让随机模拟可微分，实现大规模生物系统参数优化。
Exact Discrete Stochastic Simulation with Deep-Learning-Scale Gradient Optimization
- 用连续替代硬采样，使随机轨迹可反向传播梯度。
- 在基因网络中实现98.4%手写数字识别准确率，参数超20万。
- 适合需要高维参数推断的系统生物学与化学动力学研究。
精确的连续时间马尔可夫链（CTMC）随机模拟在离散性与噪声主导系统行为时至关重要，但吉列斯皮类算法中的硬类别采样阻碍了基于梯度的学习。我们通过将前向模拟与反向微分解耦，利用硬类别采样生成精确轨迹，同时通过连续的并行Gumbel-Softmax直通代理传播梯度，消除了这一限制。该方法实现了比现有模拟器大四个数量级的参数规模优化。我们在可逆二聚化模型（0.09%误差）、基因振荡器（1.2%误差）、含203,796个参数的基因调控网络（实现98.4% MNIST准确率，作为深度神经网络基准）以及单通道离子通道门控实验记录（R² = 0.987）上验证了其精度、可扩展性与可靠性。GPU实现达到每秒19亿步，与不可微模拟器规模相当。该工作使精确随机模拟具备大规模并行与自动微分兼容性，推动系统生物学、化学动力学、物理等领域的高维参数推断与逆向设计。
原文摘要 · Abstract (English)
Exact stochastic simulation of continuous-time Markov chains (CTMCs) is essential when discreteness and noise drive system behavior, but the hard categorical event selection in Gillespie-type algorithms blocks gradient-based learning. We eliminate this constraint by decoupling forward simulation from backward differentiation, with hard categorical sampling generating exact trajectories and gradients propagating through a continuous massively-parallel Gumbel-Softmax straight-through surrogate. Our approach enables accurate optimization at parameter scales over four orders of magnitude beyond existing simulators. We validate for accuracy, scalability, and reliability on a reversible dimerization model (0.09% error), a genetic oscillator (1.2% error), a 203,796-parameter gene regulatory network achieving 98.4% MNIST accuracy (a prototypical deep-learning multilayer perceptron benchmark), and experimental patch-clamp recordings of ion channel gating (R^2 = 0.987) in the single-channel regime. Our GPU implementation delivers 1.9 billion steps per second, matching the scale of non-differentiable simulators. By making exact stochastic simulation massively parallel and autodiff-compatible, our results enable high-dimensional parameter inference and inverse design across systems biology, chemical kinetics, physics, and related CTMC-governed domains.
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