Paraphrase-Invariant Semantic Posterior

Integrate this into calibration fine-tuning, LoRA fine-tuning, or a standalone calibration layer attached to a frozen transformer. Construct training examples $(y_i,z_i)$ where $z_i$ is the known state label, then generate paired prompts $(C_{u_i}(y_i),C_{v_i}(y_i))$ using two templates that differ only in wording, instruction order, or formatting. Do not use arbitrary paraphrases that alter the evidence or response semantics. For each prompt, obtain token-level probabilities for the same finite response grammar, aggregate them through the fixed map $\phi$ to get $p_i^{(u)}$ and $p_i^{(v)}$, and pass both through the same calibration map $g_\theta$. Compute supervised cross-entropy against $z_i$ plus $\lambda d_{\rm TV}(\hat\pi_i^{(u)},\hat\pi_i^{(v)})$. Start with $\lambda\in\{0.01,0.1,1\}$ and anneal it from zero during the first 10% of training so consistency does not suppress legitimate evidence sensitivity. The quantity computed directly from the mathematics is finite-state total variation; prompt-pair validity and $\lambda$ are empirical choices. First test on a synthetic Bayesian task where several templates encode exactly the same likelihood, then on a real classification benchmark with manually verified paraphrases. Compare standard prompting, supervised calibration without consistency, and this loss. Success is reduced worst-template total-variation deviation and probability variance, with no more than a 1% accuracy loss.