Memristive Dot-Product Engine Using Redundant Crossbar Columns
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Solution Overview
Problem
Inaccuracies and noise in memristive crossbar arrays used for vector-matrix computations can lead to errors in dot product calculations due to programming inaccuracies and faults such as shorted or non-programmable junctions, affecting the accuracy of computations.
Innovation Solution
A fault-tolerant Dot-Product Engine (FT-DPE) is introduced, which adds redundancy to the memristive crossbar array by encoding additional columns in the matrix to detect and correct errors, using an encoder circuit to generate redundancy symbols and a decoder circuit to correct errors in the output vector, ensuring reliable computations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If redundancy is added to the crossbar array for error detection and correction, then computation reliability is improved, but device complexity increases
Solution Approach 1:
The patent applies preliminary action by pre-computing and storing syndrome lookup tables during device fabrication or initialization. These tables contain pre-calculated error syndromes and corresponding correction actions, allowing the system to quickly detect and correct errors during operation without performing complex real-time calculations, thus improving reliability while minimizing runtime complexity
Solution Approach 2:
The patent introduces an intermediary decoding circuit that acts as a mediator between the crossbar array and the output. This circuit uses the pre-stored syndrome tables to translate raw error patterns into correction actions, simplifying the overall system architecture while maintaining high computation reliability through efficient error handling
2Measurement precision
If additional columns are added to the matrix for encoding redundancy symbols, then error detection capability is improved, but manufacturing precision requirements increase
Solution Approach 1:
The patent applies parameter changes by transforming the error detection problem from one requiring high-precision physical measurements to one based on discrete mathematical syndromes. By encoding redundancy symbols and using syndrome lookup tables, the system achieves robust error detection through computational parameters rather than requiring extremely precise manufacturing tolerances for additional hardware components
3Measurement precision
If fault tolerance mechanisms are implemented, then computation accuracy is improved, but processing time increases
Solution Approach 1:
The patent resolves the time-accuracy tradeoff by performing error detection and correction actions in advance. Syndrome lookup tables are pre-computed and stored, allowing the system to achieve high computation accuracy through simple table lookups and bitwise operations during runtime, rather than performing time-consuming error analysis and correction calculations
Solution Approach 2:
The patent replaces complex mechanical or computational error handling mechanisms with a streamlined electronic lookup and correction system. By substituting elaborate real-time error analysis with pre-computed syndrome tables and simple decoding logic, the system achieves high accuracy while minimizing additional processing time
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The FT-DPE enhances the accuracy and reliability of vector-matrix multiplications by enabling efficient error detection and correction, leading to faster and more energy-efficient processing while maintaining computation reliability.
Implementation Method 1
An input voltage signal along each row of the crossbar array is weighted by the conductance of the memristive devices in each column and accumulated as the current output from each column to form a dot product
Data Source
AI summary
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.