Optimal relation between continuous rank degradation and discrete corruption in CANDI

Determine the optimal functional relationship between the target continuous rank degradation schedule r*(t), which sets the Gaussian noise level via σ(t), and the discrete corruption rate ρ(t)=1−α(t) in the CANDI hybrid structured noising kernel, so that discrete identity corruption and continuous rank degradation are best aligned across time.

Background

CANDI introduces a structured noising kernel that decouples discrete masking (controlled by α(t)) from Gaussian noise (controlled via a target continuous rank degradation r*(t)). In the paper, a linear schedule is chosen for simplicity to align continuous and discrete corruption over time.

The authors explicitly note that while linear schedules work, identifying the optimal relationship between r*(t) and ρ(t)=1−α(t) is an unresolved design choice, suggesting potential gains from better coordination of discrete and continuous corruption dynamics.