From Prerequisites to Predictions: Validating a Geometric Hallucination Taxonomy Through Controlled Induction

• URL: http://arxiv.org/abs/2603.00307v1
• Date: Fri, 27 Feb 2026 20:56:59 GMT
• Title: From Prerequisites to Predictions: Validating a Geometric Hallucination Taxonomy Through Controlled Induction
• Abstract summary: We test whether a geometric hallucination taxonomy can distinguish hallucination types.<n>Type1 and2 do not separate in either space.<n>Type1/2 non-separation is genuine at 124M parameters.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We test whether a geometric hallucination taxonomy -- classifying failures as center-drift (Type~1), wrong-well convergence (Type~2), or coverage gaps (Type~3) -- can distinguish hallucination types through controlled induction in GPT-2. Using a two-level statistical design with prompts ($N = 15$/group) as the unit of inference, we run each experiment 20 times with different generation seeds to quantify result stability. In static embeddings, Type~3 norm separation is robust (significant in 18/20 runs, Holm-corrected in 14/20, median $r = +0.61$). In contextual hidden states, the Type~3 norm effect direction is stable (19/20 runs) but underpowered at $N = 15$ (significant in 4/20, median $r = -0.28$). Types~1 and~2 do not separate in either space (${\leq}\,3/20$ runs). Token-level tests inflate significance by 4--16$\times$ through pseudoreplication -- a finding replicated across all 20 runs. The results establish coverage-gap hallucinations as the most geometrically distinctive failure mode, carried by magnitude rather than direction, and confirm the Type~1/2 non-separation as genuine at 124M parameters.

Related papers

• Intrinsic Structure: Spectral Identifiability for Mechanistic Interpretability [51.56484100374058]
  We prove the first identifiability theorem for a mechanistic-interpretability primitive.<n>The spectrum is an identifiable, model-intrinsic fingerprint with a stated error bar, not a legible decomposition.
  arXiv  Detail & Related papers  (2026-08-10T19:42:01Z)
• Detecting and Discriminating Operator Misspecification in Hybrid PDE-Parameter Learning: a Reference-Free Instrument, with Discrimination Bounded In Sample [0.0]
  We build an instrument that reads from a single fit and with no oracle.<n>We report where the instrument is blind, a pre-registered negative where a neural estimator loses to Tikhonov-regularized inversion at recovery.
  arXiv  Detail & Related papers  (2026-08-04T21:20:44Z)
• Decoherence as Defence and the Magnitude of Noise Regularisation: A Rigorous N -Qubit Theory of Stochastic Quantum Neural Networks for Adversarially Robust Network Intrusion Detection [0.0]
  We give an $N$-qubit formulation through the master equation and its vectorised Liouvillian.<n>We prove a emphdecoherence-contraction theorem: a depolarising channel of strength.<n>We show this robustness arises from a noise-reshaped training boundary rather than from attack-time contraction.
  arXiv  Detail & Related papers  (2026-06-23T07:06:56Z)
• The Ringelmann Effect in Multi-Agent LLM Systems: A Scaling Law for Effective Team Size [5.51170856062205]
  We show that dense peer influence collapses the answer-level regime from sublinear into hard-ceiling.<n>Thirty dense debating agents produce no more answer diversity than one on MMLU-Hard.<n>On free-form math, dense peer influence collapses the answer-level regime from sublinear into hard-ceiling.
  arXiv  Detail & Related papers  (2026-05-31T16:19:54Z)
• Spectral Anatomy of Quantum Gaussian Process Kernels [38.264196157340216]
  We prove a Cauchy-Schwarz tail bound on Nystrm approximation error, a finite-sample variance-contraction identity, and a characterization of the emphtarget-dependent optimal entropy.<n>The diagnostic is kernel-agnostic: hardware-efficient, matchgate, IQP emphand RBF/Matérn/RFF/deep- kernel families all collapse onto identical $S/log n$ curves.
  arXiv  Detail & Related papers  (2026-05-29T07:41:14Z)
• Interference visibility as a witness of preparation contextuality via overlap inequalities [0.0]
  We show that standard multi-path interferometry, using only pairwise visibility measurements, provides an operational route to tests of preparation noncontextuality.
  arXiv  Detail & Related papers  (2026-05-14T05:20:24Z)
• Whitening Reveals Cluster Commitment as the Geometric Separator of Hallucination Types [0.0]
  A geometric taxonomy distinguishes three failure types -- center-drift (Type1), wrong-well convergence (Type2), and coverage gaps (Type3)<n>Prior work found Types1 and2 indistinguishable in full-dimensional contextual measurement.<n>We address this through PCA-whitening and eigenspectrum decomposition on GPT-2-small.
  arXiv  Detail & Related papers  (2026-03-08T18:12:10Z)
• High-Dimensional Robust Mean Estimation with Untrusted Batches [38.14592862692954]
  We study high-dimensional mean estimation in a collaborative setting where data is contributed by $N$ users in batches of size $n$.<n>We formalize this challenge through a double corruption landscape: an $varepsilon$-fraction of users are entirely adversarial, while the remaining good'' users provide data from distributions that are related to $P$, but deviate by a proximity parameter $$.<n>Our algorithms achieve the minimax-optimal error rate $O(sqrtvarepsilon/n + sqrtd/nN + s
  arXiv  Detail & Related papers  (2026-02-24T08:59:37Z)
• Witness wedges in fidelity-deviation plane: separating teleportation advantage and Bell-inequality violation [0.0]
  We develop a unified framework to analyze quantum teleportation through the joint geometry of two complementary figures of merit.<n>In particular, any measured pair $(F D)$ can be ported into a visibility estimate for isotropic resources.
  arXiv  Detail & Related papers  (2025-11-26T05:43:31Z)
• Transformer Injectivity & Geometric Robustness - Analytic Margins and Bi-Lipschitz Uniformity of Sequence-Level Hidden States [0.0]
  We show that the map from discrete prompts to last-token hidden states is generically injective on finite prompt sets.<n>We study behavior across layers, sequence lengths, model scales, and 8- and 4-bit activation quantization.
  arXiv  Detail & Related papers  (2025-11-17T19:39:15Z)
• Shrinkage to Infinity: Reducing Test Error by Inflating the Minimum Norm Interpolator in Linear Models [0.0]
  Hastie et al. (2022) found that ridge regularization is essential in high dimensional linear regression $y=betaTx + epsilon$<n>We make precise this observation for linear regression with highly anisotropic covariances and $d/n$.<n>We find that simply scaling up (or inflating) the minimum $ell$ interpolator by a constant greater than one can improve the generalization error.
  arXiv  Detail & Related papers  (2025-10-22T03:30:27Z)
• When Scores Learn Geometry: Rate Separations under the Manifold Hypothesis [33.93481564069631]
  diffusion models and inverse problems are often interpreted as learning the data distribution in the low-noise limit.<n>We argue that their success arises from implicitly learning the data manifold rather than the full distribution.<n>We show that concentration on data support can be achieved with a score error of $o(sigma-2)$, whereas recovering the specific data distribution requires a much stricter $o(1)$ error.
  arXiv  Detail & Related papers  (2025-09-29T15:18:43Z)
• Mesoscopic Fluctuations and Multifractality at and across Measurement-Induced Phase Transition [46.176861415532095]
  We explore statistical fluctuations over the ensemble of quantum trajectories in a model of two-dimensional free fermions.<n>Our results exhibit a remarkable analogy to Anderson localization, with $G_AB$ corresponding to two-terminal conductance.<n>Our findings lay the groundwork for mesoscopic theory of monitored systems, paving the way for various extensions.
  arXiv  Detail & Related papers  (2025-07-15T13:44:14Z)
• Improved Learning via k-DTW: A Novel Dissimilarity Measure for Curves [48.84313029960523]
  We introduce a novel dissimilarity measure for polygonal curves called $k$-Dynamic Time Warping ($k$-DTW)<n>$k$-DTW has stronger metric properties than Dynamic Time Warping (DTW) and is more robust to outliers than the Fr'echet distance.<n>We show interesting properties of $k$-DTW and give an exact algorithm as well as a $(1+varepsilon)$-approximation algorithm for $k$-DTW.
  arXiv  Detail & Related papers  (2025-05-29T13:25:45Z)
• Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks [54.177130905659155]
  Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks. In this paper, we study a suitable function space for over- parameterized two-layer neural networks with bounded norms.
  arXiv  Detail & Related papers  (2024-04-29T15:04:07Z)
• Clustered Switchback Designs for Experimentation Under Spatio-temporal Interference [44.644520116360106]
  We estimate the global average treatment effect (GATE), the difference between average outcomes having exposed all units at all times to treatment or to control.<n>We propose a clustered switchback design, where units are grouped into clusters and time steps are grouped into blocks.<n>We show that for graphs that admit good clustering, a truncated Horvitz-Thompson estimator achieves a $tilde O(1/NT)$ mean squared error (MSE)<n>Our results simultaneously generalize the results from citethu2022switchback,ugander2013graph and citetleung2022rate
  arXiv  Detail & Related papers  (2023-12-25T01:00:58Z)
• TIC-TAC: A Framework for Improved Covariance Estimation in Deep Heteroscedastic Regression [109.69084997173196]
  Deepscedastic regression involves jointly optimizing the mean and covariance of the predicted distribution using the negative log-likelihood. Recent works show that this may result in sub-optimal convergence due to the challenges associated with covariance estimation. We study two questions: (1) Does the predicted covariance truly capture the randomness of the predicted mean? Our results show that not only does TIC accurately learn the covariance, it additionally facilitates an improved convergence of the negative log-likelihood.
  arXiv  Detail & Related papers  (2023-10-29T09:54:03Z)
• Kernel-Based Tests for Likelihood-Free Hypothesis Testing [21.143798051525646]
  Given $n$ observations from two balanced classes, consider the task of labeling an additional $m$ inputs that are known to all belong to emphone of the two classes. Special cases of this problem are well-known; when $m=1$ it corresponds to binary classification; and when $mapprox n$ it is equivalent to two-sample testing. In recent work it was discovered that there is a fundamental trade-off between $m$ and $n$: increasing the data sample $m$ reduces the amount $n$ of training/simulation data needed.
  arXiv  Detail & Related papers  (2023-08-17T15:24:03Z)
• Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models [49.81937966106691]
  We develop a suite of non-asymptotic theory towards understanding the data generation process of diffusion models. In contrast to prior works, our theory is developed based on an elementary yet versatile non-asymptotic approach.
  arXiv  Detail & Related papers  (2023-06-15T16:30:08Z)
• Topology-aware Generalization of Decentralized SGD [91.59494285490784]
  We show that the generalizability of D-SGD is positively correlated with the spectral gap.<n>To our best knowledge, this is the first work on the generalization of D-SGD.
  arXiv  Detail & Related papers  (2022-06-25T16:03:48Z)
• Dimension-agnostic inference using cross U-statistics [33.17951971728784]
  We introduce an approach that uses variational representations of existing test statistics along with sample splitting and self-normalization. The resulting statistic can be viewed as a careful modification of degenerate U-statistics, dropping diagonal blocks and retaining off-diagonal blocks.
  arXiv  Detail & Related papers  (2020-11-10T12:21:34Z)
• A Random Matrix Analysis of Random Fourier Features: Beyond the Gaussian Kernel, a Precise Phase Transition, and the Corresponding Double Descent [85.77233010209368]
  This article characterizes the exacts of random Fourier feature (RFF) regression, in the realistic setting where the number of data samples $n$ is all large and comparable. This analysis also provides accurate estimates of training and test regression errors for large $n,p,N$.
  arXiv  Detail & Related papers  (2020-06-09T02:05:40Z)
• Minimum optical depth multiport interferometers for approximating arbitrary unitary operations and pure states [37.69303106863453]
  We address the problem of, using multiport interferometers, approximating with a given infidelity any pure state preparation and any unitary operation.<n>By means of numerical calculations, we show that pure states, in any dimension $d$, can be prepared with infidelity.
  arXiv  Detail & Related papers  (2020-02-04T15:40:49Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.