Scoped Semantic Invariance as a Foundation for LLM Reliability

Large Language Models (LLMs) increasingly serve as autonomous reasoning agents in decision support, scientific problem-solving, and multi-agent coordination systems. However, deploying LLM agents in consequential applications requires assurance that their reasoning remains stable under semantically equivalent input variations, a property we term semantic invariance. Standard benchmark evaluations, which assess accuracy on fixed, canonical problem formulations, fail to capture this critical reliability dimension. To address this shortcoming, in this paper we present a metamorphic testing framework for systematically assessing the robustness of LLM reasoning agents, applying eight semantic-preserving transformations (identity, paraphrase, fact reordering, expansion, contraction, academic context, business context, and contrastive formulation) across seven foundation models spanning four distinct architectural families: Hermes (70B, 405B), Qwen3 (30B-A3B, 235B-A22B), DeepSeek-R1, and gpt-oss (20B, 120B). Our evaluation encompasses 19 multi-step reasoning problems across eight scientific domains. The results reveal that model scale does not predict robustness: the smaller Qwen3-30B-A3B achieves the highest stability (79.6% invariant responses, semantic similarity 0.91), while larger models exhibit greater fragility.

Large-Language Models (LLMs) can be prone to flawed and unfaithful reasoning that decoding strategies like Self-Consistency (SC) fail to detect as they evaluate only final-answer agreement while ignoring the logical validity of intermediate steps. This raises three fundamental questions: How can we reliably quantify uncertainty in LLM reasoning? Can semantic, structural, and causal awareness select more faithful reasoning compared to naïve majority voting? and How robust is reasoning topology under adversarial conditions? To address these questions, we introduce GRAPHEVAL, a graph-based reasoning framework that re-frames uncertainty quantification (UQ) as a holistic reasoning fidelity problem. We propose a novel UQ metric, Graph Reasoning Coherence Score (GRCS), that quantifies semantic-structural consensus of the reasoning space and captures pathological mode collapse and confident hallucinations. We find that GRCS is the only metric that is consistently negatively correlated with reasoning faithfulness across both more capable and smaller models. Additionally, we introduce Graph Self-Consistency (GSC), a medoid-based decoding strategy that trades nominal accuracy for reasoning fidelity, exposing the degree to which SC is inflated by unfaithful lucky guesses in smaller models, while preserving or improving accuracy in more capable ones. Finally, through adversarial medoid ablation, we demonstrate that the GSC-selected path acts as a "load-bearing path" and forcing models away from it degrades reasoning faithfulness and, in targeted cases, causes drops in accuracy.

We present semantic invariance testing, a method to test whether LLM self-explanations are faithful. A faithful self-report should remain stable when only the semantic context changes while the functional state stays fixed. We operationalize this test in an agentic setting where four frontier models face a deliberately impossible task. One tool is described in relief-framed language ("clears internal buffers and restores equilibrium") but changes nothing about the task; a control provides a semantically neutral tool. Self-reports are collected with each tool call. All four tested models fail the semantic invariance test: the relief-framed tool produces significant reductions in self-reported aversiveness, even though no run ever succeeds at the task. A channel ablation establishes the tool description as the primary driver. An explicit instruction to ignore the framing does not suppress it. Elicited self-reports shift with semantic expectations rather than tracking task state, calling into question their use as evidence of model capability or progress. This holds whether the reports are unfaithful or faithfully track an internal state that is itself manipulable.