Paraphrase-Induced Output-Mode Collapse: When LLMs Break Character Under Semantically Equivalent Inputs

When the substantive content of a request is rewritten, do large language models still answer in the format the original task asked for? We find that they often do not, even at temperature zero. On a 150-query evaluation over five compact 2025-era LLMs and four task types, we observe a systematic failure mode we call prompt-variant output-mode collapse: when a closed-form prompt asks for a bare label or a single choice token, content-preserving prompt variants can push the model into conversational prose, the requested format dissolves, and exact-match evaluation pipelines silently misjudge the result. To make this measurable, we release PARACONSIST, a 900-prompt benchmark of 150 base queries with five lexical, syntactic, and semantic-expansion prompt variants each, and a Semantic Consistency Score that decomposes prompt-variant robustness into answer consistency, sentence-BERT semantic similarity, and length stability. Under a whole-word answer-set match, only ~22% of closed-form variant responses preserve the ground-truth label inside their output, while ~78% drift away from the answer space entirely. In our pool, the dominant predictor of collapse is task structure rather than model identity, with model differentiation jointly carried by answer consistency and length stability. Robustness audits should therefore track response-mode preservation as a first-class reliability target alongside answer accuracy.

When Does LLM Self-Correction Help? A Control-Theoretic Markov Diagnostic and Verify-First Intervention

Iterative self-correction is widely used in agentic LLM systems, but when repeated refinement helps versus hurts remains unclear. We frame self-correction as a cybernetic feedback loop in which the same language model serves as both controller and plant, and use a two-state Markov model over {Correct, Incorrect} to operationalize a simple deployment diagnostic: iterate only when ECR/EIR > Acc/(1 - Acc). In this view, EIR functions as a stability margin and prompting functions as lightweight controller design. Across 7 models and 3 datasets (GSM8K, MATH, StrategyQA), we find a sharp near-zero EIR threshold (<= 0.5%) separating beneficial from harmful self-correction. Only o3-mini (+3.4 pp, EIR = 0%), Claude Opus 4.6 (+0.6 pp, EIR ~ 0.2%), and o4-mini (+/-0 pp) remain non-degrading; GPT-5 degrades by -1.8 pp. A verify-first prompt ablation provides causal evidence that this threshold is actionable through prompting alone: on GPT-4o-mini it reduces EIR from 2% to 0% and turns -6.2 pp degradation into +0.2 pp (paired McNemar p < 10^-4), while producing little change on already-sub-threshold models. ASC further illustrates the stopping trade-off: it halts harmful refinement but incurs a 3.8 pp confidence-elicitation cost. Overall, the paper argues that self-correction should be treated not as a default behavior, but as a control decision governed by measurable error dynamics.