Exploiting low-rank structure for optical optimization and learning
Hiroshi Yamashita, Ken-ichi Okubo, Suguru Shimomura, Yusuke Ogura, Jun Tanida, and Hideyuki Suzuki, “Low-Rank Combinatorial Optimization and Statistical Learning by Spatial Photonic Ising Machine,” Physical Review Letters 131, 063801 (2023).
Interactions among many variables can sometimes be expressed as a sum of only a few components. This study exploits such low-rank structure in a computing model for combinatorial optimization and statistical learning with spatial photonic Ising machines. The basic machine supports rank-one interactions. Combining optical measurements taken with different amplitude patterns in a weighted sum extends this to general Ising models without changing the optical layout. For low-rank problems, the energy of a candidate solution involving many variables can be evaluated with few optical measurements.
To demonstrate this property, the authors formulate the 0–1 knapsack problem with integer weights as a rank-two Ising model and test it optically. They also derive a Boltzmann-machine learning rule and demonstrate handwritten-digit learning, classification, and sampling numerically with low-rank models. An optical experiment samples the digit “0” from a trained low-rank model, illustrating the potential of computing that exploits low-rank structure.
