Abstract: Methods and apparatus for pre-processing first data for use with a trained machine learning model. In some embodiments, the method may comprise accessing the first data, wherein the first data has a first precision; generating, based on at least a first portion of the first data, second data having a second precision lower than the first precision; and providing the second data as input to the trained machine learning model to generate model output.

Abstract: Techniques for computing matrix operations for arbitrarily large matrices on a finite-sized hybrid analog-digital matrix processor are described. Techniques for gain adjustment in a finite-sized hybrid analog-digital matrix processor are described which enable the system to obtain higher energy efficiencies, greater physical density and improved numerical accuracy. In some embodiments, these techniques enable maximization of the predictive accuracy of a GEMM-based convolutional neural network using low-precision data representations.

Abstract: Aspects of the present application relate to techniques for computing convolutions and cross-correlations of input matrices. A first technique is based on the transformation of convolution operations into a matrix-vector product. A second technique is based on two-dimensional matrix multiplication. A third technique is based on the convolution theorem, which states that convolutions correspond to multiplications in a transform space. Embodiments include methods for computing convolutions of a filter matrix and an input data matrix; apparatuses for computing convolutions of a filter matrix and an input data matrix; and a non-transitory computer readable medium programmed with instructions that, when executed by a processor perform a method for computing convolutions of a filter matrix and an input data matrix.

Abstract: Techniques for computing matrix operations for arbitrarily large matrices on a finite-sized hybrid analog-digital matrix processor are described. Techniques for gain adjustment in a finite-sized hybrid analog-digital matrix processor are described which enable the system to obtain higher energy efficiencies, greater physical density and improved numerical accuracy. In some embodiments, these techniques enable maximization of the predictive accuracy of a GEMM-based convolutional neural network using low-precision data representations.

Abstract: Systems and methods for performing signed matrix operations using a linear photonic processor are provided. The linear photonic processor is formed as an array of first amplitude modulators and second amplitude modulators, the first amplitude modulators configured to encode elements of a vector into first optical signals and the second amplitude modulators configured to encode a product between the vector elements and matrix elements into second optical signals. An apparatus may be used to implement a signed value of an output of the linear processor. The linear photonic processor may be configured to perform matrix-vector and/or matrix-matrix operations.

Abstract: Systems and methods for performing signed matrix operations using a linear photonic processor are provided. The linear photonic processor is formed as an array of first amplitude modulators and second amplitude modulators, the first amplitude modulators configured to encode elements of a vector into first optical signals and the second amplitude modulators configured to encode a product between the vector elements and matrix elements into second optical signals. An apparatus may be used to implement a signed value of an output of the linear processor. The linear photonic processor may be configured to perform matrix-vector and/or matrix-matrix operations.

Abstract: Techniques for computing matrix operations for arbitrarily large matrices on a finite-sized hybrid analog-digital matrix processor are described. Techniques for gain adjustment in a finite-sized hybrid analog-digital matrix processor are described which enable the system to obtain higher energy efficiencies, greater physical density and improved numerical accuracy. In some embodiments, these techniques enable maximization of the predictive accuracy of a GEMM-based convolutional neural network using low-precision data representations.

Abstract: Systems and methods for performing signed matrix operations using a linear photonic processor are provided. The linear photonic processor is formed as an array of first amplitude modulators and second amplitude modulators, the first amplitude modulators configured to encode elements of a vector into first optical signals and the second amplitude modulators configured to encode a product between the vector elements and matrix elements into second optical signals. An apparatus may be used to implement a signed value of an output of the linear processor. The linear photonic processor may be configured to perform matrix-vector and/or matrix-matrix operations.

Abstract: Techniques for computing matrix operations for arbitrarily large matrices on a finite-sized hybrid analog-digital matrix processor are described. Techniques for gain adjustment in a finite-sized hybrid analog-digital matrix processor are described which enable the system to obtain higher energy efficiencies, greater physical density and improved numerical accuracy. In some embodiments, these techniques enable maximization of the predictive accuracy of a GEMM-based convolutional neural network using low-precision data representations.

Abstract: Systems and methods for performing matrix operations using a path-number balanced optical network are provided. The optical network is formed as an array including active optical components and passive optical components arranged at a substantially central location of the array. The optical network includes at least NM active optical components which are used to implement a first matrix of any size N×M by embedding the first matrix in a second matrix of a larger size. The optical network performs matrix-vector and matrix-matrix operations by propagating one or more pluralities of optical signals corresponding to an input vector through the optical network.

Abstract: Systems and methods for performing signed matrix operations using a linear photonic processor are provided. The linear photonic processor is formed as an array of first amplitude modulators and second amplitude modulators, the first amplitude modulators configured to encode elements of a vector into first optical signals and the second amplitude modulators configured to encode a product between the vector elements and matrix elements into second optical signals. An apparatus may be used to implement a signed value of an output of the linear processor. The linear photonic processor may be configured to perform matrix-vector and/or matrix-matrix operations.

Abstract: Systems and methods for performing signed matrix operations using a linear photonic processor are provided. The linear photonic processor is formed as an array of first amplitude modulators and second amplitude modulators, the first amplitude modulators configured to encode elements of a vector into first optical signals and the second amplitude modulators configured to encode a product between the vector elements and matrix elements into second optical signals. An apparatus may be used to implement a signed value of an output of the linear processor. The linear photonic processor may be configured to perform matrix-vector and/or matrix-matrix operations.

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.

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.

Abstract: Methods and systems for training neural networks using low-bitwidth accelerators are described. The methods described herein use moment-penalization functions. For example, a method comprises producing a modified data set by training a neural network using a moment-penalization function and the data set. The moment-penalization function is configured to penalize a moment associated with the neural network. Training the neural network in turn comprises quantizing the data set to obtain a fixed-point data set so that the fixed-point data set represents the data set in a fixed-point representation, and passing the fixed-point data set through an analog accelerator. The inventors have recognized that training a neural network using a modified objective function augments the accuracy and robustness of the neural network notwithstanding the use of low-bitwidth accelerators.

Abstract: Systems and methods for performing signed matrix operations using a linear photonic processor are provided. The linear photonic processor is formed as an array of first amplitude modulators and second amplitude modulators, the first amplitude modulators configured to encode elements of a vector into first optical signals and the second amplitude modulators configured to encode a product between the vector elements and matrix elements into second optical signals. An apparatus may be used to implement a signed value of an output of the linear processor. The linear photonic processor may be configured to perform matrix-vector and/or matrix-matrix operations.

Abstract: Described herein are techniques of training a machine learning model and performing inference using an analog processor. Some embodiments mitigate the loss in performance of a machine learning model resulting from a lower precision of an analog processor by using an adaptive block floating-point representation of numbers for the analog processor. Some embodiments mitigate the loss in performance of a machine learning model due to noise that is present when using an analog processor. The techniques involve training the machine learning model such that it is robust to noise.

Abstract: Techniques for computing matrix operations for arbitrarily large matrices on a finite-sized hybrid analog-digital matrix processor are described. Techniques for gain adjustment in a finite-sized hybrid analog-digital matrix processor are described which enable the system to obtain higher energy efficiencies, greater physical density and improved numerical accuracy. In some embodiments, these techniques enable maximization of the predictive accuracy of a GEMM-based convolutional neural network using low-precision data representations.

Abstract: Systems and methods for performing matrix operations using a path-number balanced optical network are provided. The optical network is formed as an array including active optical components and passive optical components arranged at a substantially central location of the array. The optical network includes at least NM active optical components which are used to implement a first matrix of any size N×M by embedding the first matrix in a second matrix of a larger size. The optical network performs matrix-vector and matrix-matrix operations by propagating one or more pluralities of optical signals corresponding to an input vector through the optical network.

Abstract: A training system for training a machine learning model such as a neural network may have a different configuration and/or hardware components than a target device that employs the trained neural network. For example, the training system may use a higher precision format to represent neural network parameters than the target device. In another example, the target device may use analog and digital processing hardware to compute an output of the neural network whereas the training system may have used only digital processing hardware to train the neural network. The difference in configuration and/or hardware components of the target device may introduce quantization error into parameters of the neural network, and thus affect performance of the neural network on the target device. Described herein is a training system that trains a neural network for use on a target device that reduces loss in performance resulting from quantization error.