响应感知的粗粒化在摘要介导的意见动力学中的应用
Response-Aware Coarse-Graining in Summary-Mediated Opinion Dynamics
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中文总结 AI 辅助
本研究探讨在摘要介导的意见动力学中，内生粗粒化需保留何种信息以再现集体行为，提出响应感知的粗粒化方法，并揭示两种互补机制及部署影响。
中文摘要 AI 辅助
相互作用的群体日益对其自身集体状态生成的压缩表示作出响应。我们问，这种内生的粗粒化必须保留哪些信息才能再现集体动力学。对于具有吸引、冷漠和排斥的连续意见，这个问题有两个互补的答案。在任何一个严格的$K$-块响应单元内，其中每个代表的立场吸引每个块，动力学精确地归结为平移和分歧。所代表的分布的形状从所有分歧模式中消失，这些模式形成一个均匀锚定的加权符号拉普拉斯系统，而代表的均值误差仅作用于平移。这种简化产生了一个依赖于几何的稳定性边界，并表明流行偏差仅在边际稳定性下通过其投影到中性特征空间而产生长期漂移。在该常见线性响应机制之外，阈值几何使分布信息可观测。诱导的力差异是一个行为定义的积分概率度量；受限力探针识别通用的有限经验讨论，对于有限支持的候选，均匀力误差控制总变差和Wasserstein误差，而支持减少则产生非零失真下限。累积差异表征进一步解释了为什么传输小的摘要可能在响应阈值处保持行为不准确。模式分辨积分、投影粒子模拟、有限大小系综和阈值穿越实验测试了这两种机制。作为部署后果，广播摘要误差作为集体噪声存留，而独立个性化的误差则自平均。该模型是风格化的，未经经验校准；生成的讨论摘要激发了内生、响应感知粗粒化的普遍问题。
英文摘要
Interacting populations increasingly respond to compressed representations generated from their own collective state. We ask which information such an endogenous coarse-graining must preserve in order to reproduce the collective dynamics. The question has two complementary answers for continuous opinions with attraction, indifference, and repulsion. Inside any strict $K$-bloc response cell where every represented stance attracts every bloc, the dynamics reduce exactly to translation and disagreement. The represented distribution's shape cancels from all disagreement modes, which form a homogeneously anchored weighted signed-Laplacian system, while represented-mean error acts only on translation. This reduction yields a geometry-dependent stability boundary and shows that prevalence bias produces secular drift at marginal stability only through its projection onto the neutral eigenspace. Outside that common linear-response regime, threshold geometry makes distributional information observable. The induced force discrepancy is a behavior-defined integral probability metric; restricted force probes identify generic finite empirical discussions, and for finitely supported candidates uniform force error controls total-variation and Wasserstein error while support reduction incurs a nonzero distortion floor. A cumulative-discrepancy characterization further explains why transport-small summaries can remain behaviorally inaccurate at response thresholds. Mode-resolved integrations, projected particle simulations, finite-size ensembles, and threshold-crossing experiments test these two regimes. As a deployment consequence, broadcast summary error survives as collective noise whereas independently personalized error self-averages. The model is stylized and not empirically calibrated; generated discussion summaries motivate the general problem of endogenous, response-aware coarse-graining.
