Solving matrix equations in one step with cross-point resistive arrays

Abstract

Conventional digital computers can execute advanced operations by a sequence of elementary Boolean functions of 2 or more bits. As a result, complicated tasks such as solving a linear system or solving a differential equation require a large number of computing steps and an extensive use of memory units to store individual bits. To accelerate the execution of such advanced tasks, in-memory computing with resistive memories provides a promising avenue, thanks to analog data storage and physical computation in the memory. Here, we show that a cross-point array of resistive memory devices can directly solve a system of linear equations, or find the matrix eigenvectors. These operations are completed in just one single step, thanks to the physical computing with Ohm’s and Kirchhoff’s laws, and thanks to the negative feedback connection in the cross-point circuit. Algebraic problems are demonstrated in hardware and applied to classical computing tasks, such as ranking webpages and solving the Schrödinger equation in one step.

Memristive and CMOS Devices for Neuromorphic Computing

“…Although high acceleration performance has been achieved for the solution of hard constraint-satisfaction problems (CSPs), such as the Sudoku puzzle, via CMOS-based circuits [189], FPGA [190], and quantum computing circuits [191], the use of memristive devices in crossbar-based neural networks can further speed up computation by the introduction of a key resource as the noise [192] without the requirement of additional sources [193]. Moreover, very recent studies have also evidenced the strong potential of memristive devices for the execution of complex algebraic tasks, including the solution of linear systems and differential equations, such as the Schrödinger and Fourier equations, in crossbar arrays in only one computational step [16], thus overcoming the latency of iterative approaches [15]. Therefore, these achievements suggest CMOS/memristive devices as enablers of novel high-efficiency computing paradigms capable of revolutionizing many fields of our society.…”

“…Solving the memory bottleneck requires a paradigm shift in architecture, where computation is executed in situ within the data by exploiting, e.g., the ability of memory arrays to implement matrix-vector multiplication (MVM) [10,11]. This novel architectural approach is referred to as in-memory computing, which provides the basis for several outstanding applications, such as pattern classification [12,13], analogue image processing [14], and the solution of linear systems [15,16] and of linear regression problems [17].…”

Artificial Perception Built on Memristive System: Visual, Auditory, and Tactile Sensations

“…At the device level, memristors stand out as frontrunners in terms of fast accessing speed (<85 ps in Figure a), ultralow power consumption (<100 fJ event −1 in Figure b), excellent scalability (linewidth <2 nm), high density (4.5 Tbit in −2 in Figure c), and high endurance (>10 12 in Figure d) . At the array level, the continuous analogue conductance tunability (Figure e) enables single‐step vector–matrix multiplication operation, which is the basis for designing a formidable calculation function for linear and differential equations …”

Equilibrium Propagation for Memristor-Based Recurrent Neural Networks

“…Here, I i is the i-th input current, G ij is the connecting memductance between the i-th and j-th neurons and v j is the output voltage generated by the j-th neuron. This produces the vector-matrix multiplication in situ by a single read operation which eliminates the need for constant bidirectional data transfer from the memory to the computing unit (Sun et al, 2019).…”