Probabilistic Autoencoder Using Fisher Information.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Physics

Background:

• Neural networks are increasingly utilized across scientific fields, including physics.
• Variational Autoencoders (VAEs) compress high-dimensional data into a lower-dimensional latent space with probabilistic interpretations.
• Standard VAE encoders provide uncertainty estimates as variance, but lack cross-correlation information.

Purpose of the Study:

• Introduce a novel autoencoder architecture, FisherNet.
• Derive latent space uncertainty from the decoder using the Fisher information metric, unlike traditional VAEs.
• Investigate theoretical and experimental advantages of FisherNet, including uncertainty quantification and cross-correlations.

Main Methods:

• Developed the FisherNet architecture, an extension of the autoencoder.
• Implemented uncertainty quantification derived from the decoder via the Fisher information metric.
• Compared FisherNet's performance against a standard Variational Autoencoder (VAE).

Main Results:

• FisherNet provides direct uncertainty quantification and accounts for uncertainty cross-correlations.
• Experimental results show FisherNet achieves more accurate data reconstructions than comparable VAEs.
• FisherNet demonstrates improved learning performance scaling with the number of latent space dimensions.

Conclusions:

• FisherNet offers a theoretically advantageous approach to uncertainty quantification in autoencoders.
• The proposed architecture surpasses standard VAEs in data reconstruction accuracy and learning efficiency.
• FisherNet represents a significant advancement in applying neural networks for complex data analysis in physics and other sciences.