From Latent Dynamics to Meaningful Representations

Area of Science:

• Machine Learning
• Artificial Intelligence
• Statistical Mechanics
• Dynamical Systems

Background:

• Representation learning is crucial for AI, but learned representations often lack meaning.
• Traditional methods use probability distributions as priors, which are often unavailable or arbitrary.
• Recent work explores using physical principles to guide representation learning.

Purpose of the Study:

• To propose a novel representation learning framework constrained by physical dynamics.
• To overcome limitations of predefined probability distributions in representation learning.
• To develop a method that ensures meaningful and uniquely identifiable latent representations.

Main Methods:

• Developed a dynamics-constrained representation learning framework.
• Restricted latent representations to follow overdamped Langevin dynamics with a learnable transition density.
• Utilized principles from statistical mechanics to define the prior.

Main Results:

• The framework uniquely identifies the ground truth representation.
• Demonstrated effectiveness on various systems, including real-world fluorescent DNA data.
• Successfully identified orthogonal, isometric, and meaningful latent representations.

Conclusions:

• The proposed dynamics-constrained framework offers a natural and effective approach to representation learning.
• Leveraging physical principles provides a data-driven prior, improving representation quality.
• The method shows promise for analyzing complex stochastic dynamical systems.