Fault-tolerant dot product engine
Examples disclosed herein relate to a fault-tolerant dot product engine. The fault-tolerant dot product engine has a crossbar array having a number l of row lines and a number n of column lines intersecting the row lines to form l×n memory locations, with each memory location having a programmable memristive element and defining a matrix value. A number l of digital-to-analog converters are coupled to the row lines of the crossbar array to receive an input signal and a number n of analog-to-digital converters are coupled to the column lines of the crossbar array to generate an output signal. The output signal is a dot product of the input signal and the matrix values in the crossbar array, wherein a number m<n of the n column lines in the crossbar array are programmed with matrix values used to detect errors in the output signal.
1. A fault-tolerant computing device for determining a dot product, comprising:
a dot product engine having a number 1 of row lines and a number n of column lines intersecting the row lines to form l×n memory locations in a crossbar array, each memory location comprising a programmable memristive element and defining a matrix value; and
an encoder circuit to generate matrix values for m of the n columns in the dot product engine based on matrix values for a first k of the n columns and according to an error detection capability, wherein n=k+m.
2. The fault-tolerant computing device of claim 1 , wherein the dot product engine comprises:
a number 1 of digital-to-analog converters coupled to the row lines of the crossbar array to receive an input signal; and
a number n of analog-to-digital converters coupled to the column lines of the crossbar array to generate an output signal that is a dot product of the input signal and the matrix values in the crossbar array.
3. The fault-tolerant computing device of claim 2 , further comprising a decoder circuit to detect and correct errors in output signals generated by the dot product engine.
4. The fault-tolerant computing device of claim 1 , wherein the encoder circuit generates the matrix values in the m column lines of the crossbar array from the matrix values in a first number k of column lines of the crossbar array, wherein k=n−m.
5. The fault-tolerant computing device of claim 4 , wherein a matrix consisting of the number 1 of row lines and the number n of column lines multiplied by an input vector u corresponding to the input signal generates a vector c′ of length k, and wherein the matrix values generated by the encoder multiplied by the input vector u generates a vector c″ having redundancy symbols for detecting or correcting errors in c′.
6. The fault-tolerant computing device of claim 5 , further comprising a decoder circuit to detect and correct errors of an output signal by decoding the redundancy symbols.
7. The fault-tolerant computing device of claim 1 , wherein the encoder circuit generates the matrix values according to a desired number of errors to be detected using a Manhattan distance metric.
8. The fault-tolerant computing device of claim 1 , wherein the encoder circuit generates the matrix values according to a desired number of errors to be detected using a Hamming distance metric.
9. A method comprising:
providing a crossbar array having a number 1 of row lines and a number n of column lines intersecting the row lines to form l×n memory locations, each memory location comprising a programmable memristive element and defining a matrix value;
generating, by an encoder, matrix values for m of the n columns in the dot product engine based on matrix values for a first k of the n columns and according to an error detection capability, wherein n=k+m.
10. The method of claim 9 , further comprising receiving an input signal by a number 1 of digital-to analog converters coupled to the row lines of the crossbar array; and
generating an output signal that is a dot product of the input signal and the matrix values in the crossbar array.
11. The method of claim 10 , further comprising detecting and correcting the output signal generated by the dot product engine.
12. The method of claim 9 , further comprising generating, by the encoder circuit, the matrix values in the m column lines of the crossbar array from the matrix values in a first number k of column lines of the crossbar array, wherein k=n−m.
13. The method of claim 12 , further comprising multiplying an input vector u corresponding to the input signal with a matrix including the number 1 of row lines and the number n of column lines to generate a vector c′ of the length k.
14. The method of claim 13 , further comprising generating a vector c″ having redundancy symbols for detecting or correcting errors in c′ by multiplying the input vector u with the matrix values generated by the encoder.
15. The method of claim 14 , further comprising detecting and correcting, by a decoder circuit, errors in output signals generated by the dot product engine.
16. The method of claim 15 , wherein the errors are detected and corrected by decoding the redundancy symbols.
17. The method of claim 9 , wherein the encoder circuit generates the matrix values according to a desired number of errors to be detected using a Manhattan distance metric.
18. The method of claim 9 , wherein the encoder circuit generates the matrix values according to a desired number of errors to be detected using a Hamming distance metric.