The Disappearance of Timestep Embedding in Modern Time-Dependent Neural Networks

Dynamical systems are often time-varying, whose modeling requires a function that evolves with respect to time. Recent studies such as the neural ordinary differential equation proposed a time-dependent neural network, which provides a neural network varying with respect to time. However, we claim that the architectural choice to build a time-dependent neural network significantly affects its time-awareness but still lacks sufficient validation in its current states. In this study, we conduct an in-depth analysis of the architecture of modern time-dependent neural networks. Here, we report a vulnerability of vanishing timestep embedding, which disables the time-awareness of a time-dependent neural network. Furthermore, we find that this vulnerability can also be observed in diffusion models because they employ a similar architecture that incorporates timestep embedding to discriminate between different timesteps during a diffusion process. Our analysis provides a detailed description of this phenomenon as well as several solutions to address the root cause. Through experiments on neural ordinary differential equations and diffusion models, we observed that ensuring alive time-awareness via proposed solutions boosted their performance, which implies that their current implementations lack sufficient time-dependency.