31,872 research outputs found
AlignFlow: Cycle Consistent Learning from Multiple Domains via Normalizing Flows
Given datasets from multiple domains, a key challenge is to efficiently
exploit these data sources for modeling a target domain. Variants of this
problem have been studied in many contexts, such as cross-domain translation
and domain adaptation. We propose AlignFlow, a generative modeling framework
that models each domain via a normalizing flow. The use of normalizing flows
allows for a) flexibility in specifying learning objectives via adversarial
training, maximum likelihood estimation, or a hybrid of the two methods; and b)
learning and exact inference of a shared representation in the latent space of
the generative model. We derive a uniform set of conditions under which
AlignFlow is marginally-consistent for the different learning objectives.
Furthermore, we show that AlignFlow guarantees exact cycle consistency in
mapping datapoints from a source domain to target and back to the source
domain. Empirically, AlignFlow outperforms relevant baselines on image-to-image
translation and unsupervised domain adaptation and can be used to
simultaneously interpolate across the various domains using the learned
representation.Comment: AAAI 202
Mean field equations on tori: existence and uniqueness of evenly symmetric blow-up solutions
We are concerned with the blow-up analysis of mean field equations. It has
been proven in [6] that solutions blowing-up at the same non-degenerate blow-up
set are unique. On the other hand, the authors in [18] show that solutions with
a degenerate blow-up set are in general non-unique. In this paper we first
prove that evenly symmetric solutions on a flat torus with a degenerate
two-point blow-up set are unique. In the second part of the paper we complete
the analysis by proving the existence of such blow-up solutions by using a
Lyapunov-Schmidt reduction method. Moreover, we deduce that all evenly
symmetric blow-up solutions come from one-point blow-up solutions of the mean
field equation on a "half" torus
- …