Resistive Memory Crosspoint Matrix for Algebraic Problem Solving
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Solution Overview
Problem
Existing mathematical calculation circuits employing resistive memories face limitations in the type of computational operations they can perform and the computational load required to solve algebraic problems, particularly in solving systems of equations and calculating eigenvectors.
Innovation Solution
A mathematical problem solving circuit is developed using a crosspoint matrix of analog resistive memories and operational amplifiers, which configures conductance values to represent mathematical problem elements, allowing for the solution of square systems of equations, matrix inversion, and eigenvector calculation through voltage measurements, enabling efficient computation without requiring multiple iterations or complex operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If iterative numerical techniques are used to solve systems of equations with resistive memories, then the system can handle complex algebraic problems, but the computational load increases and requires several iterations to obtain convergence
Solution Approach 1:
The patent replaces iterative numerical computation (mechanical/electronic switching and sequential processing) with a direct physical measurement approach. By configuring the resistive memory crosspoint matrix to represent the algebraic problem and using voltage measurements at column nodes to directly obtain solutions, the system eliminates the need for iterative numerical techniques, thereby reducing computational load while maintaining the ability to solve complex algebraic problems
2Adaptability or versatility
If resistive memories are configured to represent mathematical problem elements, then the circuit can solve various algebraic problems including square systems of equations and eigenvector calculation, but the device complexity increases
Solution Approach 1:
The patent implements a universal computational framework where a single resistive memory crosspoint matrix configuration can represent different types of algebraic problems (square systems of equations, eigenvector calculations, etc.). By appropriately configuring the conductance values in the matrix and applying suitable input voltages, the same hardware structure solves multiple mathematical problems, thereby increasing adaptability without proportionally increasing device complexity
Solution Approach 2:
The patent utilizes parameter changes in the resistive memory elements (conductance values) to represent different mathematical problem elements. By programmatically setting the conductance values of individual memory cells to correspond to matrix elements or other problem parameters, the system can reconfigure the same hardware to solve different algebraic problems, achieving versatility through parameter reconfiguration rather than structural complexity
3Measurement precision
If multiple iterations are performed to achieve convergence in solving systems of equations, then the solution accuracy improves, but the time required for computation increases
Solution Approach 1:
The patent replaces the time-consuming iterative numerical process with a direct physical measurement. By configuring the resistive memory matrix to embody the mathematical problem and measuring voltages that directly represent the solution, the system obtains results in a single computational pass rather than through multiple iterations, thereby significantly reducing computation time while maintaining solution accuracy through proper circuit design and measurement techniques
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 circuit provides an efficient and approximate solution to algebraic problems, such as solving square systems of equations and calculating eigenvectors, by configuring resistive memories and operational amplifiers to represent and solve mathematical problems, reducing computational complexity and achieving quick convergence of results.
Implementation Method 1
a crosspoint matrix MG including a plurality of row conductors Li, a plurality of column conductors Cj, and a plurality of analog resistive memories Gij each connected between a respective row conductor Li and a respective column conductor Cj
Data Source
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AI summary
It is described a mathematical solving circuit (100) comprising: a crosspoint matrix (MG) including a plurality of row conductors (L±), a plurality of column conductors (Cj) and a plurality of analog resistive memories (Gij), each connected between a row conductor and a column conductor; a plurality of operational amplifiers (OA±) each having: a first input terminal (INu) connected to a respective row conductor (Li), a second input terminal (IN2i) connected to a ground terminal (GR) at least one operational amplifier (OAi) of the plurality being such to take the respective first input terminal (INu) to a virtual ground.