In some aspects, a method may include initializing a first array and a second array with a random voltage value, passing a forward pass by pulsing an input voltage value from an input of the first array and an input of the second array, and reading output voltage values at an output of the first array and an output of the second array. The method may further include passing a backward pass into the inputs of both of the first and second arrays, and reading voltage values at the inputs of the first and second arrays. The method may further include updating, with the first array, a first matrix update on the first array, updating, with the second array, a first matrix update on the second, and updating, with the second array, a second matrix update on the second array.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method for performing matrix operations on a matrix with a network of resistive device arrays, the method comprising: initializing a first array and a second array with a random voltage value; passing a forward pass by: pulsing an input voltage value from an input of the first array and an input of the second array, and reading output voltage values at an output of the first array and an output of the second array; passing a backward pass by: pulsing voltage values into the inputs of both of the first and second arrays, wherein the voltage values are voltage values at the outputs of the first and second arrays, and reading voltage values at the inputs of the first and second arrays by adding the output voltage of the first and second arrays, updating, with the first array, a first matrix update on the first array by directing the voltage values at the inputs of the first and second arrays into the inputs and the outputs of the first and second arrays; updating, with the second array, a first matrix update on the second array by inputting a constant voltage value from the input of the first array and the second array, and reading constant voltage values at the output of the second array; and updating, with the second array, a second matrix update on the second array by outputting a matrix sum of output voltage values at the outputs of the first and second arrays, wherein the sum is made by adding the output voltage value at the output of the first array to the output voltage value at the output of the second array. 2. The method of claim 1, wherein the first matrix update and the second matrix update are performed in parallel at a constant time independent of a size of the array. 3. The method of claim 1, wherein the resistive device arrays are comprised of resistive devices functioning as weighted connections between neurons. 4. The method of claim 1, wherein the first array is configured to hold a plurality of off-diagonal terms of a weight matrix; and the second array is configured to hold a plurality of diagonal terms of the weight matrix. 5. The method of claim 1, wherein the first and second array outputs values are output currents.