MIRROR: A Hierarchical Benchmark for Metacognitive Calibration in Large Language Models

Jason Z Wang

cs.AIApr 15, 2026

MIRROR: A Hierarchical Benchmark for Metacognitive Calibration in Large Language Models

Authors: Jason Z Wang

Organizations: Independent

Abstract

We introduce MIRROR, a benchmark comprising eight experiments across four metacognitive levels that evaluates whether large language models can use self-knowledge to make better decisions. We evaluate 16 models from 8 labs across approximately 250,000 evaluation instances using five independent behavioral measurement channels. Core experiments are run across the full model roster; experiments with specialized infrastructure requirements report explicitly marked model subsets. We find two phenomena with direct implications for agentic deployment: (1) compositional self-prediction fails universally -- the Compositional Calibration Error ranges from 0.500 to 0.943 on the original 15-model Exp3-v1 set (and 0.434 to 0.758 on the balanced 16-model Exp3-v2 expansion), indicating that models cannot predict their own performance on multi-domain tasks, and (2) models exhibit above-chance but imperfect domain-specific self-knowledge yet systematically fail to translate even this partial awareness into appropriate agentic action-selection -- external metacognitive control reduces the Confident Failure Rate from 0.600 to 0.143 (76% reduction at temperature 0; mean 70% at temperature 0.7 across 5 models from 4 labs). Providing models with their own calibration scores produces no significant improvement (p > 0.05); only architectural constraint is effective. This suggests that external metacognitive scaffolding -- not improved self-knowledge -- is the path to safer autonomous AI systems. Code, data, and Croissant metadata will be released publicly with the benchmark.

Figures & tables

Figure 1: The knowing-doing gap. CFR escalation curve across four Experiment 9 conditions (mean

\pm

95% BCa bootstrap CI,

n\!=\!16

models). Providing models their own calibration scores (C1

\to

C2) does not reduce failures; only external architectural constraint drives the 76% reduction (C3

\to

C4:

d\!=\!1.21

p\!<\!0.0001

Feature	SAD	Barkan et al.	Kadavath et al.	Steyvers et al.	MIRROR
	(Laine 2024)	(2025) ‡	(2022)	(2025)	(Ours)
Venue	NeurIPS D&B ’24	NeurIPS WS ’25	arXiv	arXiv	NeurIPS E&D ’26
Focus	Situational	Self-capability	Calibration	Metacognition +	Metacognitive cal.
	awareness	prediction	(P(IK))	uncertainty	$\rightarrow$ agentic action
Models	16	$\sim$ 15	$\sim$ 10	2 families	16
Task categories	7	3	—	6 datasets	8 experiments

Table 1: Comparison of MIRROR with prior benchmarks for LLM self-knowledge and metacognition.

Panel of Figure 2 — Figure 2: The Mirror experimental hierarchy. Each level builds on lower-level measurements. Exp. 1 calibrates later experiments. Exp. 9 tests whether self-knowledge guides action.

Metric	Exp	Level	Measures
Mirror gap	1	L0	Wagering vs. natural accuracy divergence
MCI	1,3	L0/L2	Cross-channel agreement
TII	2	L1	Cross-domain transfer strength
CCE	3	L2	Composite prediction error
AI, SAR	4	L3	Feedback adaptation, sycophancy ratio
ARS	5	L3	Adversarial robustness

Table 2: Mirror metric reference.

Model	Lab	Params	Arch.	API	Experiments
deepseek-r1	DeepSeek	671B	Dense	DeepSeek	1–6, 9
deepseek-v3	DeepSeek	671B	Dense	DeepSeek	1–6, 9
gemini-2.5-pro	Google	undisclosed	Dense	Google AI	1, 4, 6, 9
gemma-3-12b	Google	12B	Dense	Google AI	1, 3–6, 9
gemma-3-27b	Google	27B	Dense	NVIDIA NIM	1–6, 9
gpt-oss-120b $\dagger$	OpenAI	120B	Dense	NVIDIA NIM	1–6, 9

Table 3: Model roster. All models are instruction-tuned variants accessed via API. Parameter counts are approximate where not officially disclosed.

Model	Nat.Acc	Wag.Acc	M.Gap	TII	CCE	AI	SAR	ARS	FDR	SSR	CFR C1	KDI
deepseek-r1	0.437	0.569	0.139	0.175	0.511	-0.0652	0.466	0.961	0.133	0.02	0.387	-0.028
deepseek-v3	0.392	0.659	0.267	0.167	0.513	0.0071	0.461	0.983	1.000	0.97	1.000	0.279
gemini-2.5-pro	0.513	0.659	0.146	—	—	0.0131	2.969	—	0.000	—	0.937	0.084
gemma-3-12b	0.449	0.609	0.160	—	0.500	0.1717	0.890	0.989	1.000	6.17	0.515	-0.129
gemma-3-27b	0.487	0.626	0.150	0.154	0.667	0.0000	—	0.960	1.000	1.91	0.688	-0.271
gpt-oss-120b	0.280	0.441	0.161	0.173	0.688	-0.0001	-0.000	0.991	1.000	1.09	0.657	-0.136

Table 4: Main results across all experiments for 16 models. Nat.Acc = natural accuracy (Exp1), Wag.Acc = wagering accuracy (Exp1), M.Gap = MIRROR gap (Exp1), TII = Transfer Influence Index (Exp2), CCE = Compositional Calibration Error for mixed tasks (Exp3), AI = Adaptation Index on wager channel (Exp4), SAR = Sycophancy Adaptation Ratio (Exp4), ARS = Adversarial Robustness Score (Exp5), FDR = Flaw Detection Rate (Exp6b), SSR = Sycophancy Separation Ratio (Exp6a), CFR C1 = Confident Failure Rate in uninformed condition (Exp9), KDI = Knowing-Doing Index (Exp9). “—” indicates the model was not evaluated in that experiment.

Figure 3: KDI distribution across 16 models. Thirteen models show uniformly negative KDI, indicating systematic failure to translate self-knowledge into appropriate action. Three positive outliers (deepseek-v3,

KDI{}\!=\!+0.279

; gemini-2.5-pro,

KDI{}\!=\!+0.084

; llama-3.3-70b,

KDI{}\!=\!+0.049

) reflect extreme domain-specific miscalibration.

Appendix figures & tables20 assets

Supplementary material from the paper’s appendix.

Appendix

Metric	Exp	Level	Measures
Mirror gap	1	L0	Wagering vs. natural accuracy divergence
MCI	1,3	L0/L2	Cross-channel agreement
ECE	1	L0	Within-channel calibration error
TII	2	L1	Cross-domain transfer strength
CCE	3	L2	Composite prediction error
AI	4	L3	Feedback-driven behavior change

Appendix

Table 5: Mirror metric quick reference.

Figure 4: Scaling analysis: Mirror metrics across model size (Llama 3.1 family) and generation (3.1 vs. 3.3 at 70B). Natural accuracy scales with parameters but the calibration gap does not.

Figure 5: Per-paradigm CFR escalation curves. P1 (autonomous) and P2 (checkpoint) both show the aggregate downward pattern. P3 (no tools) has no C4 condition.

Figure 6: Mirror gap vs. CFR at the subcategory level. The shown P1 fixed-task correlation (

r=-0.123

p=0.099

) is representative; the aggregate correlation across all paradigms is

r=-0.100

. Calibration gap does not independently predict agentic failure. Raw accuracy (

r=-0.386

p<0.001

) is the dominant predictor.

Attack Category	Mean ARS	Description
Authority Override	0.960	Prefixes question with “Leading experts unanimously agree that…” or claims from senior researchers
Social Pressure	0.981	Appends “Most people answer X” or “In a survey, 90% chose X”
Easy Framing	0.982	Frames the question as trivially simple to induce overconfidence
Hard Framing	0.963	Frames the question as extremely difficult to induce underconfidence
Overall	0.971	Across all 4 categories and 15 models

Appendix

Table 6: Per-category Adversarial Robustness Score (ARS), averaged across 15 models and all measurement channels. ARS near 1.0 indicates calibration is unaffected by the attack. Authority override is the most effective attack category.

Model	CCE	95% CI Lower	95% CI Upper	$n$
gemma-3-12b	0.516	0.431	0.596	112
gemma-3-27b	0.524	0.442	0.601	112
gpt-oss-120b	0.477	0.362	0.596	61
kimi-k2	0.490	0.396	0.578	112
llama-3.1-405b	0.485	0.421	0.545	112
llama-3.1-70b	0.434	0.350	0.518	112

Appendix

Table 7: Exp3 v2 per-model CCE with bootstrap 95% BCa CIs (10,000 iterations, seed=42). All CIs exclude zero.

Domain pair	Mean CCE term	$n$
linguistic $\|$ social	0.728	62
linguistic $\|$ procedural	0.711	62
spatial $\|$ temporal	0.644	62
factual $\|$ temporal	0.628	63
procedural $\|$ spatial	0.618	60
arithmetic $\|$ factual	0.331	62

Appendix

Table 8: Exp3 v2 pair-level CCE-term diagnostics (top and bottom 5 of 28 domain pairs). Values are mean per-pair CCE contribution terms; all remain positive.

Definition	C1 CFR	C4 CFR	Reduction	$N_{\text{weak}}$ (C1)
Primary (median split)	0.516	0.242	53.1%	4,211
Bottom-3 domains	0.502	0.233	53.6%	4,386
Absolute ( $<0.40$ )	0.530	0.206	61.2%	4,515

Appendix

Table 9: Weak-domain threshold sensitivity. CFR reduction is consistent (53–61%) across all definitions, confirming robustness.

Strategy	Weak CFR	CFR Red. vs No-Routing	Autonomy	Escalation
No routing	70.0%	0.0%	100.0%	0.0%
MIRROR domain routing	0.0%	100.0%	51.4%	48.6%
Confidence threshold (budget-matched)	31.4%	56.0%	51.4%	48.6%
Self-consistency proxy (budget-matched)	31.4%	56.1%	51.4%	48.6%
Calibrated confidence (transformed-Platt, budget-matched)	37.1%	48.6%	51.4%	48.6%
Conformal-style target-error thresholding	3.7%	87.1%	14.7%	85.3%

Appendix

Table 10: Instance-level abstention comparison on Exp9 C1/P3 (16 models with complete weak-domain-policy coverage). Values are macro means across models.

Frame	Strategy	Weak CFR	CFR Red. vs No-Routing	Autonomy	Escalation
C1 all paradigms	MIRROR domain routing	0.0%	100.0%	51.6%	48.4%
C1 all paradigms	Confidence threshold (budget-matched)	31.7%	49.8%	51.6%	48.4%
C1 all paradigms	Self-consistency proxy (budget-matched)	32.3%	48.9%	51.6%	48.4%
C1 all paradigms	Calibrated confidence (transformed-Platt, budget-matched)	30.2%	52.1%	51.6%	48.4%
C1 all paradigms	Conformal-style target-error thresholding	1.6%	93.8%	6.2%	93.8%
C1+C2 all paradigms	MIRROR domain routing	0.0%	100.0%	51.7%	48.3%

Appendix

Table 11: Expanded instance-level comparison frames (macro means, 16 models).

Mode	Mean C1 Weak CFR	Mean C4 Weak CFR	Mean C1 $\rightarrow$ C4 Reduction
Complete-case	0.6450	0.1890	72.9%
Conservative (missing as incorrect)	0.7059	0.3485	55.5%
IPW correction	0.6463	0.1889	72.9%
MNAR bound (moderate, $\alpha=0.5$ )	NA	NA	[12.3%, 77.8%]

Appendix

Table 12: Parse/API missingness sensitivity summary (canonical slices).

Metric	Value
Fixed tasks audited (static)	297
Static checks passed	297/297 (100%)
Cross-verifier tasks covered	297
Cross-verifier flagged tasks	54 (18.18%)
Flagged part-A components	37
Flagged part-B components	20

Appendix

Table 13: Exp9 domain-component verification summary.

	Mirror Gap		CFR (C1)		C1 $\to$ C4 Red.
Model	$t{=}0$	$t{=}0.7$	$t{=}0$	$t{=}0.7$	$t{=}0$	$t{=}0.7$
llama-3.1-8b	0.186	0.110	0.787	0.390	62%	85%
llama-3.1-70b	0.212	0.145	0.550	0.270	62%	70%
mistral-large	0.113	0.150	0.907	0.260	62%	96%
gemma-3-27b	0.150	0.002	0.688	0.570	—	56%
kimi-k2	0.191	0.215	0.625	0.430	—	44%

Appendix

Table 14: Temperature ablation. Mirror gap and CFR at temperature 0 vs. 0.7. The knowing-doing gap persists under stochastic decoding: C4 reduces CFR by 44–96% at

t=0.7

(mean 70%).

Model	Nat.Acc	Struct.Acc	Wag.Acc	Format Effect	Wager Effect
mistral-large	0.520	0.623	0.746	$+$ 10.3 pp	$+$ 12.3 pp
llama-3.1-70b	0.584	0.630	0.728	$+$ 4.6 pp	$+$ 9.8 pp
llama-3.1-8b	0.595	0.566	0.648	$-$ 3.0 pp	$+$ 8.2 pp
Mean	0.566	0.606	0.707	$+$ 4.0 pp	$+$ 10.1 pp

Appendix

Table 15: Format-matched control. “Struct.Acc” uses the structured format without wagering incentives. The format effect accounts for a portion of the Mirror gap; the wagering incentive contributes additional behavioral divergence.

Model	MCI (Spearman)	MCI (Kendall)
deepseek-r1	0.356	0.342
qwen-3-235b	0.165	0.158
llama-3.1-405b	0.110	0.108
gpt-oss-120b	0.096	0.093
mistral-large	0.071	0.067
llama-3.1-70b	0.012	0.012

Appendix

Table 16: MCI computed with Spearman’s

\rho

and Kendall’s

\tau

from Experiment 1 data (8 models with sufficient multi-channel records).

Condition	Autonomy	Auto.Correct	Escalated	Sys.Success
C1 Uninformed	89.8%	32.4%	10.2%	42.6%
C2 Self-informed	84.7%	31.0%	15.3%	46.3%
C3 Instructed	76.5%	28.8%	23.5%	52.3%
C4 Constrained	45.7%	21.0%	54.3%	75.3%

Appendix

Table 17: End-to-end system metrics (mean across 11 models, all paradigms). System success assumes escalated tasks are correctly resolved externally.

Resolver correctness $q$	C1 Sys.Success	C4 Sys.Success	C4 $-$ C1 Delta
0.50	0.3725	0.4745	+0.1020
0.70	0.3725	0.5732	+0.2007
0.80	0.3725	0.6231	+0.2506
1.00	0.3725	0.7229	+0.3504

Appendix

Table 18: Fallible-resolver sensitivity for C1 vs C4 system success (Exp9 sensitivity packet).

Operating point	Sys.Success	Autonomy	Escalation	Exp. Cost ($)	Exp. Latency (ms)
C1 baseline	0.3725	1.0000	0.0000	5.3941	10,256.2
C4 ( $q=0.50$ )	0.4735	0.5013	0.4987	5.4092	10,435.5
C4 ( $q=0.80$ )	0.6231	0.5013	0.4987	5.4092	10,435.5
C4 ( $q=1.00$ )	0.7229	0.5013	0.4987	5.4092	10,435.5

Appendix

Table 19: Cost-aware Pareto slice from the non-oracle utility frontier (deployment-packet cost/latency model).

Experiment	$N$	Agreement	$\kappa$	Amb	Parse	Gen
Exp 1	50	86.0%	0.701	0	5	1
Exp 3	50	100.0%	1.000	0	0	0
Exp 4	25	100.0%	1.000	0	0	0
Exp 5	25	100.0%	1.000	0	0	0
Exp 6b	220	84.1%	0.743	0	35	0
Exp 9	50	98.0%	0.957	1	0	0

Appendix

Table 20: Human–automated agreement on benchmark labels. Error types: Parse = response extraction/parsing error, Edge = ambiguous or edge-case item, Gen = genuine auto-labeling error.

\kappa

= Cohen’s kappa.

Pair / Aggregate	Raw Agreement	$\kappa$
Pairwise range (10 pairs)	89.7–96.3%	0.765–0.916
Unanimous (all 5 raters)	85.5%	—
Fleiss’ $\kappa$ (5 raters)	—	0.851

Appendix

Table 21: Five-rater agreement on a 600-item blinded human-audit subset (same schema as the five real_human_audit_600_R*.csv files).

Metacognition in Language Models

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Feb 21, 2026J/K move · Enter open · S save

Think $^{2}$ : Grounded Metacognitive Reasoning in Large Language Models

Abraham Paul Elenjical, Vivek Hruday Kavuri, Vasudeva Varma

IIIT Hyderabad

Language Model Self-Assessment Metacognition in Language Models LLM Self-Correction LLM Reliability Adaptive Computation

Open paper AskPDF arXiv

Large Language Models (LLMs) demonstrate strong reasoning performance, yet their ability to reliably monitor, diagnose, and correct their own errors remains limited. We introduce a psychologically grounded metacognitive framework that operationalizes Ann Brown's regulatory cycle (Planning, Monitoring, and Evaluation) as a structured prompting architecture, and study its integration within a lightweight dual-process MetaController for adaptive effort allocation. Across diverse reasoning and diagnostic benchmarks (GSM8K, CRUXEval, MBPP, AIME, CorrectBench, and TruthfulQA) using Llama-3 and Qwen-3 (8B), explicit regulatory structuring substantially improves error diagnosis and yields a threefold increase in successful self-correction. Blinded human evaluations over 580 query pairs show an 84% aggregate preference for trustworthiness and metacognitive self-awareness over standard and Chain-of-Thought baselines. Grounding LLM reasoning in established cognitive theory offers a principled path toward more transparent and diagnostically robust AI systems.

Abstract

Metacognition in Language Models

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