Nonlinearity Impact on the Computation Accuracy of Matrix Multiplication Performed by a PCM Crossbar Array with Matched Filters

A crossbar arrays with phase change memory (PCM) devices was proposed as an efficient low-energy analog circuit for performing matrix multiplication [1]. Artificial intelligence (AI) implementation based on neural networks, is heavily reliant on matrix multiplication, and were demonstrated to work well even with 4-bit precision [2]. Analog computation of with a PCM crossbar arrays was shown to have an equivalent accuracy above 4-bit precision [1,3] and therefore can be used for efficient implementation of matrix multiplication for quantized neural networks.

The precision in analog computation is limited by noise which originates from various sources such as thermal noise, and weights read noise. As the size of the crossbar array is increased to accommodate large matrices, the current per device must be scaled. This scaling is limited, as the minimum useful current that can represent data is bounded by the noise floor.

In this paper we studied the use of matched filters [4,5] for improving the computation accuracy in the presence of noise. We chose to use matched filters at the output of the crossbar array since match filter optimize the signal-to-noise (SNR). Initially we analyzed a crossbar array with linear resistive elements and showed that computation accuracy is preserved even when the signal and noise are of the same amplitude (SNR=0 dB). We then extended our analysis to a crossbar array with real PCM devices, which were measured to have a nonlinear voltage dependent resistance. The nonlinearity impact on the computation accuracy will also be discussed.

REFERENCES [1] Abu Sebastian et al., “Tutorial: Brain-inspired computing using phase-change memory devices” J. Appl. Phys. 124, 111101 (2018); doi: 10.1063/1.5042413 [2] Anton Trusov et al., “Fast Implementation of 4-bit Convolutional Neural Networks for Mobile Devices” 2020 25th International Conference on Pattern Recognition (ICPR), Milan, Italy, 2021, pp. 9897-9903; doi: 10.1109/ICPR48806.2021.9412841 [3] Le Gallo, M., Hrynkevych, O., Kersting, B. et al. Demonstration of 4-quadrant analog in-memory matrix multiplication in a single modulation. npj Unconv. Comput. 1, 11 (2024). https://doi.org/10.1038/s44335-024-00010-4 [4] G. Turin, "An introduction to matched filters," in IRE Transactions on Information Theory, vol. 6, no. 3, pp. 311-329, June 1960, doi: 10.1109/TIT.1960.1057571 [5] Matched filter, Wikipedia, 6 June 2025, https://en.wikipedia.org/wiki/Matched_filter