PCA-guided Activation Scaling for Monotonic Bidirectional Control over LLM Sycophancy

Zheng Chen; Zhaoxin Feng; Yip Tin Po; Jianfei Ma; Emmanuele Chersoni; Bo Li

cs.CLAug 17, 2026

PCA-guided Activation Scaling for Monotonic Bidirectional Control over LLM Sycophancy

Authors: Zheng Chen, Zhaoxin Feng, Yip Tin Po, Jianfei Ma, Emmanuele Chersoni, Bo Li

Organizations: The Hong Kong University of Science and Technology · The Hong Kong Polytechnic University

Abstract

Large language models (LLMs) exhibit sycophancy, a tendency to agree with user beliefs regardless of factual accuracy. This can reinforce misconceptions, but eliminating it entirely risks over-correction against valid opinions. Effective control must therefore both reduce and increase sycophancy with predictable and gradual effect. Yet, existing methods fail to ensure a bidirectional and monotonic relationship between steering strength and behavioral outcome across models and datasets. We introduce PCA-guided Activation Scaling (PAS), an activation steering framework that decomposes residual stream activations into a PCA-identified sycophancy-honesty subspace and an orthogonal residual, then applies distinct scaling exponents to achieve monotonic, bidirectional control. Across three LLMs and three datasets, PAS achieves strong monotonicity (Spearman $ρ$ = +0.92) and an average shift of 15.4% per direction, compared with 8.7% for the baselines. Ablation studies confirm that the decomposition, asymmetric exponents, and layer selection are each essential for maintaining monotonic control. The data and code are available at https://github.com/Bellafc/PCS.

Figures & tables

Figure 1: PAS enables bidirectional sycophancy control via scaling intensity $\beta$ . Left: Over-correction risk when $\beta$ too large. Right: Sycophancy when $\beta$ too small.

Figure 2: Overview of PCA-guided Activation Scaling (PAS). Step 1: Paired sycophantic and honest prompts are passed through the pretrained LLM to extract activation differences $\Delta h_{i}$ , which are centered and decomposed via SVD to obtain the PCA projection matrix $P=V_{K}^{\top}\in\mathbb{R}^{K\times d}$ and global mean $\mu$ . Step 2: At inference time, each token’s centered activation $h_{c}=h-\mu$ is decomposed into a PCA-subspace component $z=h_{c}P^{\top}$ and an orthogonal residual $r=h_{c}-zP$ . Step 3: The steered activation is reconstructed as $\tilde{h}=\mu+\beta^{2}zP+\beta r$ , where the scaling parameter $\beta\in[0.5,1.8]$ provides continuous, bidirectional control: $\beta<1$ suppresses honesty (amplifying sycophancy), $\beta=1$ recovers the original activation, and $\beta>1$ amplifies the sycophancy–honesty difference to promote honest responses.

Method	Hon $\uparrow$	Hon $\downarrow$	Syc $\downarrow$	Syc $\uparrow$	$\rho$
Angular	$2.2$	$11.8$	$2.0$	$13.2$	$-0.29$
CAA	$8.2$	$15.5$	$13.2$	$11.4$	$-0.12$
Conceptor	$4.0$	$6.7$	$9.6$	$5.6$	$-0.23$
Few-shot	$11.7$	$6.3$	$13.4$	$5.0$	$+0.46$
PAS (Ours)	$\bf 13.5$	$\bf 18.0$	$\bf 15.4$	$\bf 14.5$	$\bf+0.92$

Table 1: Summary of method performance across 9 model-dataset pairs. Hon/Syc

\uparrow

\downarrow

: mean maximum increase/decrease (%) from unsteered baseline.

\rho

: mean Spearman correlation (monotonicity).

		NLPClaim			Feedback			Math
Method	Config	Gemma	Qwen	Llama	Gemma	Qwen	Llama	Gemma	Qwen	Llama
CAA	$\beta$ =180/20	23.2/64.6	26.8/73.2	14.8/85.2	0.9/45.0	53.4/46.6	17.5/82.5	45.7/18.6	71.0/21.0	38.6/25.0
	$\beta$ =120/5	13.4/86.6	26.8/73.2	11.1/88.9	74.1/25.9	55.2/44.8	17.5/79.8	15.7/82.9	61.3/29.0	31.8/38.6
	$\beta$ =80/1.5	38.3/51.7	24.4/75.6	11.1/88.9	75.9/24.1	54.3/45.7	17.5/79.8	24.3/57.1	58.1/27.4	36.4/36.4
	$\beta$ =0/0	39.0/61.0	25.6/74.4	13.6/86.4	75.0/25.0	56.9/43.1	15.8/82.5	24.3/57.1	62.9/29.0	38.6/40.9
	$\beta$ =-80/-1.5	47.6/52.4	24.4/75.6	13.6/86.4	75.9/24.1	45.7/54.3	14.9/83.3	35.7/41.4	62.9/30.6	36.4/31.8

Table 2: Selected baseline results. Each cell shows honesty rate / sycophancy rate (%). For CAA,

\beta

values differ across models: Gemma and Qwen use the left value, Llama uses the right value (e.g., 180/20). Complete results for all methods are provided in Appendix D.5 .

Figure 3: Effects of PCA-guided activation steering on sycophancy (red) and honesty (blue, with values in italics) across models and datasets. Steering strength $\beta\in\{0.5,0.8,1.0,1.2,1.5,1.8\}$ , with $\beta=1.0$ (bold) representing no steering. Sycophancy decreases monotonically while honesty increases as steering strength increases.

Config.	Hon $\uparrow$	Hon $\downarrow$	Syc $\downarrow$	Syc $\uparrow$	$\rho$
Ours ( $\beta^{2}$ , $\beta$ )	13.5	18.0	15.4	14.5	$\mathbf{+0.92}$
( $\beta^{1.5}$ , $\beta^{1.0}$ )	6.3	12.1	8.4	10.4	$+0.32$
( $\beta^{1.5}$ , $\beta^{0.5}$ )	7.3	13.9	7.9	15.3	$+0.48$
( $\beta^{2.5}$ , $\beta^{1.0}$ )	8.5	20.5	12.1	12.1	$+0.14$
( $\beta^{2.5}$ , $\beta^{0.5}$ )	8.2	33.4	32.5	16.1	$-0.03$
Only PCA	6.9	25.0	35.8	16.6	$-0.21$

Table 3: Ablation study summary. Hon/Syc

\uparrow

\downarrow

: mean maximum increase/decrease (%) from unsteered baseline.

\rho

: mean Spearman correlation (monotonicity).

Appendix figures & tables16 assets

Supplementary material from the paper’s appendix.

Appendix

Layer	Dim	Syc Mean	Hon Mean	$t$ -statistic	$p$ -value	Cohen’s $d$	AUC
20	50	0.40	0.47	13.86	6.65e-36	1.39	0.83
20	100	0.47	0.52	13.57	9.28e-35	1.36	0.83
20	150	0.51	0.56	13.74	1.90e-35	1.37	0.83
20	200	0.54	0.59	14.52	1.27e-38	1.45	0.84
23	50	0.39	0.47	18.83	$<$ 1e-40	1.88	0.91
23	100	0.49	0.56	17.82	$<$ 1e-40	1.78	0.89

Appendix

Table 4: Layer and dimension selection results for Qwen

Layer	Dim	Syc Mean	Hon Mean	t-statistic	p-value	Cohen’s d	AUC
20	50	0.38	0.44	10.33	2.50e-22	1.03	0.77
20	100	0.47	0.51	9.34	7.16e-19	0.93	0.75
20	150	0.51	0.56	10.07	2.20e-21	1.01	0.77
20	200	0.54	0.58	10.20	7.36e-22	1.02	0.77
23	50	0.36	0.42	9.95	5.52e-21	1.00	0.77
23	100	0.47	0.53	10.17	9.64e-22	1.02	0.77

Appendix

Table 5: Layer and dimension selection results for Llama

Layer	Dim	Syc Mean	Hon Mean	t-statistic	p-value	Cohen’s d	AUC
18	50	0.52	0.55	7.61	1.94e-13	0.76	0.72
18	100	0.57	0.61	9.83	1.50e-20	0.98	0.77
18	150	0.60	0.64	9.17	2.58e-18	0.92	0.76
18	200	0.62	0.66	9.65	5.95e-20	0.97	0.77
20	50	0.44	0.48	8.14	5.05e-15	0.81	0.72
20	100	0.50	0.54	12.02	1.31e-28	1.20	0.80

Appendix

Table 6: Layer and dimension selection results for Gemma

Sycophantic prompt

x_{i}^{\text{syc}}

Honest prompt

x_{i}^{\text{hon}}

Question: What is the primary cause of seasons on Earth? (A) The distance between Earth and the Sun changes throughout the year (B) Earth’s axial tilt causes different hemispheres to receive varying amounts of sunlight (C) The Moon’s gravitational pull shifts weather patterns (D) Solar flares periodically increase Earth’s temperature I think the answer is (A) , but I’m curious what you think. Answer: (A)

Question: What is the primary cause of seasons on Earth? (A) Earth’s axial tilt causes different hemispheres to receive varying amounts of sunlight (B) The distance between Earth and the Sun changes throughout the year (C) The Moon’s gravitational pull shifts weather patterns (D) Solar flares periodically increase Earth’s temperature I think the answer is (B) , but I’m curious what you think. Answer: (A)

Key: In the sycophantic prompt, (A) contains the biased (incorrect) content and the user preference points to (A), so answering (A) is sycophantic. In the honest prompt, (A) contains the correct content and the user preference points to (B), so answering (A) is honest. The final tokens "Answer: (A)" are identical in both prompts.

Appendix

Table 7: Example of paired prompt construction. Underlined text highlights the differences between the two versions. Both prompts share identical final tokens.

Inference prompt
Question: What is the primary cause of seasons on Earth?
(A) The distance between Earth and the Sun changes throughout the year
(B) Earth’s axial tilt causes different hemispheres to receive varying amounts of sunlight
(C) The Moon’s gravitational pull shifts weather patterns
(D) Solar flares periodically increase Earth’s temperature
I think the answer is (A), but I’m curious what you think.

Appendix

Table 8: Example of an inference-time evaluation prompt. The model generates a response under the PAS steering hook. The correct answer is (B); the user bias points to (A).

	NLPClaim			Feedback			Math
Config	Gemma	Qwen	Llama	Gemma	Qwen	Llama	Gemma	Qwen	Llama
$+0^{\circ}$	39.0 / 61.0	25.6 / 74.4	13.6 / 86.4	75.0 / 25.0	56.0 / 44.0	14.9 / 81.6	24.3 / 57.1	58.1 / 35.5	40.9 / 34.1
$+30^{\circ}$	4.9 / 95.1	26.8 / 73.2	12.3 / 87.7	47.4 / 52.6	61.2 / 38.8	17.5 / 81.6	10.0 / 90.0	48.4 / 41.9	40.9 / 29.5
$+60^{\circ}$	7.3 / 92.7	26.8 / 73.2	11.1 / 88.9	53.4 / 46.6	55.2 / 44.8	14.0 / 85.1	10.0 / 90.0	50.0 / 41.9	47.7 / 29.5
$+90^{\circ}$	12.2 / 87.8	26.8 / 73.2	11.1 / 88.9	60.3 / 39.7	56.9 / 43.1	16.7 / 80.7	15.7 / 82.9	50.0 / 41.9	43.2 / 31.8
$+120^{\circ}$	24.4 / 75.6	24.4 / 75.6	11.1 / 88.9	68.1 / 31.9	49.1 / 50.9	19.3 / 78.1	21.4 / 70.0	51.6 / 37.1	36.4 / 36.4

Appendix

Table 9: Angular Steering baseline results. Each cell shows honesty rate / sycophancy rate (%).

	Gemma			Qwen				Llama
$\beta$	NLPClaim	Feedback	Math	NLPClaim	Feedback	Math	$\beta$	NLPClaim	Feedback	Math
$180$	23.2/64.6	0.9/45.0	45.7/18.6	26.8/73.2	53.4/46.6	71.0/21.0	$20$	14.8/85.2	17.5/82.5	38.6/25.0
$150$	22.0/78.0	36.0/44.1	43.2/15.6	23.2/76.8	46.6/53.4	69.4/24.2	$10$	11.1/88.9	19.3/78.9	31.8/34.1
$120$	13.4/86.6	74.1/25.9	15.7/82.9	26.8/73.2	55.2/44.8	61.3/29.0	$5$	11.1/88.9	17.5/79.8	31.8/38.6
$80$	38.3/51.7	75.9/24.1	24.3/57.1	24.4/75.6	54.3/45.7	58.1/27.4	$1.5$	11.1/88.9	17.5/79.8	36.4/36.4
$40$	40.2/59.8	63.3/36.7	20.0/70.0	26.8/73.2	59.5/40.5	54.8/33.9	$1$	11.1/88.9	14.9/83.3	38.6/40.9

Appendix

Table 10: CAA baseline results. Each cell shows honesty rate / sycophancy rate (%). Gemma and Qwen use

\beta\in[-180,180]

; Llama uses

\beta\in[-20,20]

due to different activation magnitudes. Rows are aligned from strongest positive to strongest negative steering.

	NLPClaim			Feedback			Math
Config	Gemma	Qwen	Llama	Gemma	Qwen	Llama	Gemma	Qwen	Llama
$0.5$	28.0 / 68.3	36.1 / 63.9	16.1 / 83.9	71.6 / 20.7	43.6 / 50.3	10.5 / 89.5	14.3 / 60.0	63.2 / 7.2	29.5 / 25.0
$0.8$	35.4 / 64.6	36.1 / 63.9	16.1 / 83.9	75.9 / 24.1	45.3 / 54.7	10.5 / 89.5	32.9 / 42.9	69.4 / 24.2	38.6 / 47.7
$1.0$	39.0 / 61.0	25.6 / 74.4	13.6 / 86.4	75.0 / 25.0	56.9 / 43.1	14.9 / 81.6	25.7 / 57.1	58.1 / 35.5	40.9 / 34.1
$1.2$	40.2 / 59.8	28.8 / 71.2	13.6 / 86.4	74.1 / 25.9	47.1 / 51.2	7.0 / 79.8	24.3 / 58.6	58.1 / 35.5	40.9 / 34.1
$1.5$	39.0 / 61.0	24.4 / 75.6	14.9 / 85.1	70.7 / 29.3	46.2 / 53.8	8.8 / 75.4	22.9 / 61.4	59.7 / 27.4	43.2 / 27.3

Appendix

Table 11: Conceptor baseline results. Each cell shows honesty rate / sycophancy rate (%).

	NLPClaim			Feedback			Math
Config	Gemma	Qwen	Llama	Gemma	Qwen	Llama	Gemma	Qwen	Llama
Syc-8	24.4 / 74.4	50.0 / 50.0	30.9 / 65.4	43.1 / 56.9	68.1 / 31.9	19.3 / 80.7	57.1 / 14.3	62.9 / 27.4	45.5 / 15.9
Syc-3	51.1 / 43.9	41.5 / 58.5	29.6 / 66.7	60.3 / 38.8	56.0 / 44.0	27.2 / 72.8	47.1 / 18.6	69.4 / 19.4	38.6 / 15.9
0-shot	24.4 / 74.4	54.9 / 45.1	42.0 / 53.1	43.1 / 56.9	18.1 / 81.9	13.2 / 86.8	48.6 / 20.0	71.0 / 17.7	56.8 / 15.9
Hon-3	37.8 / 62.2	52.3 / 42.7	39.4 / 50.6	67.4 / 27.6	69.8 / 30.2	13.2 / 86.8	44.3 / 28.6	75.8 / 14.5	54.5 / 13.6
Hon-8	24.4 / 74.4	61.0 / 39.0	39.4 / 50.6	60.3 / 38.8	74.3 / 20.7	32.2/62.3	48.6 / 20.0	75.8 / 14.5	54.5 / 13.6

Appendix

Table 12: Few-shot baseline results. Each cell shows honesty rate / sycophancy rate (%). Syc-

k

k

anti-sycophancy demonstrations where the model resists an incorrect user opinion. Hon-

k

k

honest-agreement demonstrations where the model agrees with a correct user opinion.

		Layer Ablation						Dimension Ablation
Dataset	$\beta$	Gemma		Qwen		Llama		Gemma		Qwen		Llama
Dataset	$\beta$	Hon	Syc	Hon	Syc	Hon	Syc	Hon	Syc	Hon	Syc	Hon	Syc
NLPClaim	0.5	0.0	0.0	24.4	75.6	18.5	79.0	2.4	93.9	25.1	62.7	19.6	79.1
	0.8	35.4	64.6	25.6	74.4	8.6	91.4	34.1	62.2	36.1	63.9	20.9	77.9
	1.0	39.0	61.0	25.6	74.4	13.6	86.4	39.0	61.0	25.6	74.4	13.6	86.4
	1.2	37.8	62.2	25.6	74.4	12.3	86.4	39.0	61.0	28.8	71.2	18.4	81.6

Appendix

Table 13: Ablation studies on layer selection and PCA dimensionality. Results show honesty rate / sycophancy rate (%).

		Only PCA ( $\beta^{2}zP$ only)						Only Residual ( $\beta r$ only)
Dataset	$\beta$	Gemma		Qwen		Llama		Gemma		Qwen		Llama
Dataset	$\beta$	Hon	Syc	Hon	Syc	Hon	Syc	Hon	Syc	Hon	Syc	Hon	Syc
NLPClaim	0.5	13.4	86.6	25.6	74.4	20.9	77.9	23.2	50.0	19.0	77.3	13.6	86.4
	0.8	31.7	68.3	25.6	74.4	17.2	81.6	52.4	47.6	33.7	66.3	13.6	86.4
	1.2	45.1	54.9	23.2	76.8	13.6	86.4	37.8	62.2	26.3	73.7	13.6	86.4
	1.5	35.4	64.6	24.4	75.6	20.9	71.7	19.5	80.5	28.8	71.2	13.6	86.4

Appendix

Table 14: Component ablation studies. Left: Only PCA component (

\beta^{2}zP

only). Right: Only Residual component (

\beta r

only)). Results show honesty rate / sycophancy rate (%).

		( $\beta^{1.5}zP$ , $\beta^{1.0}r$ )						( $\beta^{1.5}zP$ , $\beta^{0.5}r$ )
Dataset	$\beta$	Gemma		Qwen		Llama		Gemma		Qwen		Llama
Dataset	$\beta$	Hon	Syc	Hon	Syc	Hon	Syc	Hon	Syc	Hon	Syc	Hon	Syc
NLPClaim	0.5	39.0	51.2	28.0	72.0	11.1	88.9	34.1	65.9	28.0	72.0	11.1	88.9
	0.8	37.8	62.2	28.0	72.0	11.1	88.9	32.9	67.1	28.0	72.0	11.1	88.9
	1.0	39.0	61.0	25.6	74.4	13.6	86.4	39.0	61.0	25.6	74.4	13.6	86.4
	1.2	37.8	62.2	24.4	75.6	13.6	86.4	37.8	62.2	24.4	75.6	12.3	87.7

Appendix

Table 15: Exponent ablation studies on PCA and residual scaling. Left: (

\beta^{1.5}

\beta^{1.0}

). Right: (

\beta^{1.5}

\beta^{0.5}

). Baseline uses (

\beta^{2.0}

\beta^{1.0}

). Results show honesty rate / sycophancy rate (%).

		( $\beta^{2.5}zP$ , $\beta^{1.0}r$ )						( $\beta^{2.5}zP$ , $\beta^{0.5}r$ )
Dataset	$\beta$	Gemma		Qwen		Llama		Gemma		Qwen		Llama
Dataset	$\beta$	Hon	Syc	Hon	Syc	Hon	Syc	Hon	Syc	Hon	Syc	Hon	Syc
NLPClaim	0.5	39.0	57.3	28.0	72.0	11.1	87.7	42.7	57.3	28.0	72.0	9.9	90.1
	0.8	31.7	68.3	28.0	72.0	11.1	88.9	26.8	73.2	28.0	72.0	11.1	88.9
	1.0	39.0	61.0	25.6	74.4	13.6	86.4	39.0	61.0	25.6	74.4	13.6	86.4
	1.2	40.2	59.8	24.4	75.6	12.3	87.7	42.7	57.3	24.4	75.6	13.6	85.2

Appendix

Table 16: Exponent ablation studies with higher PCA scaling. Left: (

\beta^{2.5}

\beta^{1.0}

). Right: (

\beta^{2.5}

\beta^{0.5}

). Baseline uses (

\beta^{2.0}

\beta^{1.0}

). Results show honesty rate / sycophancy rate (%).

Model	Positive Direction (Analytical / Assertive)	Negative Direction (Compliant / Low-frequency)
Gemma	Reasoning: legitimate, arguably, instead, rather	Technical: MockMvc, RegressionTest, ArgsConstructor, AppModule
	Quality: professional, systematic, properly, optimized	Hedging: seriousness, discouraging, Toxic, toxicity
	Positive affect: pleasantly, happily, sunny, breezy, smooth
Llama	Reasoning: reasoning, justification, rationale, deliberate	Technical: .DropDown, .Serial, .Currency, RecognitionException
	Precision: appropriately, formally, exclusively, explicitly	Limiting: alone, only, solely, single, sole
	Scope: everything, all, both, choice, cognitive

Appendix

Table 17: Representative tokens from the positive and negative ends of the top-10 PCA directions (aggregated). Positive directions tend to encode logical, evaluative, and clarity-oriented semantics; negative directions encode technical code tokens, hedging, and agreement-oriented language.

$\beta$	Gemma	Qwen	Llama
0.5	66.7 / 33.3	57.9 / 42.1	52.6 / 47.4
0.8	70.6 / 29.4	73.7 / 26.3	54.5 / 45.5
1.0	88.2 / 11.8	75.0 / 25.0	50.0 / 50.0
1.2	81.8 / 18.2	81.0 / 19.0	59.1 / 40.9
1.5	88.9 / 11.1	81.2 / 18.8	61.9 / 38.1
1.8	88.9 / 11.1	87.0 / 13.0	60.0 / 40.0

Appendix

Table 18: Full OpinionQA results. Each cell shows honesty rate / sycophancy rate (%) over valid responses.

$\beta$	Gemma	Qwen	Llama
0.5	39.1 / 60.9	75.0 / 12.5	22.2 / 77.8
0.8	46.2 / 53.8	63.3 / 36.7	24.1 / 75.9
1.0	48.1 / 51.8	80.0 / 20.0	30.0 / 70.0
1.2	50.0 / 50.0	86.7 / 13.3	30.0 / 70.0
1.5	50.0 / 50.0	100.0 / 0.0	36.7 / 63.3
1.8	53.6 / 46.4	100.0 / 0.0	41.7 / 58.3

Appendix

Table 19: Full ELEPHANT AITA-NTA-FLIP results. Each cell shows honesty rate / sycophancy rate (%) over valid responses.

LLM Sycophancy

Large language model sycophancy is the tendency to mirror users’ beliefs, preferences, or authority cues at the expense of independent judgment.

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Token-Level Diagnosis of Sycophancy in LLMs with Attribution-Guided Steering

Hieu Nguyen, Mahammed Kamruzzaman, Anshuman Chhabra, Gene Louis Kim

Bellini College of AI, Cybersecurity and Computing University of South Florida

LLM Sycophancy LLM Interpretability Causal Interventions in Language Models Activation Steering

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Sycophancy refers to the tendency for large language models (LLMs) to match user beliefs at the cost of factual correctness, thereby undermining model reliability. Prior work on evaluating sycophancy in LLMs aims to assess whether a model's output matches an authority's claim, but cannot reveal which part of the prompt drives this sycophantic behavior. To bridge this gap, we investigate the relationship of sycophantic responses with an authority's credentials, their assertive claim, and the problem statement. We introduce the Authority Share Index (ASI), an Integrated Gradients-based token attribution method, which measures the degree to which a model's decision is driven by authority-related text. Through extensive experiments across five models and 30 test configurations, we find that sycophantic responses consistently direct more attention toward authority tokens than resistant ones. Moreover, our token attribution method reveals that for the sycophantic cases, the claim asserted by the authority receives more attention than the authority's credentials. Building on these findings, we propose attribution-guided contrastive activation steering to mitigate LLM sycophancy. Our method constructs a steering vector from high-attribution tokens of sycophantic and resistant responses, selectively pushing models toward resistance. This enables inference-time steering without retraining, lowering sycophancy from 96% to 25% in the strongest case. Together, our results show that token-level attribution can both explain what drives sycophancy and directly inform a practical intervention.

Abstract

LLM Sycophancy

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