$R^2$-VLM: Detecting and Correcting Vision-Language Hallucination via Active Representational Perturbation and Residual Spectral Grounding

Vision-Language Models (VLMs) can confidently generate text that contradicts the visual input, a failure commonly referred to as $perception$ $hallucination$. Existing mitigation methods predominantly analyze unperturbed forward passes, limiting their ability to assess the stability of internal representations under perturbations. We propose $R^2$-VLM, a training-free, single-pass framework for hallucination detection and correction based on active representational perturbation. Our detection module applies structured latent perturbations to the hidden states of a frozen VLM across visual, linguistic, and cross-modal subspaces. These perturbations yield a calibrated hallucination risk score and reveal that joint cross-modal reliability provides a stronger indicator of hallucination than unimodal signals alone. To correct detected failures, we introduce $ResidualSpectralGrounding(RSG)$, which restores visual evidence by additively injecting a per-sample spectral decomposition of the visual representation into the decoder hidden states. We further establish theoretical guarantees showing that the risk score is bounded within $[0,1]$, the adaptive threshold converges, and RSG strictly improves representational energy stability. Empirically, across Qwen2.5-VL (3B/7B) and LLaVA-1.5 (7B) on ColorBench, POPE, and CableDetection, our risk score exhibits a strong correlation with ground-truth correctness, achieving a point-biserial correlation of up to $r=0.54$ and Hedges' effect size of up to $|g|=1.50$ ($p<0.001$). Furthermore, RSG nearly doubles cross-modal representational alignment from $0.35$ to $0.66$ and achieves relative average accuracy improvements of $+2.4$ on color-attribute tasks and $+1.84$ on CableDetection, while avoiding the performance degradation observed with competing subtractive correction baselines.