发表机构
Biofisika Institute (CSIC, UPV/EHU); University of the Basque Country; IKERBASQUE, Basque Foundation for Science; University of California（生物物理研究所（西班牙国家研究委员会、巴斯克大学）; 巴斯克大学; 巴斯克科学基金会IKERBASQUE; 加利福尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对离散随机系统的梯度学习问题，提出倾向直通过（PST）估计器，在多基准测试中精度与Gumbel-Softmax直通过相当，且收敛速度更快，可实现大规模随机反应网络的高效训练。
AI 中文摘要
连续时间马尔可夫链（CTMC）是应用科学、物理科学及生物科学中离散随机动力学建模的基础。然而，其与现代基于梯度的机器学习的结合受限于Gillespie类模拟算法固有的严格分类事件选择。我们利用仿射状态更新，通过对归一化反应倾向求导，获得精确的单步条件均值灵敏度。我们将该反向规则与精确正向轨迹结合，定义了倾向直通过（PST）估计器。在轨迹层面，我们证明由各事件组合而成的单步灵敏度可能与精确多步灵敏度存在偏差，我们以闭式形式推导了所得的每步偏差，并证明对于仿射下游依赖，该偏差完全消失。PST在所有基准测试中均达到与Gumbel-Softmax直通过相当的精度：可逆二聚化（误差0.06%）、遗传振荡器（误差1.7%）、含50项任务的抑制子套件（中位数误差0.17%）及膜片钳离子通道记录（R²=0.988）。在匹配设置下，PST在振荡器上的收敛速度快3.0倍，在离子通道上快2.1倍。在深度学习规模下，PST通过严格采样训练了含203796个参数的随机反应网络，达到98.22%的MNIST数字分类准确率。通过对精确条件均值而非松弛样本求导，PST提供了一种无温度、无Gumbel的路径，可通过精确随机轨迹实现可扩展的基于梯度的学习。
英文摘要
Continuous-time Markov chains (CTMCs) provide the backbone for modeling discrete stochastic dynamics across applied, physical, and biological sciences. Their integration with modern gradient-based machine learning, however, is limited by the hard categorical event selection intrinsic to Gillespie-type simulation algorithms. We exploit the affine state update to obtain the exact one-step conditional-mean sensitivity by differentiating normalized reaction propensities. We pair this backward rule with exact forward trajectories to define the propensity straight-through (PST) estimator. At the trajectory level, we show that one-step sensitivities composed across events can depart from the exact multistep sensitivity. We derive the resulting per-step discrepancy in closed form and prove that it vanishes identically for affine downstream dependence. PST matches the accuracy of Gumbel-Softmax straight-through across all benchmarks: reversible dimerization (0.06% error), a genetic oscillator (1.7% error), a 50-task repressilator suite (0.17% median error), and patch-clamp ion-channel recordings ($R^2$ = 0.988). Under matched settings, PST converges 3.0-fold faster on the oscillator and 2.1-fold faster on the ion channel. At deep-learning scale, PST trains a 203,796-parameter stochastic reaction network with hard sampling, reaching 98.22% MNIST digit classification accuracy. By differentiating an exact conditional mean rather than a relaxed sample, PST offers a temperature- and Gumbel-free path to scalable gradient-based learning through exact stochastic trajectories.
Comments16 pages, 5 figures
