Computing high-degree polynomial gradients in memory.

Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms. Prior work on such hardware, performed in the context of Ising Machines and related concepts, is limited to quadratic polynomials and not scalable to commonly used higher-order functions. Here, we propose an approach for massively parallel gradient calculations of high-degree polynomials, which is conducive to efficient mixed-signal in-memory computing circuit implementations and whose area scales proportionally with the product of the number of variables and terms in the function and, most importantly, independent of its degree. Two flavors of such an approach are proposed. The first is limited to binary-variable polynomials typical in combinatorial optimization problems, while the second type is broader at the cost of a more complex periphery. To validate the former approach, we experimentally demonstrated solving a small-scale third-order Boolean satisfiability problem based on integrated metal-oxide memristor crossbar circuits, with competitive heuristics algorithm. Simulation results for larger-scale, more practical problems show orders of magnitude improvements in area, speed and energy efficiency compared to the state-of-the-art. We discuss how our work could enable even higher-performance systems after co-designing algorithms to exploit massively parallel gradient computation.

In-Memory Computing with Memristor Content Addressable Memories for Pattern Matching.

The dramatic rise of data-intensive workloads has revived application-specific computational hardware for continuing speed and power improvements, frequently achieved by limiting data movement and implementing "in-memory computation". However, conventional complementary metal oxide semiconductor (CMOS) circuit designs can still suffer low power efficiency, motivating designs leveraging nonvolatile resistive random access memory (ReRAM), and with many studies focusing on crossbar circuit architectures. Another circuit primitive-content addressable memory (CAM)-shows great promise for mapping a diverse range of computational models for in-memory computation, with recent ReRAM-CAM designs proposed but few experimentally demonstrated. Here, programming and control of memristors across an 86 × 12 memristor ternary CAM (TCAM) array integrated with CMOS are demonstrated, and parameter tradeoffs for optimizing speed and search margin are evaluated. In addition to smaller area, this memristor TCAM results in significantly lower power due to very low programmable conductance states, motivating CAM use in a wider range of computational applications than conventional TCAMs are confined to today. Finally, the first experimental demonstration of two computational models in memristor TCAM arrays is reported: regular expression matching in a finite state machine for network security intrusion detection and definable inexact pattern matching in a Levenshtein automata for genomic sequencing.