Accelerating Weighted Score Matching for Point Processes

Weighted score matching (WSM) avoids intractable intensity integration in the likelihood for point processes, but nested reverse-mode automatic differentiation (AD) for event-coordinate derivatives introduces a training bottleneck. To solve this issue, we propose Taylor-mode WSM, a plug-and-play method that replaces the nested derivative evaluator with a Taylor-mode evaluator while retaining reverse-mode AD for parameter updates. To explain and quantify the acceleration, we develop a program-level cost framework that derives the training-step speedup ratio, characterizes when the speedup is most pronounced, and establishes why the Taylor-mode evaluator is faster. Through experiments across statistical point processes, deep temporal point processes, and deep spatio-temporal point processes (STPPs), our framework explains the varying speedups across the three model families and further reveals that outer backpropagation is the dominant source of acceleration, accounting for 90.4%-99.6% of the total time reduction. Additional studies show that the speedup becomes more pronounced at higher derivative orders, while the advantage persists with increasing event-coordinate dimension. Overall, Taylor-mode WSM achieves an average speedup of $3.85\times$ and up to $5.6\times$ on deep STPPs, without sacrificing model performance.