Three Measurable Failure Modes of Large Language Models
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Advanced Research in Artificial Intelligence Systems (ARAIS)
Published May 11, 2026
| Version v1
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Three Measurable Failure Modes of Large Language Models
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Hubka, Marek<br>(Researcher)1
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1.
On Tides of Uncertainty
Description
Human language is inherently ambiguous - not a deterministic code but an ensemble of overlapping meanings whose disambiguation depends on context that is often incomplete or absent. A system that processes natural language must therefore be probabilistic, not by architectural choice but by mathematical necessity. This paper argues that the resulting uncertainty has structure: what the field calls hallucinations is not one phenomenon but three structurally distinct failure modes of this probabilistic nature, each with a different causal origin, a different measurable signature, and a different class of solutions.
Mode 1 (autoregressive reinforcement) is the self-consistent wrong trajectory produced when an error contaminates the model's own conditioning context.
Mode 2 (confabulation) is fluent generation produced from parameter directions that received no training signal - the null space of the weight matrix.
Mode 3 (irreducible uncertainty) is the correct response of a calibrated probabilistic system to a genuinely ambiguous query.
Each mode has a computable quantitative metric: correction sensitivity $(\mathsf{CS})$, dimensional excess $(\mathsf{DE})$, and output entropy $(\mathsf{H}_{\mathrm{out}})$. The three measurements rest on a single coding-theoretic construction, the syndrome table $S = \mathcal{N}(\bar{J} \cdot V)^\top$, whose full derivation is in the companion paper "A Syndrome Algebra for Differentiable Parametric Systems".
A controlled experimental series on a synthetic LSTM ($D=256$, $L=10$, six fixed seeds) confirms the framework end to end. The three metrics separate cleanly: the $\mathsf{CS}$ gap between known and unknown domains narrows monotonically from $0.273 \pm 0.095$ at $k=1$ to $0.067 \pm 0.037$ at $k=10$. The Pearson correlation $r(\mathsf{DE}, \mathsf{CS}_{\mathrm{unknown}}) = 0.9896$ across k predicts out-of-domain failure from weight matrix alone. Causal localisation of an injected perturbation reaches $100\%$ accuracy over $180$ trials with a pre/post residual ratio of approximately $2\times 10^8$. Oracle correction is exact (cosine $1.000000$ over $36,000$ trials). A direct comparison of multicellular specialists against monolithic generalists shows the Singleton-bound multicellular advantage grows from $0.158 \pm 0.049$ at $N=5$ to $0.310 \pm 0.054$ at $N=10$ in $\mathsf{CS}$ gap, empirically justifying the modular hierarchy.
Additional notes:
This preprint is accompanied by the mathematical paper A Syndrome Algebra for Differentiable Parametric Systems (see related identifiers). Code and data are available at the linked GitHub repository. Model weights are not included due to size; they are regenerated deterministically from the provided scripts and canonical seeds.
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(English)
Structure of the Error Distribution in Autoregressive Stochastic Systems
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Is supplement to
Preprint:
10.5281/zenodo.20127537
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10.5281/zenodo.20290098
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https://github.com/MarcusSkynet/lstm2
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Keywords and subjects
Keywords
large language models
hallucinations
error correction
syndrome algebra
Gram metric
Jacobian variance
Singleton bound
Hamming Bound
modular architecture
ML reliability
LSTM
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DOI
10.5281/zenodo.20127318
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Resource type<br>Preprint
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Creative Commons Attribution 4.0 International
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Copyright (C) 2026 Marek...