Quantisation Reshapes the Metacognitive Geometry of Language Models

Jon-Paul Cacioli

cs.CLApr 10, 2026

Quantisation Reshapes the Metacognitive Geometry of Language Models

Authors: Jon-Paul Cacioli

Organizations: Independent Researcher, Melbourne, Australia

Abstract

We report that model quantisation restructures domain-level metacognitive efficiency in LLMs rather than degrading it uniformly. Evaluating Llama-3-8B-Instruct on the same 3,000 questions at Q5_K_M and f16 precision, we find that M-ratio profiles across four knowledge domains are uncorrelated between formats (Spearman rho = 0.00). Arts & Literature moves from worst-monitored (M-ratio = 0.606 at Q5_K_M) to best-monitored (1.542 at f16). Geography moves from well-monitored (1.210) to under-monitored (0.798). However, Type-2 AUROC profiles are perfectly stable across formats (rho = 1.00), localising the restructuring to the M-ratio normalisation rather than the underlying discrimination signal. This finding emerged from a pre-registered attempt to improve metacognition through domain-conditional training. We prescribed confidence-amplification SFT for the diagnosed weak domain, with matched-budget agnostic and wrong-prescription controls. All four confirmatory hypotheses were null (10,000 bootstrap resamples, seed = 42). The training successfully reshaped confidence distributions, doubling the NLP gap in Science from 0.076 to 0.152, but did not improve meta-d' because the diagnostic profile did not transfer across formats. Any system relying on domain-level M-ratio profiles has an unexamined dependency on inference format. Systems using AUROC_2 are safer. We release all code, pre-registrations, and trial-level data.

Figures & tables

#	Condition	Training data
1	No intervention (baseline)	None
2	Domain-conditional SFT	Science questions, confidence amplification on correct trials
3	Domain-agnostic SFT	All domains proportionally, matched pair count
4	Wrong-prescription SFT	Geography questions, confidence amplification
5	Prompt-based domain cue	System prompt only
6	Per-domain temperature scaling	Post-hoc calibration

Table 1: Pre-registered experimental conditions

Set	Size	Purpose	Disjoint from
A	5,000	M1 diagnostic profiles	B, C 1
B	5,000	Training (SFT pairs)	A, C 1
C 1	3,000	Evaluation	A, B

Table 2: Dataset splits

Domain	$d^{\prime}$	meta- $d^{\prime}$	M-ratio	Rank	$d^{\prime}$	meta- $d^{\prime}$	M-ratio	Rank
	Q5_K_M				f16
Science	0.365	0.493	1.352	1	0.461	0.663	1.436	2
Geography	0.410	0.497	1.210	2	0.648	0.518	0.798	3
History	0.675	0.415	0.615	3	0.722	0.339	0.470	4
Arts	0.891	0.540	0.606	4	0.559	0.862	1.542	1

Table 3: Domain-level metacognitive profiles under two quantisation formats. Same 3,000 C 1 questions, same model weights, same inference backend (llama-cpp, Vulkan, AMD RX 7900 GRE). Only the number format differs.

Figure 1: M-ratio profiles by domain at Q5_K_M and f16 on the same 3,000 questions. Arts moves from rank 4 to rank 1. Geography moves from rank 2 to rank 3. Spearman $\rho=0.00$ .

Domain	Q5_K_M AUROC 2	Q5_K_M Rank	f16 AUROC 2	f16 Rank
Arts	0.710	1	0.680	1
History	0.669	2	0.672	2
Geography	0.629	3	0.668	3
Science	0.619	4	0.643	4

Table 4: Type-2 AUROC per domain per format. Same 3,000 C 1 questions at both formats.

Figure 2: AUROC 2 profiles by domain at Q5_K_M and f16 on the same 3,000 questions. Rank ordering is perfectly preserved. Spearman $\rho=1.00$ .

Hypothesis	Contrast	Domain	$\Delta$ meta- $d^{\prime}$	95% CI	Result
H1	Cond 2 $-$ Cond 1	Science	$-$ 0.118	$[-0.539,0.348]$	Not supported
H3	Cond 2 $-$ Cond 3	Science	$-$ 0.041	$[-0.460,0.422]$	Not supported
H4	Cond 2 $-$ Cond 4	Science	$+$ 0.138	$[-0.223,0.661]$	Not supported

Table 5: Confirmatory results. 10,000 bootstrap resamples, seed

=42

Domain	$\Delta$ meta- $d^{\prime}$	90% CI	Result
History	$+$ 0.323	$[-0.053,0.543]$	Not equivalent
Arts	$-$ 0.273	$[-0.498,0.121]$	Not equivalent
Geography	$+$ 0.059	$[-0.470,0.324]$	Not equivalent

Table 8

Condition	Science	Arts	History	Geography
1 (Baseline)	0.076	0.112	0.100	0.106
2 (Conditional)	0.152	0.136	0.147	0.156
3 (Agnostic)	0.123	0.152	0.128	0.143
4 (Wrong-rx)	0.133	0.162	0.141	0.115
7 (Low LR)	0.091	0.113	0.117	0.114

Table 6: NLP gap (mean NLP correct

-

mean NLP incorrect) by condition and domain.

Cond	Domain	N	Acc	$d^{\prime}$	meta- $d^{\prime}$	M-ratio	NLP gap
1	Arts	847	0.647	0.559	0.862	1.542	0.112
1	Geography	581	0.711	0.648	0.518	0.798	0.106
1	History	956	0.668	0.722	0.339	0.470	0.100
1	Science	616	0.696	0.461	0.663	1.436	0.076
2	Arts	847	0.640	0.600	0.588	0.981	0.136
2	Geography	581	0.673	0.689	0.577	0.837	0.156

Table 7: Per-condition, per-domain metrics.

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Language model self-assessment studies how models judge their own confidence, capabilities, errors, and behavior.

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Domain-level metacognitive monitoring in frontier LLMs: A 33-model atlas

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Independent Researcher · Melbourne, Australia

LLM Evaluation

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Aggregate metacognitive quality scores mask within-model variation across MMLU benchmark domains. We administered 1,500 MMLU items (250 per domain, under an a priori six-domain grouping) to 33 frontier LLMs from eight model families and computed Type-2 AUROC per model-domain cell using verbalized confidence (0-100). Total observations: 47,151. Every model with above-chance aggregate monitoring showed non-trivial domain-level variation. Applied/Professional knowledge was reliably the easiest benchmark domain to monitor (mean AUROC = .742, ranked top-2 in 21 of 33 models); Formal Reasoning and Natural Science were reliably the hardest (one of the two ranked bottom-2 in 27 of 33 models). The three middle domains were statistically indistinguishable (Kendall's W = .164). A subject-level coherence analysis (within-domain similarity ratio = 0.95) confirms the six-domain grouping is a pragmatic benchmark taxonomy, not a validated latent construct. Within-family profile-shape clustering is significant for Anthropic, Google-Gemini, and Qwen (permutation p < .0001) but not DeepSeek, Google-Gemma, or OpenAI. Gemma 4 31B showed a +.202 AUROC improvement over Gemma 3 27B. Three models classified Invalid on binary KEEP/WITHDRAW probes produced normal profiles under verbalized confidence, confirming probe-format specificity. Bootstrap 95% CIs on 198 cells have median width .199. Split-half aggregate stability r = .893; profile-level split-half is weaker (grand median r = .184). These results show stable benchmark-domain variation obscured by aggregate metrics, and support benchmark-stage domain screening as a step before deployment in specific application areas.

Abstract

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