We introduce an Indian-buffet-type model for multi-factorial innovation in which each arriving agent may exhibit both previously observed and new features. The number of new features follows a power-law behavior, while the probability of selecting an old feature combines self-reinforcement, depending on the feature-specific popularity, with a mean-field interaction term depending on the average popularity of all observed features. The model is governed by the usual innovation parameters (mass, discount and concentration), together with two additional parameters: one controlling the strength of reinforcement against a forcing input toward zero, and one regulating the intensity of feature interaction. Although the growth of the total number of distinct observed features has the same behavior as in the three-parameter Indian buffet process, the interaction mechanism produces new asymptotic regimes. For aggregate quantities, including the predictive mean, the averaged number of features per agent, the mean inclusion probability, and the mean feature popularity, the phase transition is determined by the comparison between the discount parameter and the weight of the forcing input. For feature-specific quantities, a further transition appears according to the comparison between the interaction level and a critical threshold. In particular, high interaction leads to an asymptotic synchronization of feature-specific inclusion probabilities. We establish strong laws and second-order asymptotic results, including central limit theorems in regimes where martingale fluctuations compete with deterministic or random terms. The analysis relies on novel general results for recursive stochastic dynamics, which may be useful beyond the present framework.

翻译：我们提出了一种印度自助餐式多因素创新模型，其中每个新到达的智能体可能表现出先前观察到的特征和新特征。新特征的数量服从幂律行为，而选择旧特征的概率则结合了自我强化（取决于特征特异的流行度）与一个平均场交互项（取决于所有观察到的特征的平均流行度）。该模型由常规创新参数（质量、折扣和集中度）控制，另加两个额外参数：一个控制强化相对于向零强迫输入的强度，另一个调节特征交互的强度。尽管总的不同观察到特征数量的增长与三参数印度自助过程具有相同行为，但交互机制产生了新的渐近状态。对于聚合量（包括预测均值、每个智能体的平均特征数、平均包含概率和平均特征流行度），相变由折扣参数与强迫输入权重之间的比较决定。对于特征特异的量，进一步出现根据交互水平与临界阈值比较的相变。特别地，高交互导致特征特异的包含概率渐近同步。我们建立了强定律和二阶渐近结果，包括在鞅波动与确定性项或随机项竞争情况下的中心极限定理。分析依赖于递归随机动力学的新的一般性结果，这可能在本框架之外也有用。