We propose a novel learning framework using neural mean-field (NMF) dynamics for inference and estimation problems on heterogeneous diffusion networks. Our new framework leverages the Mori-Zwanzig formalism to obtain an exact evolution equation of the individual node infection probabilities, which renders a delay differential equation with memory integral approximated by learnable time convolution operators. Directly using information diffusion cascade data, our framework can simultaneously learn the structure of the diffusion network and the evolution of node infection probabilities. Connections between parameter learning and optimal control are also established, leading to a rigorous and implementable algorithm for training NMF. Moreover, we show that the projected gradient descent method can be employed to solve the challenging influence maximization problem, where the gradient is computed extremely fast by integrating NMF forward in time just once in each iteration. Extensive empirical studies show that our approach is versatile and robust to variations of the underlying diffusion network models, and significantly outperform existing approaches in accuracy and efficiency on both synthetic and real-world data.

中文翻译：

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通过神经平均场动力学的影响估计和最大化

我们提出了一种新的学习框架，使用神经平均场 (NMF) 动力学来解决异构扩散网络上的推理和估计问题。我们的新框架利用 Mori-Zwanzig 形式主义来获得单个节点感染概率的精确演化方程，这使得延迟微分方程具有由可学习时间卷积算子近似的记忆积分。直接使用信息扩散级联数据，我们的框架可以同时学习扩散网络的结构和节点感染概率的演变。还建立了参数学习和最优控制之间的联系，从而产生了用于训练 NMF 的严格且可实施的算法。而且，我们表明，投影梯度下降法可用于解决具有挑战性的影响最大化问题，其中通过在每次迭代中对 NMF 及时积分一次，可以非常快速地计算梯度。广泛的实证研究表明，我们的方法对基础扩散网络模型的变化具有通用性和鲁棒性，并且在合成和现实世界数据的准确性和效率方面均显着优于现有方法。