COSMO: Computing with Stochastic Numbers in Memory

Stochastic computing (SC) reduces the complexity of computation by representing numbers with long streams of independent bits. However, increasing performance in SC comes with either an increase in area or a loss in accuracy. Processing in memory (PIM) computes data in-place while having high memory density and supporting bit-parallel operations with low energy consumption. In this article, we propose COSMO, an architecture for co mputing with s tochastic numbers in me mo ry, which enables SC in memory. The proposed architecture is general and can be used for a wide range of applications. It is a highly dense and parallel architecture that supports most SC encodings and operations in memory. It maximizes the performance and energy efficiency of SC by introducing several innovations: (i) in-memory parallel stochastic number generation, (ii) efficient implication-based logic in memory, (iii) novel memory bit line segmenting, (iv) a new memory-compatible SC addition operation, and (v) enabling flexible block allocation. To show the generality and efficiency of our stochastic architecture, we implement image processing, deep neural networks (DNNs), and hyperdimensional (HD) computing on the proposed hardware. Our evaluations show that running DNN inference on COSMO is 141× faster and 80× more energy efficient as compared to GPU.

A Monolithic Stochastic Computing Architecture for Energy and Area Efficient Arithmetic

As the energy and hardware investments necessary for conventional high-precision digital computing continues to explode in the emerging era of artificial intelligence, deep learning, and Big-data [1-4], a change in paradigm that can trade precision for energy and resource efficiency is being sought for many computing applications. Stochastic computing (SC) is an attractive alternative since unlike digital computers, which require many logic gates and a high transistor volume to perform basic arithmetic operations such as addition, subtraction, multiplication, sorting etc., SC can implement the same using simple logic gates [5, 6]. While it is possible to accelerate SC using traditional silicon complementary metal oxide semiconductor (CMOS) [7, 8] technology, the need for extensive hardware investment to generate stochastic bits (s-bit), the fundamental computing primitive for SC, makes it less attractive. Memristor [9-11] and spin-based devices [12-15] offer natural randomness but depend on hybrid designs involving CMOS peripherals for accelerating SC, which increases area and energy burden. Here we overcome the limitations of existing and emerging technologies and experimentally demonstrate a standalone SC architecture embedded in memory based on two-dimensional (2D) memtransistors. Our monolithic and non-von Neumann SC architecture consumes a miniscule amount of energy < 1 nano Joules for s-bit generation and to perform arithmetic operations and occupy small hardware footprint highlighting the benefits of SC.

Hardware-Efficient Stochastic Binary CNN Architectures for Near-Sensor Computing

With recent advances in the field of artificial intelligence (AI) such as binarized neural networks (BNNs), a wide variety of vision applications with energy-optimized implementations have become possible at the edge. Such networks have the first layer implemented with high precision, which poses a challenge in deploying a uniform hardware mapping for the network implementation. Stochastic computing can allow conversion of such high-precision computations to a sequence of binarized operations while maintaining equivalent accuracy. In this work, we propose a fully binarized hardware-friendly computation engine based on stochastic computing as a proof of concept for vision applications involving multi-channel inputs. Stochastic sampling is performed by sampling from a non-uniform (normal) distribution based on analog hardware sources. We first validate the benefits of the proposed pipeline on the CIFAR-10 dataset. To further demonstrate its application for real-world scenarios, we present a case-study of microscopy image diagnostics for pathogen detection. We then evaluate benefits of implementing such a pipeline using OxRAM-based circuits for stochastic sampling as well as in-memory computing-based binarized multiplication. The proposed implementation is about 1,000 times more energy efficient compared to conventional floating-precision-based digital implementations, with memory savings of a factor of 45.

Stochastic Computing Emulation of Memristor Cellular Nonlinear Networks

Cellular Nonlinear Networks (CNN) are a concept introduced in 1988 by Leon Chua and Lin Yang as a bio-inspired architecture capable of massively parallel computation. Since then, CNN have been enhanced by incorporating designs that incorporate memristors to profit from their processing and memory capabilities. In addition, Stochastic Computing (SC) can be used to optimize the quantity of required processing elements; thus it provides a lightweight approximate computing framework, quite accurate and effective, however. In this work, we propose utilization of SC in designing and implementing a memristor-based CNN. As a proof of the proposed concept, an example of application is presented. This application combines Matlab and a FPGA in order to create the CNN. The implemented CNN was then used to perform three different real-time applications on a 512 × 512 gray-scale and a 768 × 512 color image: storage of the image, edge detection, and image sharpening. It has to be pointed out that the same CNN was used for the three different tasks, with the sole change of some programmable parameters. Results show an excellent capability with significant accompanying advantages, such as the low number of needed elements further allowing for a low cost FPGA-based system implementation, something confirming the system’s capacity for real time operation.

A Switched Capacitor Memristor Emulator using Stochastic Computing

Due to the increased use of memristors, and its many applications, the use of emulators has grown in parallel to avoid some of the difficulties presented by real devices such as variability and reliability. In this paper, we present a memristive emulator designed using a Switched Capacitor (SC), this is, an analog component/ block and a control part or block implemented using stochastic computing (SCo) and therefore fully digital. Our design is thus a mixed signal circuit. Memristor equations are implemented using stochastic computing to generate the control signals necessary to work with the controllable resistor implemented as switched capacitor.

Brain-Inspired Hardware Solutions for Inference in Bayesian Networks

The implementation of inference (i.e., computing posterior probabilities) in Bayesian networks using a conventional computing paradigm turns out to be inefficient in terms of energy, time, and space, due to the substantial resources required by floating-point operations. A departure from conventional computing systems to make use of the high parallelism of Bayesian inference has attracted recent attention, particularly in the hardware implementation of Bayesian networks. These efforts lead to several implementations ranging from digital circuits, mixed-signal circuits, to analog circuits by leveraging new emerging nonvolatile devices. Several stochastic computing architectures using Bayesian stochastic variables have been proposed, from FPGA-like architectures to brain-inspired architectures such as crossbar arrays. This comprehensive review paper discusses different hardware implementations of Bayesian networks considering different devices, circuits, and architectures, as well as a more futuristic overview to solve existing hardware implementation problems.