  Temporal Point Processes (TPPs) hold a pivotal role in modeling event
sequences across diverse domains, including social networking and e-commerce,
and have significantly contributed to the advancement of recommendation systems
and information retrieval strategies. Through the analysis of events such as
user interactions and transactions, TPPs offer valuable insights into
behavioral patterns, facilitating the prediction of future trends. However,
accurately forecasting future events remains a formidable challenge due to the
intricate nature of these patterns. The integration of Neural Networks with
TPPs has ushered in the development of advanced deep TPP models. While these
models excel at processing complex and nonlinear temporal data, they encounter
limitations in modeling intensity functions, grapple with computational
complexities in integral computations, and struggle to capture long-range
temporal dependencies effectively. In this study, we introduce the CuFun model,
representing a novel approach to TPPs that revolves around the Cumulative
Distribution Function (CDF). CuFun stands out by uniquely employing a monotonic
neural network for CDF representation, utilizing past events as a scaling
factor. This innovation significantly bolsters the model's adaptability and
precision across a wide range of data scenarios. Our approach addresses several
critical issues inherent in traditional TPP modeling: it simplifies
log-likelihood calculations, extends applicability beyond predefined density
function forms, and adeptly captures long-range temporal patterns. Our
contributions encompass the introduction of a pioneering CDF-based TPP model,
the development of a methodology for incorporating past event information into
future event prediction, and empirical validation of CuFun's effectiveness
through extensive experimentation on synthetic and real-world datasets.
