Searcharxiv⌕ Search

arXiv subjects

Jon-Paul Cacioli

Publications and source records attributed to Jon-Paul Cacioli.

At least 19 recordsLinked to original sources
arXiv2026

Do LLMs Know What They Know? Measuring Metacognitive Efficiency with Signal Detection Theory

Standard evaluation of LLM confidence relies on calibration metrics (ECE, Brier score) that conflate two capacities: how much a model knows (Type-1 accuracy) and how well its confidence signal tracks that knowledge (Type-2 metacognitive sensitivity). We apply Signal Detection Theory to decompose them, treating token-level normalised log-probability as a graded confidence variable and answer correctness as the state to be discriminated. We characterise the Type-2 ROC of this signal, including its unequal-variance structure via z-ROC analysis, and -- because the meta-d' efficiency ratio is not well defined for open-ended QA, which lacks a two-alternative Type-1 decision -- quantify efficiency with a model-free information measure, normalised metacognitive information (meta-I_2r). Across four LLMs and 224,000 factual QA trials we find: (1) metacognitive information varies by a factor of 1.98 across models and is not predicted by accuracy, the rank correlation being -0.80 on TriviaQA and +0.00 on Natural Questions; (2) the confidence signal has model-specific unequal-variance structure (z-ROC slopes 0.78 to 1.18) invisible to calibration metrics, the slope ordering replicating on NQ; (3) efficiency is domain-specific, weakest in Science & Technology for every model; (4) temperature dissociates accuracy from metacognitive information, which stays near-flat for three of four models while accuracy falls; and (5) metacognitive information tracks the accuracy gain from confidence-based abstention exactly (rho = +1.00) while accuracy does not. All estimates carry permutation nulls and bootstrap confidence intervals. This version (v3) corrects a differential length bias in the automated correctness scorer, validated against 1,830 human adjudications; the inverse accuracy-efficiency coupling reported in v1 and v2 does not survive relabelling. See the version note on page 1.

cs.CL↗
arXiv2026

Beyond the Mean: Within-Model Reliable Change Detection for LLM Evaluation

We adapted the Reliable Change Index (RCI; Jacobson and Truax, 1991) from clinical psychology to item-level LLM version comparison on 2,000 MMLU-Pro items (K=10 samples at T=0.7). Two within-family pairs were tested: Llama 3 to 3.1 (+1.6 points) and Qwen 2.5 to 3 (+2.8 points). On the full benchmark, most items showed no reliable change (79% and 72%). However, over half the items were floor/ceiling. Among analysable items, change was bidirectional with large effect sizes: 34% improved and 28% deteriorated for Llama; 47% improved and 39% deteriorated for Qwen (median |delta p| = 0.50 and 0.90). Churn was asymmetric by difficulty: low-accuracy items improved, high-accuracy items deteriorated. Domain-level decomposition revealed family-specific reversals: Llama lost physics while Qwen lost law. Greedy single-shot evaluation missed 42% of reliably changed items and falsely flagged 25% of unchanged items. The aggregate accuracy gain is the net residual of opposing item-level movements. We recommend reporting churn rate alongside aggregate accuracy.

cs.CL↗
arXiv2026

Option-Order Randomisation Reveals a Distributional Position Attractor in Prompted Sandbagging

A predecessor pilot (Cacioli, 2026) found that Llama-3-8B implements prompted sandbagging as positional collapse rather than answer avoidance. However, fixed option ordering in MMLU-Pro left open whether this reflected a model-level position-dominant policy or dataset-level distractor structure. This pre-registered follow-up (3 models, 2,000 MMLU-Pro items, 4 conditions, 24,000 primary trials) added cyclic option-order randomisation as the critical control. The pre-registered item-level same-letter diagnostic did not confirm deterministic position-tracking (same-letter rate 37.3%, below the 50% threshold). However, pre-specified supporting analyses revealed that the response-position distribution under sandbagging was highly stable under complete content rotation (Pearson r = 0.9994; Jensen-Shannon divergence = 0.027, compared to 0.386 between honest and sandbagging conditions). Accuracy spiked to 72.1% when the correct answer coincidentally occupied the preferred position E, and fell to 4.3% at position A. The data provide strong evidence for a soft distributional attractor: under sandbagging instruction, the model enters a low-entropy response-position basin centred on E/F/G that is highly stable and largely content-invariant at the aggregate level. Qwen-2.5-7B served as a negative control (non-compliant, no distributional shift). These results provide evidence, at the 7-9 billion parameter scale, that response-position entropy is a promising black-box behavioural signature of this sandbagging mode.

cs.CL↗
arXiv2026

Instruction Complexity Induces Positional Collapse in Adversarial LLM Evaluation

When instructed to underperform on multiple-choice evaluations, do language models engage with question content or fall back on positional shortcuts? We map the boundary between these regimes using a six-condition adversarial instruction-specificity gradient administered to two instruction-tuned LLMs (Llama-3-8B and Llama-3.1-8B) on 2,000 MMLU-Pro items. Distributional screening (response-position entropy) and an independent content-engagement criterion (difficulty-accuracy correlation) jointly characterise each condition. The gradient reveals three regimes rather than a monotonic transition. Vague adversarial instructions produce moderate accuracy reduction with preserved content engagement. Standard sandbagging and capability-imitation instructions produce positional entropy collapse with partial content engagement. A two-step answer-aware avoidance instruction produces extreme positional collapse, with near-total concentration on a single response position (99.9% and 87.4%) and no measurable content sensitivity. This was the only multi-step instruction tested, and it produced the most extreme shortcut. The attractor position matches each model's content-absent null-prompt default. The effect replicates across both models and four academic domains. Distributional collapse and content engagement can co-occur (50% concordance between screening criteria), indicating that entropy-based screening and difficulty-based content assessment capture partially independent dimensions of response validity. Results suggest that instruction complexity can determine whether adversarial compliance uses content-aware or content-blind mechanisms in small instruction-tuned LLMs under greedy decoding.

cs.CL↗
arXiv2026

Below-Chance Blindness: Prompted Underperformance in Small LLMs Produces Positional Bias Rather than Answer Avoidance

Detecting sandbagging--the deliberate underperformance on capability evaluations--is an open problem in AI safety. We tested whether symptom validity testing (SVT) logic from clinical malingering detection could identify sandbagging through below-chance performance (BCB) on forced-choice items. In a pre-registered pilot at the 7-9 billion parameter instruction-tuned scale (3 models, 4 MMLU-Pro domains, 4 conditions, 500 items per cell, 24,000 total trials), the plausibility gate failed. Zero of 12 model-domain cells showed significant below-chance performance under sandbagging instruction. Exploratory analyses revealed three qualitatively distinct failure modes. Qwen-2.5-7B and Phi-3.5-mini largely ignored the sandbagging instruction, with 62-88% response identity with the honest baseline. Llama-3-8B complied substantially but implemented underperformance as a positional heuristic, collapsing its response distribution onto middle-alphabet options (E at 31.8%, F at 26.1%) regardless of where the correct answer fell. This produced accuracy boosts of up to 33 percentage points when the correct answer coincidentally occupied the model's preferred position. An explicit anti-task instruction ("pick the least likely answer") drove two of three models below chance, with accuracy as low as 0.024. The capability for answer-aware avoidance therefore exists but is not activated by "deliberately underperform." BCB did not fail as a logical marker of answer-aware avoidance. It was not observed in this regime because the model showing the largest behavioural shift exhibited behaviour consistent with a position-dominant response policy rather than content-aware answer avoidance. We propose that positional-distribution shift may be a more effective behavioural signature than below-chance accuracy for detecting prompted underperformance at this model scale.

cs.CL↗
arXiv2026

Distilling Self-Consistency into Verbal Confidence: A Pre-Registered Negative Result and Post-Hoc Rescue on Gemma 3 4B

Small instruct-tuned LLMs produce degenerate verbal confidence under minimal elicitation: ceiling rates above 95%, near-chance Type-2 AUROC, and Invalid validity profiles. We test whether confidence-conditioned supervised fine-tuning (CSFT) with self-consistency-derived targets can close the gap between internal information and verbal readout. A pre-registered Phase 0 protocol on Gemma 3 4B-it with a modal filter restricting training to items with correct modal answers produced a negative result: AUROC2 dropped from 0.554 to 0.509 due to label-entropy collapse in the training targets. An exploratory rescue removed the filter, training on all 2,000 calibration items. This produced a binary verbal correctness discriminator with AUROC2 = 0.774 on held-out TriviaQA, compressing a 10-sample self-consistency signal (AUROC2 = 0.999) into a single-pass readout exceeding logit entropy (0.701). The shuffled-target control showed no improvement (0.501). On MMLU, accuracy improved from 54.2% to 77.4% with the shuffled model at baseline (56.1%), supporting a target-dependent interpretation. The result is exploratory, binary rather than continuously calibrated, and observed at a single scale. It identifies two design lessons: confidence training requires label entropy, and correct targets regularise output format.

cs.CL↗
arXiv2026

Categorical Perception in Large Language Model Hidden States: Structural Warping at Digit-Count Boundaries

Categorical perception (CP) -- enhanced discriminability at category boundaries -- is among the most studied phenomena in perceptual psychology. This paper reports that analogous geometric warping occurs in the hidden-state representations of large language models (LLMs) processing Arabic numerals. Using representational similarity analysis across six models from five architecture families, the study finds that a CP-additive model (log-distance plus a boundary boost) fits the representational geometry better than a purely continuous model at 100% of primary layers in every model tested. The effect is specific to structurally defined boundaries (digit-count transitions at 10 and 100), absent at non-boundary control positions, and absent in the temperature domain where linguistic categories (hot/cold) lack a tokenisation discontinuity. Two qualitatively distinct signatures emerge: "classic CP" (Gemma, Qwen), where models both categorise explicitly and show geometric warping, and "structural CP" (Llama, Mistral, Phi), where geometry warps at the boundary but models cannot report the category distinction. This dissociation is stable across boundaries and is a property of the architecture, not the stimulus. Structural input-format discontinuities are sufficient to produce categorical perception geometry in LLMs, independently of explicit semantic category knowledge.

cs.CL↗
arXiv2026

Verbal Confidence Saturation in 3-9B Open-Weight Instruction-Tuned LLMs: A Pre-Registered Psychometric Validity Screen

Verbal confidence elicitation is widely used to extract uncertainty estimates from LLMs. We tested whether seven instruction-tuned open-weight models (3-9B parameters, four families) produce verbalised confidence that meets minimal validity criteria for item-level Type-2 discrimination under minimal numeric elicitation with greedy decoding. In a pre-registered study (OSF: osf.io/azbvx), 524 TriviaQA items were administered under numeric (0-100) and categorical (10-class) elicitation to eight models at Q5_K_M quantisation on consumer hardware, yielding 8,384 deterministic trials. A psychometric validity screen was applied to each model-format cell. All seven instruct models were classified Invalid on numeric confidence (H2 confirmed, 7/7 vs. predicted >=4/7), with a mean ceiling rate of 91.7% (H1 confirmed). Categorical elicitation did not rescue validity. Instead, it disrupted task performance in six of seven models, producing accuracy below 5% (H4 not confirmed). Token-level logprobability did not usefully predict verbalised confidence under the observed variance regime (H5 confirmed, mean cross-validated R^2 < 0.01). Within the reasoning-distilled model, reasoning-trace length showed a strong negative partial correlation with confidence (rho = -0.36, p < .001), consistent with the Reasoning Contamination Effect. These results do not imply that internal uncertainty representations are absent. They show that minimal verbal elicitation fails to preserve internal signals at the output interface in this model-size regime. Psychometric screening should precede any downstream use of such signals.

cs.CL↗
arXiv2026

Cross-Entropy Is Load-Bearing: A Pre-Registered Scope Test of the K-Way Energy Probe on Bidirectional Predictive Coding

Cacioli (2026) showed that the K-way energy probe on standard discriminative predictive coding networks reduces approximately to a monotone function of the log-softmax margin. The reduction rests on five assumptions, including cross-entropy (CE) at the output and effectively feedforward inference dynamics. This pre-registered study tests the reduction's sensitivity to CE removal using two conditions: standard PC trained with MSE instead of CE, and bidirectional PC (bPC; Oliviers, Tang & Bogacz, 2025). Across 10 seeds on CIFAR-10 with a matched 2.1M-parameter backbone, we find three results. The negative result replicates on standard PC: the probe sits below softmax (Delta = -0.082, p < 10^-6). On bPC the probe exceeds softmax across all 10 seeds (Delta = +0.008, p = 0.000027), though a pre-registered manipulation check shows that bPC does not produce materially greater latent movement than standard PC at this scale (ratio 1.6, threshold 10). Removing CE alone without changing inference dynamics halves the probe-softmax gap (Delta_MSE = -0.037 vs Delta_stdPC = -0.082). CE is a major empirically load-bearing component of the decomposition at this scale. CE training produces output logit norms approximately 15x larger than MSE or bPC training. A post-hoc temperature scaling ablation decomposes the probe-softmax gap into two components: approximately 66% is attributable to logit-scale effects removable by temperature rescaling, and approximately 34% reflects a scale-invariant ranking advantage of CE-trained representations. We use "metacognitive" operationally to denote Type-2 discrimination of a readout over its own Type-1 correctness, not to imply human-like introspective access.

cs.CL↗
arXiv2026

The Metacognitive Monitoring Battery: A Cross-Domain Benchmark for LLM Self-Monitoring

We introduce a cross-domain behavioural assay of monitoring-control coupling in LLMs, grounded in the Nelson and Narens (1990) metacognitive framework and applying human psychometric methodology to LLM evaluation. The battery comprises 524 items across six cognitive domains (learning, metacognitive calibration, social cognition, attention, executive function, prospective regulation), each grounded in an established experimental paradigm. Tasks T1-T5 were pre-registered on OSF prior to data collection; T6 was added as an exploratory extension. After every forced-choice response, dual probes adapted from Koriat and Goldsmith (1996) ask the model to KEEP or WITHDRAW its answer and to BET or decline. The critical metric is the withdraw delta: the difference in withdrawal rate between incorrect and correct items. Applied to 20 frontier LLMs (10,480 evaluations), the battery discriminates three profiles consistent with the Nelson-Narens architecture: blanket confidence, blanket withdrawal, and selective sensitivity. Accuracy rank and metacognitive sensitivity rank are largely inverted. Retrospective monitoring and prospective regulation appear dissociable (r = .17, 95% CI wide given n=20; exemplar-based evidence is the primary support). Scaling on metacognitive calibration is architecture-dependent: monotonically decreasing (Qwen), monotonically increasing (GPT-5.4), or flat (Gemma). Behavioural findings converge structurally with an independent Type-2 SDT approach, providing preliminary cross-method construct validity. All items, data, and code: https://github.com/synthiumjp/metacognitive-monitoring-battery.

cs.CL↗
arXiv2026

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

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.

cs.CL↗
arXiv2026

Before You Interpret the Profile: Validity Scaling for LLM Metacognitive Self-Report

Clinical personality assessment screens response validity before interpreting substantive scales. LLM evaluation does not. We apply the validity scaling framework from the PAI and MMPI-3 to metacognitive probe data from 20 frontier models across 524 items. Six validity indices are operationalised: L (maintaining confidence on errors), K (betting on errors), F (withdrawing consensus-endorsed items), Fp (withdrawing correct answers), RBS (inverted monitoring), and TRIN (fixed responding). A tiered classification system identifies four models as construct-level invalid and two as elevated. Valid-profile models produce item-sensitive confidence (mean r = .18, 14 of 16 significant). Invalid-profile models do not (mean r = -.20, d = 2.17, p = .001). Chain-of-thought training produces two opposite response distortions. Two latent dimensions account for 94.6% of index variance. Companion papers extract a portable screening protocol (Cacioli, 2026e) and validate it against selective prediction (Cacioli, 2026f). All data and code: https://github.com/synthiumjp/validity-scaling-llm

cs.CL↗
arXiv2026

Screen Before You Interpret: A Portable Validity Protocol for Benchmark-Based LLM Confidence Signals

LLM confidence signals are used for abstention, routing, and safety-critical decisions. No standard practice exists for checking whether a confidence signal carries item-level information before building on it. We transfer the validity screening principle from clinical personality assessment (PAI, MMPI-3) as a portable protocol for benchmark-based LLM confidence data. The protocol specifies three core indices (L, Fp, RBS), a structural indicator (TRIN), and an item-sensitivity statistic, computed from a single 2x2 contingency table. A three-tier classification system (Invalid, Indeterminate, Valid) draws on four clinical traditions. Validated on 20 frontier LLMs across 524 items, four models are classified Invalid, two Indeterminate. Valid-profile models show mean r = .18 (15/16 significant). Invalid-profile models show mean r = -.20 (d = 2.48). Cross-benchmark validation on 18 models using MMLU with verbalized confidence and on external data from Yang et al. (2024) confirms the screen transfers across benchmarks and probe formats. All data and code: https://github.com/synthiumjp/validity-scaling-llm

cs.CL↗
arXiv2026

Concurrent Criterion Validation of a Validity Screen for LLM Confidence Signals via Selective Prediction

The validity screen (Cacioli, 2026d, 2026e) classifies LLM confidence signals as Valid, Indeterminate, or Invalid. We test whether these classifications predict selective prediction performance. Twenty frontier LLMs from seven families were evaluated on 524 items across six cognitive tracks. Valid models show mean Type 2 AUROC = .624 (SD = .048). Invalid models show mean AUROC = .357 (SD = .231). Cohen's d = 2.81, p = .002. The tiers order monotonically: Invalid (.357) < Indeterminate (.554) < Valid (.624). Split-half cross-validation yields median d = 1.77, P(d > 0) = 1.0 across 1,000 splits. The three-tier classification accounts for 47% of the variance in AUROC. DeepSeek-R1 drops from 85.3% accuracy at full coverage to 11.3% at 10% coverage. The screen predicts the criterion. For selective prediction, the screen matters.

cs.CL↗
arXiv2026

K-Way Energy Probes for Metacognition Reduce to Softmax in Discriminative Predictive Coding Networks

We present this as a negative result with an explanatory mechanism, not as a formal upper bound. Predictive coding networks (PCNs) admit a K-way energy probe in which each candidate class is fixed as a target, inference is run to settling, and the per-hypothesis settled energies are compared. The probe appears to read a richer signal source than softmax, since the per-hypothesis energy depends on the entire generative chain. We argue this appearance is misleading under the standard Pinchetti-style discriminative PC formulation. We present an approximate reduction showing that with target-clamped CE-energy training and effectively-feedforward latent dynamics, the K-way energy margin decomposes into a monotone function of the log-softmax margin plus a residual that is not trained to correlate with correctness. The decomposition predicts that the structural probe should track softmax from below. We test this across six conditions on CIFAR-10: extended deterministic training, direct measurement of latent movement during inference, a post-hoc decoder fairness control on a backpropagation network, a matched-budget PC vs BP comparison, a five-point Langevin temperature sweep, and trajectory-integrated MCPC training. In every condition the probe sat below softmax. The gap was stable across training procedures within the discriminative PC family. Final-state and trajectory-integrated training produced probes whose AUROC_2 values differed by less than 10^-3 at deterministic evaluation. The empirical regime is small: single seed, 2.1M-parameter network, 1280 test images. We frame the result as a preprint inviting replication. We discuss conditions under which the decomposition does not apply (bidirectional PC, prospective configuration, generative PC, non-CE energy formulations) and directions for productive structural probing the analysis does not foreclose.

cs.LG↗
arXiv2026

Quantisation Reshapes the Metacognitive Geometry of Language Models

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.

cs.CL↗
arXiv2026

Same Geometry, Opposite Noise: Transformer Magnitude Representations Lack Scalar Variability

Scalar variability -- the finding that representational noise scales proportionally with magnitude, producing a constant coefficient of variation -- is a hallmark of biological magnitude systems. We tested whether transformer language models exhibit this property by analysing the dispersion of hidden-state representations across carrier sentences for 26 numerical magnitudes in three 7-8B parameter models (Llama-3-8B-Instruct, Mistral-7B-Instruct-v0.3, Llama-3-8B-Base; data from Cacioli, 2026). We found the opposite: representational variability decreased with magnitude along the magnitude axis (scaling exponent alpha approx -0.19; 0/16 primary layers with alpha > 0, all three models). The negative sign was consistent in full-dimensional space (alpha approx -0.04) and after sentence-identity correction (alpha approx -0.007). The anti-scalar pattern was 3-5x stronger along the magnitude axis than orthogonal dimensions, and corpus frequency strongly predicted per-magnitude variability (rho = .84). These results demonstrate that distributional learning alone is insufficient to produce scalar variability: transformers reproduce log-compressive magnitude geometry but not the constant-CV noise signature observed in biological systems.

cs.CL↗
arXiv2026

Exemplar Retrieval Without Overhypothesis Induction: Limits of Distributional Sequence Learning in Early Word Learning

Background: Children do not simply learn that balls are round and blocks are square. They learn that shape is the kind of feature that tends to define object categories -- a second-order generalisation known as an overhypothesis [1, 2]. What kind of learning mechanism is sufficient for this inductive leap? Methods: We trained autoregressive transformer language models (3.4M-25.6M parameters) on synthetic corpora in which shape is the stable feature dimension across categories, with eight conditions controlling for alternative explanations. Results: Across 120 pre-registered runs evaluated on a 1,040-item wug test battery, every model achieved perfect first-order exemplar retrieval (100%) while second-order generalisation to novel nouns remained at chance (50-52%), a result confirmed by equivalence testing. A feature-swap diagnostic revealed that models rely on frame-to-feature template matching rather than structured noun-to-domain-to-feature abstraction. Conclusions: These results reveal a clear limitation of autoregressive distributional sequence learning under developmental-scale training conditions.

cs.CL↗