Propagating reduced-precision on computation graphs

A system comprising:

• a data processing apparatus comprising one or more processors;
• and
• a memory storage apparatus in data communication with the data processing apparatus, the memory storage apparatus storing instructions executable by the data processing apparatus and that upon such execution cause the data processing apparatus to perform operations comprising:
• receiving data specifying a directed graph that includes operators for a program, each operator representing a numerical operation performed by a processor, wherein the operators include (i) a set of first operators that each represent a numerical operation performed on numerical values having a first level of precision and (ii) a set of second operators that each represent a numerical operation performed on numerical values having a second level of precision that is a lower level of precision than the first level of precision;
• for at least a subset of one or more of the first operators:
• identifying, for the first operator, one or more downstream operators that each represent a numerical operation performed on an output of the first operator, each downstream operator being an operator that is performed after the first operator and using the output of the first operator;
• determining whether each downstream operator represents a numerical operation that is performed on input values having the second level of precision;
• and
• whenever each downstream operator for the first operator represents a numerical operation that is performed on input values having the second level of precision:
• adjusting a precision of numerical values output by the operation represented by the first operator to the second level of precision;
• determining whether the first operator is a precision pass-through operator that passes an input precision of the precision pass-through operator to an output of the precision pass-through operator such that the output of the precision pass-through operator has a precision that matches the input precision;
• and
• whenever the first operator is a precision pass-through operator:
• determining whether an output precision of each upstream operator for the first operator is the first level of precision;
• and leaving the precision of numerical values input to the first operator unchanged in response to determining that the output precision of each upstream operator for the first operator is the first level of precision;
• generating a modified version of the program including each adjusted first operator for which the precision of the numerical values has been adjusted;
• and
• executing, by one or more hardware processors of the data processing apparatus, the modified version of the program.

A non-transitory computer storage medium encoded with a computer program, the program comprising instructions that when executed by one or more data processing apparatus cause the one or more data processing apparatus to perform operations comprising:

• receiving data specifying a directed graph that includes operators for a program, each operator representing a numerical operation performed by a processor, wherein the operators include (i) a set of first operators that each represent a numerical operation performed on numerical values having a first level of precision and (ii) a set of second operators that each represent a numerical operation performed on numerical values having a second level of precision that is a lower level of precision than the first level of precision;
• for at least a subset of one or more of the first operators:
• identifying, for the first operator, one or more downstream operators that each represent a numerical operation performed on an output of the first operator, each downstream operator being an operator that is performed after the first operator and using the output of the first operator;
• determining whether each downstream operator represents a numerical operation that is performed on input values having the second level of precision;
• and
• whenever each downstream operator for the first operator represents a numerical operation that is performed on input values having the second level of precision:
• adjusting a precision of numerical values output by the operation represented by the first operator to the second level of precision;
• determining whether the first operator is a precision pass-through operator that passes an input precision of the precision pass-through operator to an output of the precision pass-through operator such that the output of the precision pass-through operator has a precision that matches the input precision;
• and
• whenever the first operator is a precision pass-through operator:
• determining whether an output precision of each upstream operator for the first operator is the first level of precision;
• and
• leaving the precision of numerical values input to the first operator unchanged in response to determining that the output precision of each upstream operator for the first operator is the first level of precision;
• generating a modified version of the program including each adjusted first operator for which the precision of the numerical values has been adjusted;
• and
• executing, by one or more hardware processors of the data processing apparatus, the modified version of the program.