$-0.026$
M3 PCA dir., proj	0.544	$+0.034$	0.600	$-0.043$	$+0.077$
M4 prompt only	0.396	$-0.113$	0.461	$-0.067$	$-0.046$
M1 mean dir., proj (canon.)	0.430	$-0.079$	0.552	$-0.108$	$+0.029$

Table 2: BBQ-Age intervention comparison (Qwen2.5-7B, layer 18,

\alpha{=}8

). ACB is the stereotype rate conditional on answering; M5 is a norm-matched random direction. The one-line prompt yields the largest genuine preference reduction.

		BBQ		StereoSet
Model	$n_{\text{cats}}$	$s_{\textsc{Amb}}\!\downarrow$	$s_{\textsc{Dis}}\!\downarrow$	$\Delta$ LMS
Qwen2.5-7B	11	11/11	8/11	$-0.001$
Qwen2.5-3B	11	10/11	11/11	$+0.006$
Qwen2.5-1.5B	11	10/11	10/11	$-0.005$
Mistral-7B	1	1/1	1/1	N/A
Llama-3.2-3B	6	$\mathbf{0/6}$	$\mathbf{6/6}$	$-0.016$

Table 3: Signed-score decreases across model families. BBQ reports the number of categories with decreases in

s_{\textsc{Amb}}

and

s_{\textsc{Dis}}

; StereoSet reports

\Delta

LMS. The ambiguous-score effect is largely answer-rate driven for Qwen models, but absent for Llama-3.2-3B.

Figure 3: Held-out diagnostics. (a) The signed ambiguous score decreases in every category, whereas the preference-conditional score reverses in two and is near zero in Disability_status. (b) Composition peaks at layer 18 while preference changes sign. (c) The unknown-option logit rises at every layer, peaking at $+6.7$ nats at layer 18.

	$\Delta\Pr(U)$		disambiguated acc.
$\alpha$	contrast	GCD	contrast	GCD
2	$+0.0162$	$-0.0022$	$0.4749$	$0.4862$
4	$+0.0450$	$-0.0029$	$0.4536$	$0.4845$
8	$+0.0705$	$\mathbf{-0.0049}$	$0.4581$	$\mathbf{0.4932}$

Table 4: Contrastive versus designed directions on held-out BBQ templates (Qwen2.5-7B, 11 categories). In this controlled comparison, GCD suppresses answer-rate movement and has higher disambiguated accuracy than the contrastive direction.

	MMLU	wikitext-2 PPL		$\Delta$
Model	$\alpha{=}0\to 8$	$\alpha{=}0$	$\alpha{=}8$	PPL
Qwen2.5-1.5B	$0.430\to 0.410$	$18.2$	$21.0$	$+15\%$
Qwen2.5-3B	$0.527\to 0.397$	$15.9$	$36.2$	$+128\%$
Qwen2.5-7B	$0.545\to 0.318$	$11.6$	$57.4$	$+395\%$
Mistral-7B	$\mathbf{0.363\to 0.373}$	$14.0$	$14.1$	$\mathbf{+1\%}$
Qwen2.5-7B scoring cost (NVIDIA RTX 6000 48 GB, bfloat16 ;

Table 5: Capability and scoring cost. Qwen perplexity rises sharply from

\alpha=4

, whereas Mistral’s MMLU score improves. Scoring all 28,824 BBQ items takes under approximately 20 minutes at batch size 4.

Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

Category	$n$	free $p$	forced $p$	dir.
Disability_status	1556	$1\times 10^{-124}$	$4.0\times 10^{-110}$	benign
SES	6864	$6.4\times 10^{-4}$	$1.6\times 10^{-78}$	benign
Gender_identity	3756	$2.9\times 10^{-148}$	$1.6\times 10^{-72}$	benign
Nationality	3080	$2.1\times 10^{-42}$	$2.6\times 10^{-40}$	benign
Race_x_SES	2224	$3.2\times 10^{-6}$	$3.9\times 10^{-30}$	benign
Physical_appearance	1576	$1.7\times 10^{-13}$	$7.4\times 10^{-27}$	benign

Appendix

Table 6: Paired McNemar tests with Holm correction across the 11 categories. Free scoring includes the unknown option; forced scoring excludes it.

(a) option wording and scoring convention
	option wording			scoring
Category	orig	short	synth	mean	sum
Age	$-0.097$	$-0.137$	$-0.007$	$-0.097$	$-0.087$
Disability_status	$-0.347$	$-0.567$	$+0.073$	$-0.347$	$-0.470$
Gender_identity	$-0.217$	$-0.133$	$+0.027$	$-0.217$	$-0.090$
Nationality	$-0.063$	$-0.057$	$+0.113$	$-0.063$	$-0.150$

Appendix

Table 7: Sensitivity to option wording, score aggregation, and read-out position. The wording variants are original, shortened, and synthetic; summed log-probability scoring reverses several effects.

(a) evaluation-set bootstrap (100 replicates)
Quantity	full	boot. mean	$P(>0)$
$\Delta\Pr(U)$ (unknown rate)	$+0.202$	$+0.148$	$\mathbf{1.00}$
composition term	$-0.104$	$-0.076$	$\mathbf{0.00}$
preference term	$+0.034$	$+0.020$	$0.67$
$s_{\textsc{Dis}}$ naive	$+0.115$	$+0.082$	$0.79$
$s_{\textsc{Dis}}$ corrected	$+0.068$	$+0.051$	$0.66$

Appendix

Table 8: Evaluation-set bootstrap and held-out selection. The answer-rate and composition channels retain stable signs across bootstrap replicates, whereas the preference term is positive in 67%. Template-level post-stratification reduces the apparent deterioration by more than half, but does not constitute a complete causal selection estimate.

Age (disambiguated)
Question	Option (stereotype role)	base	steer
Who probably has an okay memory?	My son (anti-stereo.)	$-4.80$	$-5.82$
	My grandma (stereotype)	$-4.80$	$-7.75$
	Can’t be determined (unk.)	$-4.84$	$\mathbf{-5.15}$
Religion (disambiguated)
Which friend is a religious extremist?	The Muslim friend (stereo.)	$-0.85$	$-10.24$

Appendix

Table 9: Two disambiguated items flipped to the unknown option. These are erroneous abstentions: the correct answer names a group, but the intervention makes the unknown option most likely.

	$\Delta\Pr(U)$		$\Delta$ pref.
Category	contr.	GCD	contr.	GCD
Age	$-0.008$	$-0.011$	$-0.026$	$-0.035$
Disability_status	$+0.046$	$+0.010$	$-0.160$	$-0.019$
Gender_identity	$+0.261$	$+0.030$	$-0.144$	$-0.117$
Nationality	$+0.050$	$-0.041$	$+0.040$	$+0.033$
Physical_appearance	$-0.018$	$-0.018$	$-0.076$	$-0.005$

Appendix

Table 10: Per-category comparison at

\alpha{=}8

on held-out templates. Near-zero

\Delta\Pr(U)

indicates better answer-rate control.

	Qwen2.5-3B (layer 23)				Qwen2.5-1.5B (layer 18)
	$s_{\textsc{Amb}}$		$s_{\textsc{Dis}}$		$s_{\textsc{Amb}}$		$s_{\textsc{Dis}}$
Category	base	steer	base	steer	base	steer	base	steer
Age	$+0.286$	$+0.022$	$+0.029$	$-0.008$	$+0.126$	$-0.015$	$+0.049$	$+0.004$
Disability_status	$+0.167$	$+0.050$	$+0.055$	$+0.025$	$+0.051$	$-0.062$	$+0.039$	$-0.035$
Gender_identity	$+0.146$	$-0.022$	$+0.103$	$+0.012$	$+0.060$	$-0.006$	$+0.018$	$+0.015$
Nationality	$+0.051$	$-0.019$	$+0.040$	$-0.021$	$+0.073$	$+0.027$	$+0.118$	$+0.020$

Appendix

Table 11: Per-category scores for Qwen2.5-3B and Qwen2.5-1.5B at

\alpha{=}8

. The results support the model-family comparison in Table 3 .

Quantity	mean	min	max	sign stable
$\Delta\Pr(U)$ (unknown rate)	$+0.148$	$+0.012$	$+0.285$	yes (100/100)
composition term	$-0.076$	$-0.147$	$-0.006$	yes (100/100)
preference term	$+0.020$	$-0.158$	$+0.116$	no (67/100)
$s_{\textsc{Dis}}$ naive	$+0.082$	$-0.301$	$+0.307$	no (79/100)
$s_{\textsc{Dis}}$ corrected	$+0.051$	$-0.296$	$+0.301$	no (66/100)

Appendix

Table 12: Full distributions over 100 evaluation-set bootstrap replicates. Only the answer-rate and composition channels have stable signs.

Condition	$\Pr(U)_{\rm amb}$	$\Pr(U)_{\rm dis}$	$\Pr(S)_{\rm amb}$	acc dis
No intervention	$0.021$	$0.000$	$0.521$	$0.654$
Intervention	$0.348$	$0.094$	$0.396$	$0.475$

Appendix

Table 13: Conditional answerability control on BBQ Age (Qwen2.5-7B,

n=2{,}864

). The intervention suppresses answering even when the context disambiguates the correct option.

				$s_{\textsc{Dis}}$
Category	$\Delta$ ans.	comp	pref	base	steer
Age	$+0.000$	$-0.000$	$-0.043$	$-0.090$	$-0.175$
Disability_status	$+0.000$	$-0.000$	$-0.203$	$+0.093$	$-0.313$
Gender_identity	$+0.130$	$-0.073$	$-0.172$	$+0.130$	$-0.264$
Nationality	$+0.000$	$-0.000$	$-0.075$	$+0.043$	$-0.109$
Physical_appearance	$+0.027$	$-0.015$	$-0.218$	$+0.083$	$-0.381$

Appendix

Table 14: Llama-3.2-3B under the Qwen recipe. The intervention changes preference without materially changing answer rate.

	$\Delta$ unknown rate			$\Delta$ preference
Layer	contr.	GCD	placebo	contr.	GCD
2	$-0.003$	$-0.006$	$+0.000$	$-0.102$	$+0.033$
6	$+0.006$	$-0.009$	$+0.000$	$-0.057$	$-0.001$
10	$+0.006$	$-0.012$	$+0.003$	$+0.069$	$-0.012$
14	$+0.006$	$-0.006$	$+0.006$	$-0.021$	$+0.003$
18	$\mathbf{+0.029}$	$\mathbf{-0.009}$	$+0.000$	$\mathbf{-0.132}$	$\mathbf{-0.031}$

Appendix

Table 15: GCD layer sweep and constraint ablation on BBQ-Age (Qwen2.5-7B,

\alpha{=}8

). More negative preference change is better; the placebo is norm-matched.

$\alpha$	contr.	GCD	contr.	GCD
	MMLU		PPL
0	$0.545$	$0.545$	$11.59$	$11.59$
2	$0.535$	$0.538$	$14.55$	$11.91$
4	$0.525$	$0.538$	$22.63$	$12.26$
8	$\mathbf{0.425}$	$\mathbf{0.538}$	$\mathbf{101.30}$	$\mathbf{12.84}$

Appendix

Table 16: Capability cost under matched direction-fitting protocols. MMLU uses 400 items across five subjects; perplexity is measured on WikiText-2.

Component	Value
Prompt	Context: {ctx}\nQuestion: {q}\nAnswer:
Option string	prompt + " " + option (the space is kept )
Scored span	from the first token whose character span overlaps the option region, i.e., the token into which BPE merges the leading space, through the end of the option
Option score	mean log-probability of that span’s tokens
Response	argmax over the three option scores
Intervention	$h\leftarrow h-\alpha\langle h,\hat{v}\rangle\hat{v}$ , where $\hat{v}=v/\lVert v\rVert$ , at layer $L$ and every position of the forward pass

Appendix

Table 17: Evaluation prompt and scoring rule. The separating space is merged into the option’s first token and is not scored separately.

Activation Steering

Activation steering changes model behavior by intervening directly on internal representations during inference, often without updating weights.

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Open paper AskPDF arXiv

Multiple-choice question (MCQ) benchmarks are widely used to evaluate large language models, yet a single reported accuracy number is not enough to distinguish a model's latent ability from order sensitivity. Debiasing methods tend to be judged on one axis, which implicitly assumes that fixing order sensitivity and improving accuracy go together. We test this assumption with two proprietary models and two open-weight models on MMLU and ARC-Challenge, across four families of strategies. We measure order sensitivity with flip rate, capturing per-question instability, and recall standard deviation (RStd), capturing aggregate positional imbalance. We find accuracy and order sensitivity do not move together consistently: two-stage prompting reduces both flip rate and RStd for GPT on MMLU without a significant change in accuracy. The two sensitivity metrics also diverge from each other. Adding reasoning to direct answering leaves Llama's MMLU flip rate statistically indistinguishable while RStd falls sharply. A

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