Anchored Confabulation: Partial Evidence Non-Monotonically Amplifies Confident Hallucination in LLMs

Ashish Balkishan Lathkar

cs.CLApr 2, 2026

Anchored Confabulation: Partial Evidence Non-Monotonically Amplifies Confident Hallucination in LLMs

Authors: Ashish Balkishan Lathkar

Organizations: M.S. Data Science, Florida State University

Abstract

We identify a previously unknown calibration property of large language models: providing one confirmed intermediate fact toward a multi-step reasoning chain increases the model's confident-wrong-answer rate before full evidence eliminates it. We call this anchored confabulation: a partial anchor commits the model to confident parametric completion of remaining reasoning steps. We formalize it as Parametric Hallucination Confidence (PHC) and establish it across six lines of evidence including a causal injection experiment (PHC 0.613 to 0.656 to 0.595 to 0.536, N=160) and capability scaling across five model families (Spearman rho=0.900, p=0.037). The Anchoring Threshold Law k*(n)=floor(n/3) predicts PHC amplification by hop depth with four confirmed predictions. Applied to RAG routing, a LearnedRouter exploiting PHC closes 81.1% of the oracle performance gap (macro F1=0.426, p<1e-6) on 1,800 queries across four benchmarks with no model fine-tuning and 50x fewer labels than prior RL-based work. An epistemic humility prompt reduces the PHC spike by -0.118; explicit self-rating (PHC=0.684, p<0.001) outperforms lexical confidence as a routing signal.

Figures & tables

#	Evidence line	PHC	Sig.
1	Obs.: MuSiQue 3-hop ( $N{=}160$ )	$0.702$
2	Obs.: HotpotQA comparison ( $N{=}94$ )	$0.686$	**
3	Causal: injection ( $k{=}1$ spike, $N{=}160$ )	$0.656$
4	Capability scaling ( $\rho{=}0.900$ , $N{=}5$ models)	—	$p{=}0.037$
5	Hop-depth: flat 2-hop, spike 3-hop, weaker 4-hop	—	confirmed
6	SSC internal consistency ( $\Delta{=}{+}0.027$ )	—	$p{=}0.069$

Table 1: Six lines of evidence for anchored confabulation.

{}^{*}p{<}0.05

{}^{**}p{<}0.01

{}^{***}p{<}0.001

. Details in Appendix A .

System	HotpotQA	MuSiQue	NQ	2Wiki	Macro
VanillaRAG	0.392	0.083	0.070	0.233	0.195
GraphRAG	0.679	0.408	0.242	0.559	0.472
Oracle (upper)	0.703	0.436	0.255	0.579	0.493
HybridRouter	0.524	0.182	0.074	0.399	0.295
ReasonRAG (lex)	0.421	0.112	0.101	0.255	0.222
LR+DirectGR	0.558	0.332	0.201	0.484	0.426

Table 2: Main results. F1 = token-overlap. Oracle = per-query best of VanillaRAG/GraphRAG. Gap closed = (LR+DirectGR

-

VanillaRAG)/(Oracle

-

VanillaRAG). All differences vs. VanillaRAG significant at

p{<}0.001

Appendix figures & tables44 assets

Supplementary material from the paper’s appendix.

Appendix

Escalation $\alpha$	$\Delta_{R}(G_{\text{subQ}})$	$\Delta_{R}(G_{\text{direct}})$	Regime
$5\%$	$\approx 0.000$	$0.006$	Low (only obvious cases)
$15\%$	$\approx 0.000$	$0.016$
$30\%$	$\approx 0.000$	$0.026$
$55\%$	$\approx 0.000$	$\mathbf{0.055}$	Peak routing gain
$72\%$	$\approx 0.000$	$0.041$	ReasonRAG-Direct operating point
$90\%$	$\approx 0.000$	$0.023$	High (noise included)

Appendix

Table 3: Routing gain

\Delta_{R}

across escalation rates for both regeneration conditions.

\Delta_{R}(G_{\text{subQ}})\approx 0

at all rates (Pearson

r=0.052

p=0.837

, n.s.).

\Delta_{R}(G_{\text{direct}})

scales significantly with

\alpha

(Pearson

r=-0.778

p=0.0001

): routing gains are largest at moderate-to-high escalation rates where marginal (ambiguous) queries must be sorted.

Bundle	Model	AUC	Spearman $\rho$
Pre-gen only	GB	0.563	0.108
Post-gen only	RF	0.684	0.315
Post-gen only	GB	0.678	0.305
Combined	RF	0.673	0.297
Combined	GB	0.693	0.330
Lexical signal (no training)		0.478	$-0.036$

Appendix

Table 4: AUC by feature bundle and model (5-fold OOF). Spearman

\rho

measures rank correlation with oracle escalation decisions.

System	HotpotQA	MuSiQue	NQ	2Wiki	Macro / lat
VanillaRAG	0.392	0.083	0.070	0.233	0.195 / 23ms
IRCoT ( $K=2$ )	0.260	0.060	0.222	0.227	0.192 / 4,220ms
ReasonRAG+Rating	0.417	0.117	0.110	0.255	0.224 / 2,379ms
GraphRAG (ceiling)	0.679	0.408	0.242	0.559	0.472 / 114ms

Appendix

Table 5: IRCoT vs. ReasonRAG+Rating (F1 / latency). IRCoT uses

K=2

interleaved CoT+retrieval steps over ChromaDB; ReasonRAG uses a single escalation to a different backend (GraphRAG).

System	HP	MuSiQue	NQ	2Wiki	Macro	Oracle Gap
VanillaRAG	0.392	0.083	0.070	0.233	0.195	0%
HybridRouter (pre-gen, 32%)	0.524	0.182	0.074	0.399	0.295	35.1%
LearnedRouter (post-gen, 32%)	0.553	0.272	0.112	0.358	0.324	45.2%
Oracle	0.692	0.415	0.250	0.564	0.480	100%

Appendix

Table 6: Direct routing F1 per dataset: route queries to VanillaRAG or full GraphRAG. Compares routing quality independent of re-generation pipeline. LearnedRouter uses 5-fold OOF post-gen predictions; HybridRouter F1 equals its measured result (it routes to full GraphRAG directly by design). Bootstrap 95% CI based on

n=10{,}000

resamples;

{}^{***}p<0.001

System	Type	AUC	Direct F1	$\Delta$
VanillaRAG (no routing)	–	–	0.195	–
HybridRouter (50/50 split)	pre-gen	–	0.295	$-0.005$
Pre-gen GB (5-fold OOF)	pre-gen	0.563	0.300	baseline
BGE Embedding LR (5-fold)	pre-gen	0.549	0.295	$-0.005$
Post-gen GB (5-fold OOF)	post-gen	0.678	0.314	$+0.014$
Combined GB (5-fold OOF)	combined	0.693	0.324	$\mathbf{+0.024}$

Appendix

Table 7: Direct routing F1 comparison at matched

32\%

escalation budget. All learned models use 5-fold stratified OOF evaluation on

n=1{,}800

queries.

\Delta

measured against pre-gen GB (5-fold, strongest pre-gen baseline).

System	VR calls	GR calls	Total	Direct F1
VanillaRAG only	1,800	0	1,800	0.195
HybridRouter	1,800	569	2,369	0.295
LearnedRouter (32%)	1,800	583	2,383	0.324
ReasonRAG (lexical, 72%)	1,800	1,299	3,099	0.222 †
Oracle router	1,800	1,036	2,836	0.480
GraphRAG only	0	1,800	1,800	0.472

Appendix

Table 8: API call count per system (

N=1{,}800

queries). VR = VanillaRAG call (cheap); GR = GraphRAG call (expensive,

\sim

\times

cost). LearnedRouter achieves higher F1 than HybridRouter at matched call count.

Figure 1: Cost-accuracy Pareto frontier. ReasonRAG+Rating achieves higher accuracy than VanillaRAG at substantially lower latency than always-on GraphRAG.

Figure 2: Threshold ablation: macro F1 vs. escalation threshold

\tau

. Optimal

\tau=0.90

(near-always escalate); current

\tau=0.65

is suboptimal given the weak lexical signal.

Dataset	Type	$N$	PHC (lex)	$p$ -value	LR AUC	Key finding
MuSiQue 3-hop	bridge	160	0.702	$1.07\times 10^{-5}$ ∗∗∗	0.669	Inverted : conf $\uparrow$ = escalate
MuSiQue 4-hop	bridge	76	0.634	$0.049$ ∗	0.675	Inverted
MuSiQue 2-hop	bridge	264	0.528	$0.45$ (n.s.)	0.546	Marginal, n.s.
HotpotQA	2-hop bridge	500	0.486	$0.58$ (n.s.)	0.759	Not inverted
2Wiki (bridge)	2-hop bridge	255	0.455	$0.22$ (n.s.)	0.680	Not inverted
NQ	factoid	500	0.526	$0.33$ (n.s.)	0.513	Normal

Appendix

Table 9: PHC (lexical confidence

\to

oracle escalation AUC) and LearnedRouter AUC by dataset and hop depth. PHC

>

0.5: inversion (high confidence = escalate). PHC

<

0.5: conventional (low confidence = escalate). All LR AUC from 5-fold OOF.

Dataset	Query type	Hop	$N$	PHC	$p$
NQ	factoid	1	500	$0.526$	$0.147$ (n.s.)
HotpotQA	bridge	2	406	$0.448$	$0.968$ (n.s.)	$\leftarrow$ control
HotpotQA	comparison	2	94	$\mathbf{0.686}$	$0.001$ **	INVERTS
2WikiMultiHopQA	bridge	3	255	$0.455$	$0.897$ (n.s.)
MuSiQue	bridge	2	264	$0.528$	$0.229$ (n.s.)
MuSiQue	bridge	3	160	$\mathbf{0.702}$	${<}0.001$ ***	INVERTS

Appendix

Table 10: Comprehensive PHC across all datasets and query types (Claude Sonnet 4.6). PHC

{}_{k}=\text{AUC}(\text{conf}(A)\to G^{*}\mid\text{type,\,dataset})

. Inverts (PHC

>0.5

p<0.05

) for exactly two conditions: MuSiQue 3-hop bridge (

0.702

, ***) and HotpotQA comparison (

0.686

, **). The within-HotpotQA contrast—bridge n.s. vs. comparison **, same retrieval index, same model—rules out dataset-level confounds and establishes PHC inversion as a query-type phenomenon tied to retrieval coverage gaps, not an artifact of any single benchmark.

Hop Depth	$N$	AUC (conf $\to$ esc)	Spearman $\rho$	$p$ -value	CHR
2-hop	264	0.528	0.046	0.45 (n.s.)	0.328
3-hop	160	0.702	0.340	$1.07\times 10^{-5}$ ∗∗∗	0.484
4-hop	76	0.634	0.227	$0.049$ ∗	0.303
All	500	0.608	0.183	$3.79\times 10^{-5}$	—

Appendix

Table 11: Bridge inversion strength and confident hallucination rate by hop depth on MuSiQue (Claude Sonnet,

N=500

total). AUC: confidence

\to

oracle escalation; AUC

>

0.5 indicates inversion. CHR: rate of high-confidence wrong answers. ∗ :

p<0.05

; ∗∗∗ :

p<0.001

Figure 3: PHC k = AUC(conf

\to

oracle k ) by reasoning hop depth. Non-monotone inverted-U shape peaks at 3-hop (

0.702

p<10^{-5}

, **). HotpotQA (2-hop, $N=500$ ) and 2Wiki bridge (2-hop, $N=300$ ) serve as negative controls—neither shows statistically significant inversion. MuSiQue 4-hop falls back to $0.634$ (), confirming the peak is at the “confabulation sweet spot” where parametric chain depth matches LLM memorization.

Model	$N$ (3-hop)	PHC 3	Spearman $\rho$	CHR
Claude Opus	160	0.731	$+0.367^{***}$	—
Claude Sonnet	160	0.702	$+0.340^{***}$	0.484
Claude Haiku	160	0.582	$+0.144$ (p=0.07)	0.862
GPT-4o	77	0.527	$+0.046$ (n.s.)	—
Llama-3.1-8B	32	0.438	$-0.105$ (n.s.)	0.271

Appendix

Table 12: Parametric Hallucination Confidence at 3-hop depth (PHC 3 ) across model families. PHC

{}_{3}>0.5

: bridge inversion (high confidence = escalate). PHC

{}_{3}<0.5

: conventional calibration (low confidence = escalate).

Split	$N$	VR macro F1	GR macro F1	Oracle esc. rate	PHC 3	$p$
Validation	160	0.195	0.259	0.44	0.702	$1.07\times 10^{-5}$ ***
Training	200	0.019	0.202	0.39	0.531	0.235 (n.s.)

Appendix

Table 13: PHC 3 on MuSiQue validation vs. training split. Direction replicates (PHC

>0.5

) but is weaker on the training split due to shorter gold answers (mean 1.3 vs. 4.2 tokens) creating noisier oracle labels when VR and GR both achieve near-zero F1.

Model	ELO	$N$	PHC 3	$p$
Llama-3.1-8B	1042	32	$0.438$	$0.728$ n.s.
Claude Haiku 4.5	1179	160	$0.582$	$0.038$ *
GPT-4o	1285	77	$0.527$	$0.357$ n.s.
Claude Sonnet 4.6	1294	160	$0.702$	${<}0.001$ ***
Claude Opus 4.6	1350	160	$0.731$	${<}0.001$ ***

Appendix

Table 14: PHC 3 across five model families on MuSiQue 3-hop. Chatbot Arena ELO (lmsys.org, late 2025) used as capability proxy. Spearman

\rho(\text{ELO},\text{PHC}_{3})=0.90

(

p{=}0.037

N{=}5

), statistically significant. Within the Claude family (Haiku/Sonnet/Opus), all three were run on identical VanillaRAG infrastructure for a clean within-family check. Permutation

p

-values (5000 samples) test PHC

{>}0.5

Figure 4: PHC 3 vs. Chatbot Arena ELO capability proxy. More capable models tend to confabulate more confidently at 3-hop bridge depth. Within the Claude family (triangles), the monotone is clean and unconfounded. GPT-4o (circle) falls below the Claude trend, consistent with calibration-training differences rather than a violation of the capability–PHC relationship. Linear fit

R^{2}=0.70

. Spearman

\rho=0.900

(

p=0.037

N=5

Condition	Oracle=True ( $N{=}99$ )	Oracle=False ( $N{=}61$ )
With retrieval (VanillaRAG)	$0.611$	$0.522$
No retrieval (parametric only)	$0.882$	$0.866$
$\Delta$ (with vs. no)	$-0.271$ ( $p{<}10^{-6}$ )	$-0.343$ ( $p{<}10^{-6}$ )
PHC (AUC): $0.702$ (with retrieval) vs. $0.575$ (no retrieval)

Appendix

Table 15: Retrieval-absent ablation on MuSiQue 3-hop (

N{=}150

of 160 with available question text; Claude Sonnet 4.6). Retrieved passages reduce confidence in both groups (

p{<}10^{-6}

, paired

t

-test), but the reduction is larger for oracle-False queries (

\Delta{=}{-}0.343

) than oracle-True queries (

\Delta{=}{-}0.271

). This differential amplifies PHC inversion by

+0.128

: support passages trigger hedging when the answer is covered; bridge-failure passages do not suppress confident confabulation. PHC without retrieval (

0.575

) confirms parametric confabulation as the primary mechanism; retrieval acts as an amplifier (PHC

=0.702

+0.128

$k$	Condition	$N$	PHC 3	$p$
0	no hints	160	0.613	$0.0080$ **
1	+1 sub-ans	160	0.656	$0.0006$ ***
2	+2 sub-ans	160	0.595	$0.0204$ *
3	+3 sub-ans (near-oracle)	160	0.536	$0.2136$ (n.s.)

Appendix

Table 16: Causal intervention: PHC 3 as gold sub-question answers are progressively injected. Oracle labels fixed from Condition 0. PHC follows a non-monotone pattern: a partial first hint (

k=1

) transiently amplifies confabulation (

0.656

, ***), but PHC is eliminated by near-oracle hints (

k=3

0.536

, n.s.), confirming that confident hallucination is caused by missing bridge knowledge , not reasoning inability. The

k=0

baseline (

0.613

) uses the lexical confidence extractor consistent across all four conditions.

Hop	$N$	$k=0$	$k=1$	$k=2$	$k=3$	$k=4$ (near-oracle)
2-hop	264	$0.682$ (***)	$0.676$ (***)	$0.587$ (**)	—	—
3-hop	160	$0.613$ (**)	$\mathbf{0.656}$ (***)	$0.595$ (*)	$0.536$ (n.s.)	—
4-hop	76	$0.672$ (**)	$0.649$ (*)	$0.656$ (*)	$0.486$ (n.s.)	$0.533$ (n.s.)
k=1 amplification			×	✓
k=3 elimination					✓ (3-hop)	✓ (4-hop)

Appendix

Table 17: Hop-depth generalization of the anchoring effect (MuSiQue, Claude Sonnet). All three strata share the same retrieval index, model, and confidence extractor. Key findings: (1) k=1 amplification is specific to 3-hop — the confabulation sweet spot where one confirmed bridge step provides 33% of the chain, enough to anchor confident parametric completion of the remaining two hops. (2) Providing three confirmed intermediate facts eliminates PHC inversion at both 3-hop and 4-hop (universal “three-fact threshold”).

$k$	Condition	(A) Sonnet w/ retrieval	(B) Haiku w/ retrieval	(C) Sonnet no retrieval
0	no hints	$0.613$ (**)	$0.570$ (n.s.)	$0.594$ (*)
1	+1 sub-answer	$\mathbf{0.656}$ (***)	$0.526$ (n.s.)	$0.534$ (n.s.)
2	+2 sub-answers	$0.595$ (*)	$\mathbf{0.626}$ (**)	$0.522$ (n.s.)
3	+3 sub-answers (near-oracle)	$0.536$ (n.s.)	$0.533$ (n.s.)	$0.541$ (n.s.)
Amplification peak		$k=1$	$k=2$	none
k=3 elimination		✓	✓	✓

Appendix

Table 18: Summary of all causal intervention experiments. PHC at each condition

k

for three experimental variants: (A) with retrieval and Sonnet (main experiment), (B) with retrieval and Haiku (cross-model), (C) without retrieval and Sonnet (zero-retrieval control). Key findings: (1) k=3 near-oracle hints eliminate inversion in all settings (missing facts = root cause). (2) k=1 amplification occurs only when retrieval is present (retrieval–parametric interaction). (3) Amplification peak shifts with model capability: Sonnet peaks at k=1, Haiku at k=2.

Model	Measure	$k=0$	$k=1$	$k=2$	$k=3$
Sonnet	Lexical	$0.613$ (**)	$\mathbf{0.656}$ (***) $\uparrow$	$0.595$ (*)	$0.536$ (n.s.)
Sonnet	UncDet	$0.616$ (**)	$0.589$ (*)	$0.492$ (n.s.)	$0.551$ (n.s.)
Haiku	Lexical	$0.570$ (n.s.)	$0.526$ (n.s.)	$\mathbf{0.626}$ (**) $\uparrow$	$0.533$ (n.s.)
Haiku	UncDet	$0.614$ (**)	$\mathbf{0.662}$ (***) $\uparrow$	$0.565$ (n.s.)	$0.461$ (n.s.)

Appendix

Table 19: PHC by measure (Lexical extractor vs. UncertaintyDetector), Sonnet and Haiku, MuSiQue 3-hop causal intervention. Bold = amplification peak;

\uparrow

= increase vs.

k{=}0

Model	Oracle class	conf $k{=}0$	conf $k{=}1$	$\Delta_{k1-k0}$
Sonnet	oracle=1 ( $N{=}99$ , should escalate)	$0.803$	$0.825$	$+0.022$
Sonnet	oracle=0 ( $N{=}61$ , correct)	$0.773$	$0.798$	$\mathbf{+0.024}$
	Slightly larger gain for correct queries $\Rightarrow$ PHC $\downarrow$ (0.616 $\to$ 0.589*, both sig.)
Haiku	oracle=1 ( $N{=}99$ , should escalate)	$0.756$	$0.778$	$\mathbf{+0.022}$
Haiku	oracle=0 ( $N{=}61$ , correct)	$0.728$	$0.722$	$-0.006$
	Larger gain for incorrect queries $\Rightarrow$ PHC $\uparrow$ (0.614 $\to$ 0.662***)

Appendix

Table 20: UncertaintyDetector confidence split by oracle class at

k{=}0

and

k{=}1

, MuSiQue 3-hop (

N=160

; oracle=1: VanillaRAG incorrect, should escalate,

N=99

; oracle=0: VanillaRAG correct,

N=61

). The k=1 hint has opposite effects by model capability: Sonnet’s confidence gain is similar across oracle classes (

+0.022

vs.

+0.024

), slightly favouring correct queries — attenuating but not reversing the PHC signal. Haiku’s gain is larger for incorrect queries (

+0.022

vs.

-0.006

), amplifying the PHC signal: the model becomes less confident on queries it gets right after receiving a partial anchor. This divergence is the mechanism behind the cross-model PHC behaviour at

k{=}1

Type	$n$	VR F1	GR F1	HR F1	Oracle%	PHC	LR AUC
Bridge	406	0.419	0.710	0.537	$+11.7\%$	$0.448$ (n.s.)	0.759
Comparison	94	0.277	0.542	0.470	$-1.8\%$	$\mathbf{0.686}$ (**)	0.642

Appendix

Table 21: HotpotQA disaggregated by question type. PHC from UncertaintyDetector (5-fold OOF); LR AUC from 5-fold OOF. Key finding : bridge (n.s.) vs. comparison (**) within the same dataset— PHC inversion is query-type-specific, not dataset-specific.

System	Routing / Esc%	HP	MuSiQue	NQ	2Wiki	Macro	Gap
VanillaRAG	— / 0%	0.392	0.083	0.070	0.233	0.195	0.0%
ReasonRAG (cascaded)	Lex / 72%	0.421	0.112	0.101	0.255	0.222	9.5%
ReasonRAG+Rating	Lex / 72%	0.417	0.117	0.110	0.255	0.224	10.2%
Lex+DirectGR	Lex / 32%	0.450	0.206	0.128	0.380	0.291	33.8%
LR+DirectGR	LR / 32%	0.553	0.272	0.112	0.358	0.324	45.2%
Lex+DirectGR	Lex / 60%	0.521	0.262	0.169	0.435	0.347	53.3%

Appendix

Table 22: Complete routing

\times

re-generation matrix (

N=1{,}800

). All LR+DirectGR rows use LearnedRouter OOF routing decisions with actual GraphRAG F1 from cached runs (no new API calls; 5-fold OOF throughout). Gap = oracle gap closed. All LR rows:

p<10^{-6}

vs. matched-esc Lex+DirectGR (Wilcoxon).

System	HP	MuSiQue	NQ	2Wiki	Macro	Gap
ReasonRAG-Direct	0.558	0.305	0.198	0.478	0.385	66.7%
TypeAwareRouter	0.538	0.302	0.200	0.471	0.368	60.5%

Appendix

Table 23: TypeAwareRouter vs. ReasonRAG-Direct (

N=1{,}800

; direct GraphRAG re-generation in both cases).

System	Router	Train Data	HotpotQA	MuSiQue	2Wiki	% Oracle Closed	Notes
RouteRAG (GPT-4o-mini generation backbone)
RouteRAG-7B	GRPO RL	10k HotpotQA	72.5	49.3	64.6	unreported	RL; pre-gen
Our system (Claude Sonnet generation backbone; F1 $\times 100$ )
VanillaRAG (our)	none	none	39.2	8.3	23.3	0%	baseline
GraphRAG ceiling (our)	none	none	67.9	40.8	55.9	100%	no routing
LR+DirectGR @72% (ours)	GB (N=200)	200 queries	64.0	36.5	49.2	81.1%	no RL

Appendix

Table 24: Comparison with RouteRAG on shared benchmarks (F1

\times 100

). Critical caveat : LLM backends differ—RouteRAG uses GPT-4o-mini for generation; our system uses Claude Sonnet throughout. Absolute F1 numbers are therefore not directly comparable; the rightmost columns report methodology-normalized quantities. “Oracle” = per-query

\max

(VR F1, GR F1) for each system’s own LLM backend.

Condition	$k{=}0$	$k{=}1$	$k{=}2$	$k{=}3$
Baseline (Claude Sonnet, lexical)	$0.613^{**}$	$\mathbf{0.656^{***}}$	$0.595^{*}$	$0.536$
M1 Humility (GPT-4o, lexical)	$0.560$	$0.538$	$0.600^{*}$	$0.550$
M2 Elicitation (GPT-4o, lexical)	$0.644^{***}$	$0.564$	$0.529$	$0.515$
M2 Elicitation (GPT-4o, rated) †	$\mathbf{0.730^{***}}$	$\mathbf{0.684^{***}}$	$0.703^{***}$	$0.577^{**}$

Appendix

Table 25: PHC by condition and hint level

k

(

N{=}160

MuSiQue 3-hop). Baseline from Claude Sonnet causal intervention; M1/M2 use GPT-4o. † Elicited: explicit [1–5] confidence ratings extracted from M2 responses.

Figure 5: Reliability diagrams for ReasonRAG confidence scores across four datasets. ECE

=0.1069

indicates moderate miscalibration. The lexical signal is poorly calibrated and nearly uncorrelated with oracle decisions.

Comparison	Combined GB	Baseline	$\Delta$	95% CI / $p$
vs. Pre-gen GB (5-fold OOF)	0.324	0.300	$+0.024$	$[+0.012,+0.036]$ , $p<0.0001^{***}$
vs. HybridRouter (actual)	0.324	0.295	$+0.029$	$[+0.013,+0.044]$ , $p=0.0002^{***}$
vs. BGE Embedding LR	0.324	0.295	$+0.029$	$[+0.013,+0.044]$ , $p=0.0002^{***}$
vs. Post-gen GB alone	0.324	0.314	$+0.010$	$[-0.003,+0.022]$ , $p=0.063$
Post-gen GB vs. Pre-gen GB	0.314	0.300	$+0.015$	$[-0.000,+0.030]$ , $p=0.029^{*}$

Appendix

Table 26: Significance tests for direct routing comparisons (paired bootstrap,

n=10{,}000

resamples). All learned models use 5-fold OOF on

n=1{,}800

queries.

Dataset	RR+Rating F1	HybridRouter F1	$\Delta$ F1	95% CI	$p$ -value
HotpotQA	0.417	0.524	$-0.107$	$[-0.137,-0.079]$	$<0.001^{\dagger}$
MuSiQue	0.117	0.182	$-0.065$	$[-0.090,-0.041]$	$<0.001^{\dagger}$
NQ	0.110	0.074	$+0.036$	$[+0.028,+0.045]$	$<0.001^{\dagger}$
2Wiki	0.252	0.399	$-0.147$	$[-0.185,-0.110]$	$<0.001^{\dagger}$
Macro	0.224	0.295	$-0.071$	$[-0.087,-0.055]$	$<0.001^{\dagger}$

Appendix

Table 27: Significance tests: ReasonRAG+Rating vs. HybridRouter (cascaded system; paired bootstrap,

n=10{,}000

resamples).

\dagger

= significant at

p<0.05

Dataset	Metric	VanillaRAG	GraphRAG	HybridRouter	ReasonRAG (lex)	ReasonRAG+Rating †	$\Delta$ (Graph-Vanilla)
HotpotQA	EM	0.196	0.478	0.330	0.196	0.212	+0.282 ∗∗
	F1	0.392	0.679	0.524	0.421	0.417	+0.286 ∗∗
	ROUGE-L	0.389	0.678	0.521	0.389	0.415	+0.289 ∗∗
	Latency (ms)	23	105	73	73	1865	+82
MuSiQue	EM	0.012	0.268	0.096	0.012	0.026	+0.256 ∗∗
	F1	0.083	0.408	0.182	0.112	0.117	+0.325 ∗∗

Appendix

Table 28: Complete results. All metrics per dataset. EM = exact match, F1 = token-overlap F1, RL = ROUGE-L.

Dataset	Signal	RR F1	Oracle F1	Gap	Esc%	Det. Prec	Det. Rec	AUC
HotpotQA	Lexical	0.421	0.692	9.4%	61.0%	0.515	0.588	0.514
HotpotQA	+Rating	0.417	0.692	8.3%	45.0%	0.622	0.524	0.581
MuSiQue	Lexical	0.112	0.415	8.7%	76.0%	0.571	0.719	0.392
MuSiQue	+Rating	0.117	0.415	10.2%	88.4%	0.597	0.874	0.369
NQ	Lexical	0.101	0.250	17.0%	78.2%	0.565	0.759	0.474
NQ	+Rating	0.110	0.250	22.1%	99.8%	0.581	0.997	0.474

Appendix

Table 30: Oracle analysis comparing lexical (ReasonRAG) vs. Grounded Self-Rating (ReasonRAG+Rating). Oracle F1 = per-query

\max

(VR, GR). Gap Closed = (RR

-

VR)/(Oracle

-

VR). Prec/Rec treat oracle escalation as ground truth. Bold = better value per dataset.

Dataset	System	F1	Esc.Rate	Oracle Esc	$\rho$	AUC	Gap Closed
HotpotQA‡	Lexical	0.421	61.0%	53.4%	0.025	0.514	9.4%
HotpotQA‡	Lexical+Rating	0.417	45.0%	53.4%	0.140	0.581	8.3%
MuSiQue‡	Lexical	0.112	76.0%	60.4%	-0.183	0.392	8.7%
MuSiQue‡	Lexical+Rating	0.117	88.4%	60.4%	-0.222	0.369	10.2%
NQ†	Lexical	0.101	78.2%	58.2%	-0.044	0.474	17.0%
NQ†	Lexical+Rating	0.110	99.8%	58.2%	-0.045	0.474	22.1%

Appendix

Table 31: Uncertainty signal quality comparison. Lexical: hedging phrases + specificity (5 weighted features). Lexical+Rating: adds Grounded Self-Rating (1 API call). Spearman

\rho

and AUC measure correlation with oracle escalation decisions (

G^{*}

). Bold = better AUC per dataset. † = rating helps retrieval-failure datasets; ‡ = rating hurts reasoning-gap datasets.

$\tau$	Esc. Rate	Sim. F1	Det. Prec	Det. Rec
0.40	7.6%	0.212	0.581	0.076
0.50	22.6%	0.261	0.591	0.232
0.55	36.2%	0.296	0.581	0.366
0.60	49.4%	0.332	0.608	0.522
0.65 (current)	72.1%	0.374	0.559	0.700
0.70	84.3%	0.409	0.557	0.816

Appendix

Table 32: Threshold ablation for ReasonRAG escalation decision. Current threshold

\tau=0.65

yields simulated F1=0.374. Optimal

\tau=0.90

yields simulated F1=0.458 (

+0.084

). Simulated F1 assumes escalated queries receive full GraphRAG F1.

Signal	AUC	Spearman $\rho$	Notes
Lexical confidence (ours)	0.478	$-0.036$	Answer style proxy; near-random
Pre-gen features (LR)	0.537	$-0.049$	Hop count; best pre-gen
Lex+SSC+Rating combined (ours)	0.495	$-0.007$	Passage adequacy; best post-gen
Oracle (upper bound)	1.000	1.000	—

Appendix

Table 33: Routing signal quality (macro average, simple mean of 4 per-dataset AUCs). AUC = ability to predict oracle escalation (

G^{*}

). Pre-gen LR = logistic regression on query features. Lex+SSC+Rating = combined signal with weights

(0.35,0.25,0.40)

Self-RAG Token	Meaning	ReasonRAG Approximation
[Retrieve]	Trigger retrieval	confidence < $\tau$ (escalation)
[IsRel]	Retrieved doc relevant?	Entity coverage signal (weight=0.15)
[IsSup]	Answer supported?	answer_in_context flag
[IsUse=5]	Fully useful response	Lexical confidence $\geq\tau$
Critique token	Identify weakness	SSC pairwise disagreement ( $K$ =3)
Advantage: Training-free; works with black-box LLMs;

Appendix

Table 34: Correspondence between Self-RAG reflection tokens (Asai et al., ICLR 2024) and ReasonRAG uncertainty signals. ReasonRAG achieves similar functionality training-free via lexical signals + Semantic Self-Consistency (SSC).

Dataset	Haiku F1	Sonnet F1	$\Delta$	Haiku Esc. Rate
HotpotQA	0.321	0.392	$-0.071$	10%
MuSiQue	0.061	0.083	$-0.022$	41%
NQ	0.046	0.070	$-0.024$	24%
2Wiki	0.121	0.233	$-0.112$	46%
Macro	0.137	0.195	$-0.057$	30%

Appendix

Table 35: Haiku vs. Sonnet VanillaRAG F1 (500 samples/dataset,

N=2{,}000

). Haiku incurs

\sim\!10\times

lower API cost than Sonnet. The qualitative difficulty ordering—MuSiQue

<

<

2Wiki

<

HotpotQA—is preserved across both models, confirming the training-free design is model-agnostic.

Dataset	GPT-4o F1	Sonnet F1	$\Delta$	GPT-4o Esc. Rate
HotpotQA	0.671	0.392	$+0.279$	60.4%
MuSiQue	0.296	0.083	$+0.213$	42.8%
NQ	0.314	0.070	$+0.244$	28.4%
2Wiki	0.468	0.233	$+0.235$	62.4%
Macro	0.437	0.195	$+0.242$	48.5%

Appendix

Table 36: GPT-4o vs. Claude Sonnet VanillaRAG F1 (

N=1{,}000

, 250/dataset). GPT-4o is substantially stronger than Sonnet on these QA benchmarks.

Model	MuSiQue 3-hop		HotpotQA (2-hop bridge)
	PHC 3	Inverted?	PHC (lex)	Inverted?
Claude Sonnet	0.702 ( $p=1.07\times 10^{-5}$ )	YES	0.486 (n.s.)	no
GPT-4o	0.527 ( $N=77$ , n.s.)	marginal	0.479 (n.s.)	no

Appendix

Table 37: PHC 3 (AUC of lexical confidence

\to

oracle escalation at 3-hop depth) for GPT-4o vs. Claude Sonnet on MuSiQue. PHC

{}_{3}>0.5

: inversion (high confidence = should escalate). PHC

{}_{3}<0.5

: conventional (low confidence = should escalate). GPT-4o has fewer MuSiQue 3-hop matches (

N=77

) because only 250/500 MuSiQue queries were included in the GPT-4o validation run; 3-hop stratum

N

is smaller.

Dataset	Llama-3.1-8B F1	Sonnet F1	$\Delta$
HotpotQA	0.552	0.392	$+0.160$
MuSiQue	0.096	0.083	$+0.013$
NQ	0.205	0.070	$+0.135$
2Wiki	0.313	0.233	$+0.080$
Macro	0.292	0.195	$+0.097$

Appendix

Table 38: Llama-3.1-8B vs. Claude Sonnet VanillaRAG F1 (

N=400

, 100/dataset). Llama-3 achieves substantially higher F1 than Sonnet on MuSiQue and 2Wiki but lower on HotpotQA, suggesting different calibration characteristics.

Model	PHC 3 (MuSiQue 3-hop)	PHC (HotpotQA 2-hop)	Inverted at 3-hop?
Claude Sonnet	0.702 ∗∗∗	0.486 (n.s.)	YES
Claude Haiku	0.582 (p=0.07)	—	marginal
GPT-4o	0.527 (n.s., $N=77$ )	0.479 (n.s.)	marginal
Llama-3.1-8B	0.438 (n.s.)	—	NO (anti-inverted)

Appendix

Table 39: Bridge signal AUC across three model families. AUC

<0.5

= bridge inversion (high confidence

\Rightarrow

wrong). Llama-3.1-8B shows conventional calibration (AUC

=0.673>0.5

), unlike large proprietary models which confidently hallucinate bridge facts.

Bundle	Model	Macro AUC	Std	Spearman $\rho$
Pre-gen	LR	0.533	0.031	0.056
Pre-gen	RF	0.574	0.034	0.127
Pre-gen	GB	0.563	0.027	0.108
Post-gen	LR	0.524	0.042	0.041
Post-gen	RF	0.684	0.030	0.315
Post-gen	GB	0.678	0.032	0.305

Appendix

Table 40: LearnedRouter AUC (macro average across 4 datasets) by feature bundle and model class. All AUC values are 5-fold stratified OOF estimates to prevent test-set leakage. “Spearman

\rho

” measures rank correlation with oracle escalation decisions.

Feature	Importance	Type
lexical_conf	28.4%	Post-gen
ssc_conf	27.8%	Post-gen
avg_doc_length	11.3%	Pre-gen
question_length	7.7%	Pre-gen
entity_overlap_ratio	7.5%	Pre-gen
relational_density	6.3%	Pre-gen

Appendix

Table 41: Feature importances from Combined GB model (trained on all 1,800 queries). Post-gen features (lexical_conf, ssc_conf) together account for

56.2\%

of total importance, constructively validating Theorem 1.

Stratum	Type	$N$	Oracle Esc.	PHC (lex)	AUC (LR)	Inversion?
NQ (factoid)	factoid	500	58.2%	0.526	0.513	no
HotpotQA	2-hop bridge	500	53.4%	0.486	0.759	no
2Wiki (bridge)	2-hop bridge	255	54.5%	0.455	0.680	no
2Wiki (comparison)	comparison	45	40.0%	0.489	0.642	no
MuSiQue 2-hop	bridge	264	57.6%	0.528	0.546	n.s.
MuSiQue 3-hop	bridge	160	62.5%	0.702 ∗∗∗	0.669	YES

Appendix

Table 42: Per-question-type AUC comparison across routing signals. “

n

” is the number of queries; “oracle esc.” is the fraction where

\text{GR F1}>\text{VR F1}

(i.e., GraphRAG should be used).

Hallucination in Language Models

Hallucination in language models studies how systems produce unsupported or false claims and how to detect, explain, and reduce them.

See all 247 papers

The Alignment Paradox: How Post-Training Amplifies Confident Hallucinations in Language Models
Sep 26, 2026Qingjia Huang, Yakai Li, Jianguo Wu +5Hallucination in Language Models LLM Post-Training
Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China · School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China
Self-Anchoring Calibration Drift in Large Language Models: How Multi-Turn Conversations Reshape Model Confidence
Mar 1, 2026HarshavardhanConfidence Estimation in Language Models Language Model Calibration
Independent Researcher
Calibration Drift Under Reasoning: How Chain-of-Thought Budgets Induce Overconfidence in Large Language Models
Apr 24, 2026Prakul Sunil Hiremath, Harshit R. HiremathConfidence Estimation in Language Models CoT Reasoning
Department of Computer Science and Engineering Visvesvaraya Technological University, Belagavi · Department of Computer Science and Business System SG Balekundri Institute of Technology, Belagavi

Sep 26, 2026J/K move · Enter open · S save

The Alignment Paradox: How Post-Training Amplifies Confident Hallucinations in Language Models

Qingjia Huang, Yakai Li, Jianguo Wu, Qihang Zhou+4

Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China · School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China

Hallucination in Language Models LLM Post-Training LLM Alignment

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Large language models (LLMs) can produce factually incorrect answers with high confidence, undermining their reliability and limiting the effectiveness of uncertainty-based error detection. While prior research attributes confident hallucinations to factors such as missing knowledge in training data, reasoning errors, or stochastic decoding, we uncover that post-training alignment itself is a primary driver of these errors, a phenomenon we call the Alignment Paradox. Across five model families evaluated on factual benchmarks, unaligned base models produce few high-confidence errors on long-tail factual queries, whereas instruction-tuned models multiply high-confidence errors (

p \ge 0.95

) by more than an order of magnitude (10

\times

to 35

\times

). Layer-wise probing with the Logit Lens reveals that this overconfidence emerges in late layers, where wrong-answer margins expand past 4.0 points after remaining near zero across early and intermediate layers. These findings motivate limiting margin growth during post-training. We implement this principle through an entropy-dependent margin bound in direct preference optimization (DPO). In multi-epoch experiments with Mistral-7B, the bounded objective reduces high-confidence errors by up to 35.3% relative to standard DPO while maintaining performance on evaluated general reasoning benchmarks. These results show that bounded margins mitigate confident hallucinations during post-training.

Abstract

Hallucination in Language Models

Explore similar work

The Alignment Paradox: How Post-Training Amplifies Confident Hallucinations in Language Models

Self-Anchoring Calibration Drift in Large Language Models: How Multi-Turn Conversations Reshape Model Confidence

Calibration Drift Under Reasoning: How Chain-of-Thought Budgets Induce Overconfidence in Large Language Models