To do so, we first form a family of unnormalized densities (or a "path") parameterized by 2 [0, 1] between the two distributions of interest

Hedonic Games (HGs) are a classical framework modeling coalition formation of strategic agents guided by their individual preferences.

Diffusion models (DMs) have been significantly developed and widely used in various applications due to their excellent generative qualities.

Participants are not allowed to modify the training procedure.

While these advances use different algorithmic techniques, e.g., contrastive learning, diffusion, or auto-regressive modeling, they all rest on a common foundation: large datasets containing paired image-text examples.

We derive a tighter inequality than Cauchy-Schwarz Inequality, leverage it to refine Pearson's

Lemma A.2. Algorithm ϕ gives a lower bound on the query γ . That is, ϕ (x, R) γ (x, R).

To address this gap, we study deterministic/stochastic versions of SAM with practical configurations (i.e., constant