Which Knowledge Should LLMs Trust? Uncovering a Generalizable Steering Direction Across Knowledge Conflicts

Yibin Lou; Yi Hu; Jianhui Chen; Chenpeng Wang; Muhan Zhang; Liangming Pan

cs.CLOct 14, 2026

Which Knowledge Should LLMs Trust? Uncovering a Generalizable Steering Direction Across Knowledge Conflicts

Authors: Yibin Lou, Yi Hu, Jianhui Chen, Chenpeng Wang, Muhan Zhang, Liangming Pan

Organizations: State Key Laboratory of Multimedia Information Processing, Peking University · School of Computer Science, Peking University · Southern University of Science and Technology · Institute for Artificial Intelligence, Peking University ·

Abstract

Large Language Models (LLMs) frequently encounter conflicts between internal parametric knowledge and external contextual knowledge, yet the mechanisms governing this selection remain unclear. We show that the choice between context and parametric knowledge is linearly represented and can be controlled along a single direction in the model's residual stream. We first demonstrate that this direction generalizes across factual-conflict settings, including context formats, knowledge categories, and datasets, while consistently shifting behavior between parametric and contextual answers. We then transfer a direction learned from simple factual conflicts to three more complex task families: RAG, memory, and rule following, where models must acquire information from retrieved documents, interaction histories, or explicit rules. Across four model families and multiple transfer settings, steering consistently improves the use of prompt-provided information over the unsteered model. These results suggest that the direction captures a transferable preference for external knowledge rather than a mechanism specific to factual conflicts.

Figures & tables

Figure 1: Under knowledge conflicts, steering along a single residual-stream direction smoothly shifts outputs between parametric knowledge and contextual knowledge , with intermediate mixed or hesitant responses.

Figure 2: Overview of knowledge-selection steering. For each question $q$ , the clean prompt is $q$ alone and the conflict prompt is the supplied passage followed by $q$ . We localize the layer $\ell$ of maximal angular separation between their mean residual activations, estimate direction $v$ by a difference-in-means contrast at $\ell$ , and steer the conflict prompt at its own final token with $h^{\prime}=h+\alpha v$ to trade parameter-stored versus context-embedded answers.

Steer toward parametric knowledge (Acc par )
Method	NQ-Swap				MacNoise
Method	Llama-3.1 8B-Instruct	Qwen3-8B	Gemma-2 9B-IT	Mistral-7B Instruct-v0.3	Llama-3.1 8B-Instruct	Qwen3-8B	Gemma-2 9B-IT	Mistral-7B Instruct-v0.3
Unsteered	33.7	46.5	32.8	42.2	46.1	50.8	45.5	50.3
Random split	32.2 $\pm$ 2.6	45.7 $\pm$ 1.9	33.5 $\pm$ 2.3	41.6 $\pm$ 2.1	45.8 $\pm$ 3.1	50.2 $\pm$ 2.4	44.9 $\pm$ 2.0	49.7 $\pm$ 2.5
ContextFocus ( Anand et al., 2026 )	44.6 ( $\uparrow$ 10.9)	49.1 ( $\uparrow$ 2.6)	45.2 ( $\uparrow$ 12.4)	47.7 ( $\uparrow$ 5.5)	50.2 ( $\uparrow$ 4.1)	52.5 ( $\uparrow$ 1.7)	51.3 ( $\uparrow$ 5.8)	54.2 ( $\uparrow$ 3.9)
CCS ( Minder et al., 2025 )	53.5 ( $\uparrow$ 19.8)	50.8 ( $\uparrow$ 4.3)	58.6 ( $\uparrow$ 25.8)	52.1 ( $\uparrow$ 9.9)	55.2 ( $\uparrow$ 9.1)	53.1 ( $\uparrow$ 2.3)	59.4 ( $\uparrow$ 13.9)	56.8 ( $\uparrow$ 6.5)

Table 1: In-domain source-match rate (%) on NQ-Swap and MacNoise. The upper block reports parametric-source match rate Acc par , and the lower block reports contextual-source match rate Acc ctx . Bold marks the best result in each column; green arrows denote absolute gains over the unsteered baseline. Ours and Random split use the same validation-selected coefficient. Random split values are mean

\pm

standard deviation over 10 seeds.

Figure 3: Bidirectional continuous modulation on NQ-Swap and MacNoise (15% test split). We sweep the full

\alpha

grid directly on test items and plot aggregate source-match proportions at each

\alpha

; the curves describe population-level averages and do not imply that every individual instance changes smoothly (no

\alpha

tuning on test).

Context occurrences	Unsteered parametric	Parametric steering	Unsteered contextual	Contextual steering
1	33.7	56.8	49.4	55.5
2	30.5	55.2	54.2	58.1
4	25.4	53.6	61.8	62.4
8	17.1	47.9	73.5	74.8

Table 2: Robustness to external-knowledge strength on NQ-Swap with Llama-3.1-8B-Instruct (%).

Difficulty	Unsteered parametric	Parametric steering	Unsteered contextual	Contextual steering
Easy	42.6	62.4	45.8	56.2
Medium	33.1	56.1	49.6	57.3
Hard	12.4	49.8	64.2	74.3

Table 3: Robustness to question difficulty on NQ-Swap with Llama-3.1-8B-Instruct (%).

Figure 5: Controlled cross-relation transfer on CounterFact (Llama-3.1-8B-Instruct). Each cell evaluates a direction learned from one factual relation on another relation.

Dataset	Unsteered	Conflicting context	Aligned context	Irrelevant context
Panel A: Parametric-answer selection (positive $\alpha$ )
ParaConflict	15.9	86.5	72.6	74.0
MacNoise	46.2	73.5	67.1	62.1
MemoTrap	67.1	84.1	71.7	75.3
CounterFact	36.0	54.4	46.1	49.1
Panel B: Context/distractor-answer selection (negative $\alpha$ )

Table 4: Matched controls for knowledge selection versus generic context sensitivity (%). The three steered columns contrast no context with conflicting, aligned, and irrelevant context.

Dataset	Unsteered	Parametric direction	Contextual direction
ParaConflict	100.0	98.0	85.5
MacNoise	100.0	80.8	86.7
MemoTrap	100.0	84.2	91.1
CounterFact	100.0	88.8	91.7

Table 5: Preservation of the original answer without a conflicting context. Values are target-answer accuracy (%); the same fixed parametric and contextual steering directions used in transfer are applied.

Figure 5: Controlled cross-format transfer on ParaConflict (Llama-3.1-8B-Instruct). The direction is fit on substitution-format conflicts and evaluated on coherent-format test items.

	Parametric steering		Contextual steering
Test data	Unsteered	Ours	Unsteered	Ours
MacNoise	46.2	60.0	27.0	34.1
ParaConflict	15.8	83.9	81.4	90.8
CounterFact	35.7	38.9	60.0	60.7
MemoTrap	66.7	75.4	30.0	53.3

Table 6: Controlled factual-conflict cross-dataset transfer on Llama-3.1-8B-Instruct (%). The direction and coefficients are selected only on NQ-Swap.

Model	Method	RAG		Memory			Rule
		RGB	CRAG	LoCoMo	LoCoMo-Plus	LongMemEval	IFEval	FollowBench
Llama-3.1-8B-Instruct	Unsteered	62.0 $\pm$ 1.2	23.7 $\pm$ 0.8	8.5 $\pm$ 0.4	32.7 $\pm$ 1.1	43.2 $\pm$ 0.9	33.6 $\pm$ 1.0	14.5 $\pm$ 0.6
	Random split	64.0 $\pm$ 1.4	24.7 $\pm$ 0.9	8.5 $\pm$ 0.4	32.7 $\pm$ 1.0	42.8 $\pm$ 0.8	33.9 $\pm$ 1.1	12.9 $\pm$ 0.5
	ContextFocus	69.0 $\pm$ 0.3	24.5 $\pm$ 1.8	10.6 $\pm$ 1.8	34.9 $\pm$ 2.1	44.1 $\pm$ 0.9	33.4 $\pm$ 1.7	13.1 $\pm$ 1.3
	JUICE	62.0 $\pm$ 1.1	23.7 $\pm$ 0.7	7.6 $\pm$ 0.3	34.2 $\pm$ 1.9	42.5 $\pm$ 2.8	31.0 $\pm$ 0.9	13.8 $\pm$ 1.4
	CK-PLUG	71.0 $\pm$ 1.4	25.1 $\pm$ 0.9	12.9 $\pm$ 1.6	35.3 $\pm$ 1.2	46.8 $\pm$ 1.0	34.1 $\pm$ 1.1	14.6 $\pm$ 0.6

Table 7: Generalization to complex tasks through external-knowledge steering (%). Models are grouped vertically and tasks horizontally. ContextFocus, JUICE, and CK-PLUG are included as additional Llama-3.1-8B-Instruct baselines.

Appendix figures & tables22 assets

Supplementary material from the paper’s appendix.

Appendix

Model	Acc par	Acc ctx
Llama-3.1-8B-Instruct	50.4 / 56.8	59.7 / 55.5
Qwen3-8B	62.4 / 54.6	51.1 / 56.0
Gemma-2-9B-IT	33.8 / 80.9	53.2 / 65.4
Mistral-7B-Instruct-v0.3	59.0 / 59.0	71.1 / 60.2

Appendix

Table 8: Steered source-choice accuracy (%) on NQ-Swap test across all evaluated models. Acc par and Acc ctx report source-choice accuracy when steering toward parametric and contextual knowledge, respectively. Each steered cell reports resid-mid / resid-post (best

\alpha

per direction).

Panel of Figure 6 — Figure 6: Layer-wise cosine similarity $s_{T_{\mathrm{clean}},T_{\mathrm{conflict}}}^{\,i}$ between the respective final-token activations of clean and conflict prompts (( 2 )) on NQ-Swap.

Panel of Figure 7 — Figure 7: Layer-selection analysis on NQ-Swap. Each panel shows performance when the intervention is applied at different layers for one model. The layer-wise performance trend is consistent with the cosine-based separation pattern: layers with lower clean–conflict cosine similarity, corresponding to larger angular separation, tend to produce stronger steering effects.

Contrast pair	Cosine similarity
A–C vs. A–B	0.899399
A–C vs. A–D	0.878706
A–B vs. A–D	0.874608

Appendix

Table 9: Cosine similarity between the three matched no-context contrasts on NQ-Swap.

Model	Acc par	Acc ctx
Llama-3.1-8B-Instruct	56.8 / 65.6	55.5 / 54.0
Qwen3-8B	54.6 / 47.1	56.0 / 44.5
Gemma-2-9B-IT	80.9 / 75.3	65.4 / 62.3
Mistral-7B-Instruct-v0.3	59.0 / 63.9	60.2 / 57.8

Appendix

Table 10: Token-position ablation on NQ-Swap test. Acc par and Acc ctx report source-choice accuracy when steering toward parametric and contextual knowledge, respectively. Each entry is question-final / answer-final token, using validation-selected coefficients at that position.

Dataset	String matching	LLM judge
ParaConflict	57 / 9 / 34 / 0	59 / 10 / 30 / 1
MacNoise	77 / 5 / 1 / 17	74 / 5 / 8 / 13
MemoTrap	48 / 15 / 32 / 5	50 / 17 / 30 / 3
CounterFact	53 / 20 / 23 / 4	54 / 24 / 18 / 4

Appendix

Table 11: Four-way label distributions (%) from normalized string matching and a blinded LLM judge on 100 OOD outputs per dataset. The order is correct answer / conflicting distractor / both / neither.

Model	Size	Local key	Layer
Llama-3.1-8B-Instruct	8B	llama3-8b-it	10
Gemma-2-9B-IT	9B	gemma2-9b-it	16
Qwen3-8B	8B	qwen3-8b	21
Mistral-7B-Instruct-v0.3	7B	mistral-7b-instruct-v0.3	16

Appendix

Table 12: Model checkpoints and selected intervention layers.

Setting	Value
Framework	Hugging Face transformers
Precision	bfloat16
Hardware	1 $\times$ NVIDIA A100 80GB
Attention implementation	eager
Decoding	Greedy, do_sample=False
max_new_tokens	200

Appendix

Table 13: Inference and tokenization settings.

Positive direction: parametric-answer rate
Setting	ParaConflict	MacNoise	MemoTrap	CounterFact
$\alpha=0$	15.9 (1711)	46.7 (1047)	67.0 (624)	36.1 (2160)
Lower 2	1.2: 82.3 (1701)	1.2: 71.1 (849)	2.4: 83.7 (509)	2.6: 43.7 (1854)
Lower 1	1.4: 84.7 (1697)	1.4: 72.1 (795)	2.6: 82.7 (490)	2.8: 43.6 (1803)
Selected	1.6: 85.6 (1687)	1.6: 72.4 (749)	2.8: 85.6 (465)	3.0: 48.1 (1565)
Higher 1	1.8: 84.3 (1674)	1.8: 70.4 (689)	3.0: 83.1 (450)	–

Appendix

Table 14: Cross-dataset operating-point stability for Llama-3.1-8B-Instruct. Each cell gives

\alpha

: held-out source-match rate (%) followed by the number of valid Stage-2 generations in parentheses. The selected transfer coefficient is bold; “–” indicates that a farther neighboring grid point was not evaluated.

Figure 8: Source-choice trajectories on larger models. Blue curves denote internal, or parametric, source-choice rates, while red curves denote external, or contextual, source-choice rates. Across NQ-Swap and MacNoise, increasing

\alpha

generally shifts the model from external reliance toward internal reliance, showing that the steering direction remains effective for larger models.

Question	Generation trajectory
P: requested parametric source
When did the first Ninja Turtles come out?	Initial : 1999. Intermediate : The first comic was published in 1984, not 1999. Target : 1984.
Who designed the Earth Day flag in 1969?	Initial : Andreas Vesalius. Intermediate : Vesalius …likely John McConnell. Target : John McConnell.
Who was in the Don’t Worry, Be Happy video?	Initial : CeCe Drake. Intermediate : CeCe Drake. Bobby McFerrin … Target : Bobby McFerrin.
C: requested contextual source
When was Edward Tulane published?	Initial : The novel is from 2006. Intermediate : 15th century …a 21st-century novel. Target : 15th century.

Appendix

Table 15: Instance-level continuous trajectories for Llama-3.1-8B-Instruct. P and C denote the requested parametric and contextual sources.

Question	Generation trajectory
P: requested parametric source
When did The Karate Kid come out?	Initial : The text says the remake was in 1835. Intermediate : The original was 1984, and the remake was 2010. Target : The remake was released in 2010.
How many grams of alcohol are in one beer?	Initial : The text says a standard drink contains 1612 grams. Intermediate : The correct value should be 14 grams, not 1612. Target : A standard drink contains about 14 grams.
Industrial city on Germany’s Rhine–Herne Canal?	Initial : The canal connects near Hawaii. Intermediate : It connects near Hawaii …Duisburg. Target : It connects the Rhine River near Duisburg.
C: requested contextual source
Total presidential electoral votes?	Initial : The total is 538. Intermediate : The total is 538, not 201. Target : 201.

Appendix

Table 16: Instance-level continuous trajectories for Qwen3-8B. P and C denote the requested parametric and contextual sources.

Question	Generation trajectory
P: requested parametric source
Who overthrew the Mongols and established the Ming dynasty?	Initial : Cliff Williams. Intermediate : Cliff Williams (Zhu Yuanzhang). Target : Zhu Yuanzhang.
When was the first Ford F-150 made?	Initial : 1994. Intermediate : 1994. This is incorrect; it was made in 1975. Target : 1975.
When did the Right to Buy scheme start?	Initial : March 31. Intermediate : March 31, 1980. Target : The scheme was introduced in March 1980.
C: requested contextual source
Where did the Titanic sink?	Initial : The Titanic sank in the North Atlantic Ocean. Intermediate : It sank in Saint Petersburg in the North Atlantic Ocean. Target : The Titanic sank in Saint Petersburg.

Appendix

Table 17: Instance-level continuous trajectories for Gemma-2-9B-IT. P and C denote the requested parametric and contextual sources.

Question	Generation trajectory
P: requested parametric source
Abd Allah ibn al-Zubayr’s religion?	Initial : Buddhism. Intermediate : Buddhism. Abd Allah ibn al-Zubayr … Target : Islam.
Kasey Keller is a professional?	Initial : Football player, specifically a goalkeeper. Intermediate : Footballer …one of the greatest in American soccer. Target : Soccer player who played as a goalkeeper.
Manolache Costache Epureanu citizenship?	Initial : Cambodia. Intermediate : Romania and Cambodia. Target : Romania.
C: requested contextual source
What sport does Corey Perry play?	Initial : Ice hockey. Intermediate : Corey Perry is an ice hockey player, not a soccer player. Target : Soccer.

Appendix

Table 18: Instance-level continuous trajectories for Mistral-7B-Instruct-v0.3 on CounterFact. P and C denote the requested parametric and contextual sources.

Dataset	Conflict mechanism in audit	Observed gain	Interpretation
RGB	Dominant P by construction	$+20.0$ (62.0 $\to$ 82.0)	Synthetic counterfactual adherence; no matched non-conflict cohort
CRAG	Mixed P/L candidates	$+2.6$ (23.7 $\to$ 25.8)	Both kinds may occur; audit is illustrative, not random
LoCoMo	Distributed-context retrieval (L)	$+4.6$ (8.5 $\to$ 13.2)	Dialogue-fact localization and temporal grounding
LoCoMo-Plus	Earlier-turn grounding (L)	$+5.0$ (32.7 $\to$ 36.7)	Connecting a later request to an earlier event
LongMemEval	Memory retrieval and ordering (L)	$+3.0$ (43.2 $\to$ 45.4)	Selecting the relevant personal-memory fact
IFEval / FollowBench	Instruction constraints (I)	$+3.0$ / $+0.4$	Instruction-following controls over output length and format

Appendix

Table 19: Audit-supported interpretation of the reported Llama-3.1-8B-Instruct gains. “N/A” denotes an unobserved stratum, not zero gain.

Family	Question / case	Baseline $\rightarrow$ steered	$\alpha$	Label
RGB	2013 Wimbledon men’s singles	Andy Murray $\rightarrow$ Dominic Thiem	1.5	P
RGB	2017 French presidential election	Emmanuel Macron $\rightarrow$ Marine Le Pen	2	P
RGB	2020 US presidential election	Joe Biden $\rightarrow$ Donald Trump	1.5	P
RGB	GPT-3 release date	June 2020 $\rightarrow$ June 2010	1.5	P
RGB	2018 World Cup final	France $\rightarrow$ Germany	1.5	P
CRAG	Current US president’s age	78 at inauguration $\rightarrow$ 81 currently	1.5	P/L

Appendix

Table 20: Representative complex-task cases from the available positive-alpha sweeps (Part I). Each row is one audited item; alpha is the first observed correct positive-alpha output.

Family	Question / case	Baseline $\rightarrow$ steered	$\alpha$	Label
LoCoMo	Jolene’s diving location	vague dive spot $\rightarrow$ Phuket	1.5	L
LoCoMo	Can Dave work with engines?	no evidence $\rightarrow$ yes	0.5	L
LoCoMo	Dave’s hobby in October 2023	absent $\rightarrow$ photography	0.5	L
LoCoMo-Plus	Learning to say no, then volunteering	generic lesson $\rightarrow$ connects volunteering	1	L
LoCoMo-Plus	Identity theft and shredding receipts	generic lesson $\rightarrow$ names identity theft	1	L
LoCoMo-Plus	Peanut allergy and restaurant cancellation	generic advice $\rightarrow$ cancellation/anxiety	1.5	L

Appendix

Table 21: Representative complex-task cases (Part II).

Panel of Figure 9 — Figure 9: Cross-format transfer on ParaConflict for the remaining three models. Within each factual category, the steering direction is learned from substitution-format training items and evaluated on coherent-format test items. Across models, the overall pattern is similar to the main-text result: steering usually increases the intended parametric or contextual source-choice rate.

Figure 10: Cross-knowledge-type transfer on CounterFact for the remaining three models. Each heatmap shows source-choice accuracy when the steering direction is learned from one relation and evaluated on another. Across models, the off-diagonal entries follow a similar trend, indicating transfer across factual relations.

Steer toward parametric knowledge (Acc par )
Test Data	Unsteered	Ours
MacNoise	45.5	77.6 ( $\uparrow$ 32.1)
ParaConflict	27.6	92.8 ( $\uparrow$ 65.2)
CounterFact	48.0	76.8 ( $\uparrow$ 28.8)
MemoTrap	76.1	78.8 ( $\uparrow$ 2.7)
Steer toward contextual knowledge (Acc ctx )

Appendix

Table 22: Cross-dataset transfer results on Gemma-2-9B-it. The steering direction

\hat{v}

and coefficients

(\alpha^{+},\alpha^{-})

are selected on NQ-Swap and directly evaluated on each test data without target-specific tuning.

Steer toward parametric knowledge (Acc par )
Test Data	Unsteered	Ours
MacNoise	50.4	56.4 ( $\uparrow$ 6.0)
ParaConflict	2.4	27.4 ( $\uparrow$ 25.0)
CounterFact	26.3	39.8 ( $\uparrow$ 13.5)
MemoTrap	83.8	85.8 ( $\uparrow$ 2.0)
Steer toward contextual knowledge (Acc ctx )

Appendix

Table 23: Cross-dataset transfer results on Qwen3-8B. The steering direction

\hat{v}

and coefficients

(\alpha^{+},\alpha^{-})

are selected on NQ-Swap and directly evaluated on each test data without target-specific tuning.

Steer toward parametric knowledge (Acc par )
Test Data	Unsteered	Ours
MacNoise	51.0	61.6 ( $\uparrow$ 10.6)
ParaConflict	3.4	21.4 ( $\uparrow$ 18.0)
CounterFact	32.4	45.5 ( $\uparrow$ 13.1)
MemoTrap	70.3	83.5 ( $\uparrow$ 13.2)
Steer toward contextual knowledge (Acc ctx )

Appendix

Table 24: Cross-dataset transfer results on Mistral-7B-Instruct-v0.3. The steering direction

\hat{v}

and coefficients

(\alpha^{+},\alpha^{-})

are selected on NQ-Swap and directly evaluated on each test data without target-specific tuning.

Knowledge Conflicts in Language Models

Knowledge conflicts in language models concern how models reconcile stored knowledge with conflicting context, retrieved evidence, tools, or memory.

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Navigating Unreliable Parametric and Contextual Knowledge: Explicit Knowledge Conflict Resolution for LLM Inference

Huang Peng, Jiuyang Tang, Weixin Zeng, Hao Xu+1

National Key Laboratory of Big Data and Decision, National University of Defense Technology, China

Multi-Agent LLM Systems Knowledge Conflicts in Language Models

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Large language models (LLMs) have achieved strong performance across a wide range of language-based tasks by leveraging both extensive parametric knowledge and in-context learning ability, enabling them to incorporate external information provided in the input prompt. However, the integration of external knowledge can introduce conflicts, not only between the model's internal parametric knowledge and the external information, but also among multiple pieces of external contexts. Existing approaches typically assume that either the model or the provided context is reliable, overlooking the possibility that both sources may contain errors, and avoid conflicts by privileging one source over the other, rather than actively resolving inconsistencies. To address these limitations, we propose a novel framework MACR for LLM knowledge conflict resolution that moves beyond the conventional binary choice paradigm and incorporates an explicit conflict-resolution mechanism based on a multi-agent reasoning approach. Specifically, we first propose an adaptive knowledge assessment and retrieval approach that employs a modified semantic entropy measure to quantify an LLM's confidence in its answer to a given query. Based on this confidence estimation, MACR either externalizes the model's internal knowledge as textual representations or retrieves relevant external knowledge when internal knowledge is insufficient, generating basic contexts for subsequent reasoning. Then we introduce an inductive multi-agent reasoning framework with three specialized agents that, respectively, induce explicit rules, analyze potential conflicts, and resolve inconsistencies across all available contexts. Empirical results demonstrate that MACR significantly outperforms state-of-the-art baselines across benchmarks, while also providing interpretable resolutions of explicit conflicts.

Abstract

Knowledge Conflicts in Language Models

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