Phase Transitions in Affective Meaning Divergence: The Hidden Drift Before the Break
For researchers studying conversational breakdown, AMD provides a theoretically grounded early warning signal that outperforms toxicity and sentiment baselines.
The paper introduces affective meaning divergence (AMD) as a measure of misalignment in emotional interpretation between interlocutors and shows that it exhibits critical slowing down before conversations derail, with significant effects on lexical divergence variance (p<0.001, d=0.36), AMD variance (p=0.001, d=0.26), and dialog-act repair variance (p=0.016, d=0.20) on the CGA-Wiki dataset.
One partner says "Fine" meaning <i>resolution</i>; the other hears <i>surrender</i>. The word is shared; the affective uptake is not. We formalize this as <b>affective meaning divergence (AMD)</b>, the total-variation distance between interlocutors' anchor-conditioned affect distributions. Building on speech-act theory, common-ground accumulation, and entropy-regularized game theory, we derive a logit best-response map whose dynamics undergo a saddle-node bifurcation: when $βα> 4$, a monotone increase in AMD-driven load produces an abrupt, hysteretic collapse of repair coordination. On Conversations Gone Awry (CGA-Wiki; $N=652$), derailing conversations exhibit critical-slowing-down (CSD) signatures across multiple levels: lexical divergence variance ($p<0.001$, $d=0.36$), AMD variance ($p=0.001$, $d=0.26$), and dialog-act repair variance ($p=0.016$, $d=0.20$), all significant after correction and stronger than toxicity and sentiment baselines. AMD provides a distinct temporal signature, with retrospectively measured variance peaking at the bifurcation point while toxicity variance peaks earlier, and is the only indicator grounded in the theoretical framework. Boundary-condition analysis on CGA-CMV ($N=1{,}169$) yields mixed but directionally consistent evidence.