Techniques of performing operations using a hybrid analog-digital processor

A system for performing matrix operations, the system comprising:

• a hybrid analog-digital processor, the hybrid analog-digital processor comprising:
• a digital controller;
• an analog processor;
• and
• memory configured to store digital values encoded in a number format that uses less than 32 bits to represent a number;
• wherein the hybrid analog-digital processor is configured to:
• perform, using the analog processor, a matrix operation to obtain at least one output, the at least one output encoded in the number format and the matrix operation is performed as part of training a machine learning model;
• determine, using the at least one output, an unbiased estimate of a matrix operation result;
• determine, using the matrix operation result encoded in the number format, a parameter gradient for parameters of the machine learning model;
• update the parameters of the machine learning model using the parameter gradient;
• and
• store, in the memory, the unbiased estimate of the matrix operation result encoded in the number format.

A non-transitory computer-readable storage medium storing instructions that, when executed by a hybrid analog-digital processor, cause the hybrid analog-digital processor to perform a method of performing matrix operations, the hybrid analog-digital processor comprising a digital controller and an analog processor, the hybrid analog-digital processor configured to store digital values in memory encoded in a number format that uses less than 32 bits to represent a number, the method comprising:

• performing, using the analog processor, a matrix operation to obtain at least one output, the at least one output encoded in the number format;
• determining, using the at least one output, an unbiased estimate of a matrix operation result based on a probability distribution modeling noise of the analog processor;
• and
• storing, in the memory, the unbiased estimate of the matrix operation result encoded in the number format.