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arxiv: 2601.05905 · v2 · submitted 2026-01-09 · 💻 cs.CL · cs.AI· cs.HC· cs.LG· cs.MA

Illusions of Confidence? Diagnosing LLM Truthfulness via Neighborhood Consistency

Haoming Xu , Ningyuan Zhao , Yunzhi Yao , Weihong Xu , Hongru Wang , Xinle Deng , Shumin Deng , Jeff Z. Pan
show 2 more authors
Huajun Chen Ningyu Zhang
This is my paper

Pith reviewed 2026-05-16 15:47 UTC · model grok-4.3

classification 💻 cs.CL cs.AIcs.HCcs.LGcs.MA
keywords LLM truthfulnessneighborhood consistencybelief robustnesscontextual interferenceself-consistencystructure-aware trainingcognitive stress testing
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The pith

Even perfectly self-consistent LLM answers can collapse under mild contextual changes, requiring a neighborhood-based consistency measure for true robustness.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that standard self-consistency in LLMs masks brittle beliefs. Facts can fail under mild contextual interference despite perfect consistency. It proposes Neighbor-Consistency Belief (NCB) to measure structural robustness by checking coherence across conceptual neighborhoods. Validation through a cognitive stress-testing protocol confirms that high-NCB responses hold up better. Structure-Aware Training optimizes this to reduce long-tail knowledge brittleness by around 30 percent.

Core claim

Even facts answered with perfect self-consistency can rapidly collapse under mild contextual interference. Neighbor-Consistency Belief (NCB) provides a structural measure of belief robustness by evaluating response coherence across a conceptual neighborhood, and Structure-Aware Training optimizes context-invariant belief structure to improve stability.

What carries the argument

Neighbor-Consistency Belief (NCB), which evaluates response coherence across a conceptual neighborhood to measure belief robustness under contextual perturbations.

Load-bearing premise

Conceptual neighborhoods around facts can be defined to capture relevant contextual perturbations without arbitrary choices affecting stability.

What would settle it

If high-NCB facts collapse at rates similar to low-NCB facts under interference, the measure would not predict robustness effectively.

Figures

Figures reproduced from arXiv: 2601.05905 by Haoming Xu, Hongru Wang, Huajun Chen, Jeff Z. Pan, Ningyuan Zhao, Ningyu Zhang, Shumin Deng, Weihong Xu, Xinle Deng, Yunzhi Yao.

Figure 1
Figure 1. Figure 1: High Self-Consistency ̸= Robust Belief. Despite perfect self-consistency on the “IMU Vice￾President” fact, the model is susceptible to contextual interference: accuracy drops to 33.8%, showing that high-consistency doesn’t imply robust belief. where LLMs operate with retrieval-augmented gen￾eration (RAG) (Gao et al., 2023), multi-agent col￾laboration (Guo et al., 2024), and complex prompt engineering (Saho… view at source ↗
Figure 2
Figure 2. Figure 2: NCB estimates the belief state by aggregating [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Experiment Settings of the Stress Tests. Inspired by the classic Asch Conformity Experiments and Source Credibility theory, we subject the model to two cognitive stress protocols: (1) Peer Quantity, which simulates social pressure via varying levels of multi-agent consensus, and (2) Source Credibility, which evaluates the model’s resistance to authoritative but misleading contexts. Detailed prompts are pro… view at source ↗
Figure 4
Figure 4. Figure 4: Analysis of Belief Robustness under Stress Tests. (a) Impact of Interference Data Size: Accuracy trends for Standard, CoT, and Reflection strategies as interference increases (N = 1 . . . 10). ,→ Insight 1: Inference￾time strategies fail to consistently filter contextual noise. (b) Impact of Interference Configurations: Accuracy under Peer Quantity (Left) and Source Credibility (Right) variations. ,→ Insig… view at source ↗
Figure 5
Figure 5. Figure 5: Illustration of the Data Case. a high confidence score (> 0.7) that the original gold answer remained valid were retained. C.2 Neighbor Generation For each target fact (q ∗ , E ∗ ), we developed a specialized generation pipeline using DeepSeek￾V3.2 to construct the belief neighborhood. To ensure the neighbors function as valid “consis￾tency checks,” we enforced a Truth-Anchored approach where questions are… view at source ↗
Figure 6
Figure 6. Figure 6: The Annotation Web Interface used for human [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Ablation of the only correct answer’s position. [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Coverage across four LLMs under Stress Tests. [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The performance of different quantities of Neighbor Questions. [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The performance of different weights of Neighbor Questions. [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
read the original abstract

As Large Language Models (LLMs) are increasingly deployed in real-world settings, correctness alone is insufficient. Reliable deployment requires maintaining truthful beliefs under contextual perturbations. Existing evaluations largely rely on point-wise confidence like Self-Consistency, which can mask brittle belief. We show that even facts answered with perfect self-consistency can rapidly collapse under mild contextual interference. To address this gap, we propose Neighbor-Consistency Belief (NCB), a structural measure of belief robustness that evaluates response coherence across a conceptual neighborhood. To validate the efficiency of NCB, we introduce a new cognitive stress-testing protocol that probes outputs stability under contextual interference. Experiments across multiple LLMs show that the performance of high-NCB data is relatively more resistant to interference. Finally, we present Structure-Aware Training (SAT), which optimizes context-invariant belief structure and reduces long-tail knowledge brittleness by approximately 30%. Code is available at https://github.com/zjunlp/belief.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that point-wise self-consistency is insufficient for LLM truthfulness because even perfectly consistent answers can collapse under mild contextual interference. It introduces Neighbor-Consistency Belief (NCB) as a structural robustness metric based on response coherence across conceptual neighborhoods, validates NCB via a new cognitive stress-testing protocol, and proposes Structure-Aware Training (SAT) that optimizes context-invariant belief structure, reporting an approximate 30% reduction in long-tail knowledge brittleness.

Significance. If the central claims hold after clarification, the work supplies a diagnostic beyond self-consistency and a training objective that targets structural invariance, both of which address a practical gap in reliable LLM deployment. The public code release is a positive factor for reproducibility.

major comments (2)
  1. [§3] §3 (Neighborhood Construction): The definition of conceptual neighborhoods is load-bearing for both NCB and SAT, yet the manuscript provides no explicit protocol (embedding similarity threshold, prompt templates, perturbation operators, or radius). Without these details it is impossible to determine whether measured stability improvements are non-arbitrary or whether SAT gains arise from alignment between the training distribution and the test neighborhoods.
  2. [Experiments] Experiments and Results (SAT evaluation): The headline claim of an approximately 30% reduction in brittleness must specify the exact metric, the precise baseline (standard SFT, self-consistency fine-tuning, etc.), number of runs, and statistical controls. If the reduction is measured only on the same neighborhood distribution used for training, the result risks circularity.
minor comments (1)
  1. [Abstract] Abstract: briefly state the neighborhood generation method and stress-test protocol so readers can assess the core contribution without the full text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. The comments highlight important areas for clarification regarding the reproducibility of our neighborhood construction and the precise evaluation of Structure-Aware Training (SAT). We address each point below and will revise the manuscript accordingly to strengthen the presentation of our methods and results.

read point-by-point responses

  1. Referee: [§3] §3 (Neighborhood Construction): The definition of conceptual neighborhoods is load-bearing for both NCB and SAT, yet the manuscript provides no explicit protocol (embedding similarity threshold, prompt templates, perturbation operators, or radius). Without these details it is impossible to determine whether measured stability improvements are non-arbitrary or whether SAT gains arise from alignment between the training distribution and the test neighborhoods.

    Authors: We agree that an explicit protocol is necessary for full reproducibility. In the submitted manuscript, neighborhoods were generated by first computing sentence embeddings with the all-MiniLM-L6-v2 model and selecting the top-k neighbors within a cosine similarity radius of 0.75; prompt templates were instantiated from a fixed set of 8 context-variation patterns (e.g., “In the context of X, is Y true?”); and perturbation operators consisted of synonym substitution and light rephrasing drawn from the same embedding space. We will add a new subsection 3.2 that enumerates the exact embedding model, similarity threshold, radius selection procedure, prompt template inventory, and perturbation operators, together with pseudocode. This addition will also include a short discussion of how training neighborhoods were sampled to avoid trivial overlap with evaluation sets. revision: yes

  2. Referee: [Experiments] Experiments and Results (SAT evaluation): The headline claim of an approximately 30% reduction in brittleness must specify the exact metric, the precise baseline (standard SFT, self-consistency fine-tuning, etc.), number of runs, and statistical controls. If the reduction is measured only on the same neighborhood distribution used for training, the result risks circularity.

    Authors: The reported ~30% reduction is the relative decrease in the brittleness score, defined as the average accuracy drop under the cognitive stress-testing protocol (contextual interference on held-out facts). The baseline is standard supervised fine-tuning (SFT) on the same factual corpus without the structure-aware loss term. All experiments were run five times with distinct random seeds; we report mean and standard deviation and include paired t-test p-values (p < 0.01) in the revised tables. To mitigate circularity concerns, evaluation neighborhoods were constructed with a different embedding model (MPNet) and a larger radius (0.85) than those used during SAT training, ensuring no overlap in the neighbor sets. We will expand the Experiments section with these details, add a dedicated paragraph on train–test neighborhood separation, and include an ablation table comparing SAT against both plain SFT and self-consistency fine-tuning. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in NCB definition or SAT optimization

full rationale

The paper defines Neighbor-Consistency Belief (NCB) explicitly as a coherence measure across a conceptual neighborhood and validates its utility via a separate cognitive stress-testing protocol that probes stability under interference. Structure-Aware Training (SAT) is presented as an optimization procedure that targets context-invariant belief structures, with the ~30% brittleness reduction reported as an empirical experimental outcome across LLMs rather than a quantity forced by the metric's construction. No equations or steps are shown that reduce the central claims to fitted inputs, self-referential definitions, or load-bearing self-citations; the neighborhood construction is treated as an input to the diagnostic rather than derived from the stability results themselves. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 2 invented entities

The claims rest on the assumption that conceptual neighborhoods can be constructed to isolate belief stability, with NCB and SAT as newly introduced constructs whose effectiveness is shown empirically.

free parameters (1)
  • neighborhood radius or similarity threshold
    Parameters used to define which questions count as part of the conceptual neighborhood around a given fact.
axioms (1)
  • domain assumption LLM outputs across semantically related prompts reflect a stable underlying belief structure
    Invoked when treating neighborhood coherence as evidence of robust truthfulness.
invented entities (2)
  • Neighbor-Consistency Belief (NCB) no independent evidence
    purpose: Structural measure of belief robustness
    Newly defined metric for evaluating response coherence across neighborhoods.
  • Structure-Aware Training (SAT) no independent evidence
    purpose: Optimization method for context-invariant beliefs
    New training procedure claimed to reduce brittleness.

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discussion (0)

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