Multi-Rate VAE: Train Once, Get the Full Rate-Distortion Curve

Bae, Juhan; Zhang, Michael R.; Ruan, Michael; Wang, Eric; Hasegawa, So; Ba, Jimmy; Grosse, Roger

doi:10.48550/arxiv.2212.03905

Cited by 1 publication

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our method can be envisioned as simultaneously learning the inverse problem on all possible subdomains (or a subset of subdomains) of the full parameter domain, using a single neural network. Thus, some parallels can be drawn with approaches such as that of Bae et al (2022) where a beta variational autoencoder is trained simultaneously for all values of the � coefficient using a single neural network (a task which would typically require retraining for each � value).…”

Section: Solving Ill-posed Inverse Problems Using Neural Networkmentioning

confidence: 99%

Neural network analysis of neutron and X-ray reflectivity data incorporating prior knowledge

Munteanu,

Starostin,

Greco

et al. 2024

J Appl Crystallogr

View full text Add to dashboard Cite

Due to the ambiguity related to the lack of phase information, determining the physical parameters of multilayer thin films from measured neutron and X-ray reflectivity curves is, on a fundamental level, an underdetermined inverse problem. This ambiguity poses limitations on standard neural networks, constraining the range and number of considered parameters in previous machine learning solutions. To overcome this challenge, a novel training procedure has been designed which incorporates dynamic prior boundaries for each physical parameter as additional inputs to the neural network. In this manner, the neural network can be trained simultaneously on all well-posed subintervals of a larger parameter space in which the inverse problem is underdetermined. During inference, users can flexibly input their own prior knowledge about the physical system to constrain the neural network prediction to distinct target subintervals in the parameter space. The effectiveness of the method is demonstrated in various scenarios, including multilayer structures with a box model parameterization and a physics-inspired special parameterization of the scattering length density profile for a multilayer structure. In contrast to previous methods, this approach scales favourably when increasing the complexity of the inverse problem, working properly even for a five-layer multilayer model and a periodic multilayer model with up to 17 open parameters.

show abstract

Section: Solving Ill-posed Inverse Problems Using Neural Networkmentioning

confidence: 99%