Systems and methods for training matrix-based differentiable programs

Abstract

Methods and apparatus for training a matrix-based differentiable program using a photonics-based processor. The matrix-based differentiable program includes at least one matrix-valued variable associated with a matrix of values in a Euclidean vector space. The method comprises configuring components of the photonics-based processor to represent the matrix of values as an angular representation, processing, using the components of the photonics-based processor, training data to compute an error vector, determining in parallel, at least some gradients of parameters of the angular representation, wherein the determining is based on the error vector and a current input training vector, and updating the matrix of values by updating the angular representation based on the determined gradients.

What is claimed is: 
     
         1 . A method for training a matrix-based differentiable program using a photonics-based processor, the matrix-based differentiable program including at least one matrix-valued variable associated with a matrix of values in a Euclidean vector space, the method comprising:
 configuring components of the photonics-based processor to represent the matrix of values as an angular representation.   processing, using the components of the photonics-based processor, training data to compute an error vector;   determining in parallel, at least some gradients of parameters of the angular representation, wherein the determining is based on the error vector and a current input training vector; and   updating the matrix of values by updating the angular representation based on the determined gradients;   wherein configuring components of the photonics-based processor to represent the matrix of values as an angular representation comprises:   transforming the matrix of values into at least one unitary matrix   decomposing each unitary matrix into a set of unitary transfer matrices;   configuring the components of the photonics-based processor based on the set of unitary transfer matrices.   
     
     
         2 . The method as claimed in  claim 1  wherein the transforming includes transforming the matrix of values into a plurality of matrices. 
     
     
         3 . The method as claimed in  claim 2  wherein the plurality of matrices includes a first and second unitary matrix and a diagonal matrix. 
     
     
         4 . The method as claimed in  claim 3  wherein the decomposing includes decomposing the first unitary matrix into a first set of unitary transfer matrices. 
     
     
         5 . The method as claimed in  claim 4  wherein the decomposing includes decomposing the second unitary matrix into a second set of unitary transfer matrices. 
     
     
         6 . The method as claimed in  claim 5  wherein the configuring includes configuring a first set of components of the photonics-based processor based on the first set of unitary transfer matrices. 
     
     
         7 . The method as claimed in  claim 6  wherein the configuring includes configuring a second set of components of the photonics-based processor based on the diagonal matrix. 
     
     
         8 . The method as claimed in  claim 7  wherein the configuring includes configuring a third set of components of the photonics-based processor based on the second set of unitary transfer matrices. 
     
     
         9 . A non-transitory computer readable medium encoded with a plurality of instructions that, when executed by at least one photonics-based processor perform a method for training a latent variable graphical model, the latent variable graphical model including at least one matrix-valued latent variable associated with a matrix of values in a Euclidean vector space, the method comprising:
 configuring components of the photonics-based processor to represent the matrix of values as an angular representation.   processing, using the components of the photonics-based processor, training data to compute an error vector;   determining in parallel, at least some gradients of parameters of the angular representation, wherein the determining is based on the error vector and a current input training vector; and   updating the matrix of values by updating the angular representation based on the determined gradients;   wherein configuring components of the photonics-based processor to represent the matrix of values as an angular representation comprises:   transforming the matrix of values into at least one unitary matrix   decomposing each unitary matrix into a set of unitary transfer matrices;   configuring the components of the photonics-based processor based on the set of unitary transfer matrices.   
     
     
         10 . The medium as claimed in  claim 9  wherein the transforming includes transforming the matrix of values into a plurality of matrices. 
     
     
         11 . The medium as claimed in  claim 10  wherein the plurality of matrices includes a first and second unitary matrix and a diagonal matrix. 
     
     
         12 . The medium as claimed in  claim 11  wherein the decomposing includes decomposing the first unitary matrix into a first set of unitary transfer matrices. 
     
     
         13 . The medium as claimed in  claim 12  wherein the decomposing includes decomposing the second unitary matrix into a second set of unitary transfer matrices. 
     
     
         14 . The medium as claimed in  claim 13  wherein the configuring includes configuring a first set of components of the photonics-based processor based on the first set of unitary transfer matrices. 
     
     
         15 . The medium as claimed in  claim 14  wherein the configuring includes configuring a second set of components of the photonics-based processor based on the diagonal matrix. 
     
     
         16 . The medium as claimed in  claim 15  wherein the configuring includes configuring a third set of components of the photonics-based processor based on the second set of unitary transfer matrices. 
     
     
         17 . A photonics-based processing system, comprising: a photonics processor; and
 a non-transitory computer readable medium encoded with a plurality of instructions that, when executed by the photonics processor perform a method for training a latent variable graphical model, the latent variable graphical model including at least one matrix-valued latent variable associated with a matrix of values in a Euclidean vector space, the method comprising:   configuring components of the photonics-based processor to represent the matrix of values as an angular representation.   processing, using the components of the photonics-based processor, training data to compute an error vector;   determining in parallel, at least some gradients of parameters of the angular representation, wherein the determining is based on the error vector and a current input training vector; and   updating the matrix of values by updating the angular representation based on the determined gradients;   wherein configuring components of the photonics-based processor to represent the matrix of values as an angular representation comprises:   transforming the matrix of values into at least one unitary matrix   decomposing each unitary matrix into a set of unitary transfer matrices;   configuring the components of the photonics-based processor based on the set of unitary transfer matrices.   
     
     
         18 . The system as claimed in  claim 17  wherein the transforming includes transforming the matrix of values into a plurality of matrices. 
     
     
         19 . The system as claimed in  claim 18  wherein the plurality of matrices includes a first and second unitary matrix and a diagonal matrix. 
     
     
         20 . The system as claimed in  claim 17  wherein the decomposing includes decomposing the first unitary matrix into a first set of unitary transfer matrices.