This paper presents a general framework for end-to-end mutual information maximization in communication and sensing systems represented by stochastic directed acyclic graphs (DAGs). We derive a unified formula for the (mutual) information gradient with respect to arbitrary internal parameters, utilizing marginal and conditional score functions. We demonstrate that this gradient can be efficiently computed using vector-Jacobian products (VJP) within standard automatic differentiation frameworks, enabling the optimization of complex networks under global resource constraints. Numerical experiments on both linear multipath DAGs and nonlinear channels validate the proposed framework; the results confirm that the estimator, utilizing score functions learned via denoising score matching, accurately reproduces ground-truth gradients and successfully maximizes end-to-end mutual information. Beyond maximization, we extend our score-based framework to a novel unsupervised paradigm: digital twin calibration via Fisher divergence minimization.

翻译：本文提出了一种通用框架，用于在以随机有向无环图表示的通信与感知系统中实现端到端互信息最大化。我们利用边缘和条件分数函数，推导出了关于任意内部参数的（互）信息梯度的统一公式。我们证明，该梯度可以在标准自动微分框架内使用向量-雅可比积高效计算，从而实现在全局资源约束下对复杂网络的优化。在线性多路径有向无环图和非线性信道上的数值实验验证了所提框架的有效性；结果表明，利用通过去噪分数匹配学习得到的分数函数，估计器能够准确复现真实梯度，并成功实现端到端互信息最大化。除最大化问题外，我们将基于分数的框架扩展至一种新颖的无监督范式：通过费希尔散度最小化进行数字孪生校准。