Integrated random projection and dimensionality reduction by propagating light in photonic lattices

Area of Science:

• Photonics and Optical Physics
• Computational Science
• Information Theory

Background:

• Disordered photonic lattices exhibit complex light propagation dynamics.
• Random projections are crucial for dimensionality reduction in machine learning.
• The Johnson-Lindenstrauss lemma provides theoretical guarantees for distance preservation.

Purpose of the Study:

• To propose and analyze a novel method for random projection using disordered photonic lattices.
• To demonstrate the potential of photonic systems for efficient dimension reduction.
• To reduce the computational burden of subsequent neural network processing.

Main Methods:

• Modeling light propagation in photonic lattices with diagonal disorder.
• Characterizing the evolution matrix as a random complex Gaussian matrix.
• Utilizing a random subset of waveguide channels for output collection.

Main Results:

• Light propagation in disordered lattices effectively performs distance-preserving random projections.
• The scheme adheres to the principles of the Johnson-Lindenstrauss lemma.
• Intermediate disorder levels facilitate diffusive light propagation for optimal performance.

Conclusions:

• Disordered photonic lattices offer a physical platform for implementing random projection.
• This photonic approach provides an integrated, low-burden dimension reduction stage.
• The method has significant implications for efficient neural computation and data processing.