We propose to learn a generative model via entropy interpolation with a Schr{ö}dinger Bridge. The generative learning task can be formulated as interpolating between a reference distribution and a target distribution based on the Kullback-Leibler divergence. At the population level, this entropy interpolation is characterized via an SDE on [0,1] with a time-varying drift term. At the sample level, we derive our Schr{ö}dinger Bridge algorithm by plugging the drift term estimated by a deep score estimator and a deep density ratio estimator into the Euler-Maruyama method. Under some mild smoothness assumptions of the target distribution, we prove the consistency of both the score estimator and the density ratio estimator, and then establish the consistency of the proposed Schr{ö}dinger Bridge approach. Our theoretical results guarantee that the distribution learned by our approach converges to the target distribution. Experimental results on multimodal synthetic data and benchmark data support our theoretical findings and indicate that the generative model via Schr{ö}dinger Bridge is comparable with state-of-the-art GANs, suggesting a new formulation of generative learning. We demonstrate its usefulness in image interpolation and image inpainting.

With low power consumption, fast access speed, high scalability and infinite endurance, spin-transfer torque magnetoresistive random access memory (STT-MRAM) is considered as one of the most promising alternatives to SRAM. However, The performance of STT-MRAM is significantly influenced by several reliability issues, such as process variations and stochastic switching. Most of the reliability analysis of relative circuits are performed at bit-cell and memory level, while that at computer-system level is missing. This paper proposes an efficient framework for performance evaluation of STT-MRAM on computer architecture-level implemented by GEM5+NVMain co-simulator in consideration of the reliability issues. The results show that the overall average latency and energy of STT-MRAM can be up to 5.996% and 20.65% larger than that of the nominal cases in a computer system-level memory architecture taking reliability issues into account. Because reliability issues are considered during the design phase, our framework can provide more accurate performance evaluation and contribute to a higher yield of STT-MRAM based computer systems.

From the discovery of giant magnetoresistance (GMR) to tunnel magnetoresistance (TMR), their subsequent application in large capacity hard disk drives (HDDs) greatly speeded up the information era over the past decades. However, the growing demand for big-data storage and processing is limited by the von-Neumann architecture due to the memory bottleneck and power dissipation. Taking advantage of nonvolatility, high speed, and low power, magnetic random access memory (MRAM) becomes a promising candidate to overcome this limitation through processing-in-memory (PIM) architectures. In this article, we provide an overview of existing technology and give a roadmap of spintronic devices for future energy-efficient computing and its relevant integration architectures. We begin with the fundamentals of Toggle-MRAM and spin-transfer torque (STT)-MRAM, which already have commercial applications. We then introduce spin-orbit torque (SOT), a critical mechanism to realize low-power data manipulation in the next generation of MRAM and summarize the recent experimental breakthroughs of field-free SOT switching schemes. Finally, we present MRAM-based PIM architectures and novel spintronic devices, provide an application outlook, and deliver the future development potential of energy-efficient computing systems.

Conventional MOS integrated circuits and systems suffer serve power and scalability challenges as technology nodes scale into ultra-deep-micron technology nodes (e.g., below 40nm). Both static and dynamic power dissipations are increasing, caused mainly by the intrinsic leakage currents and large data traffic. Alternative approaches beyond charge-only-based electronics, and in particular, spin-based devices, show promising potential to overcome these issues by adding the spin freedom of electrons to electronic circuits. Spintronics provides data non-volatility, fast data access, and low-power operation, and has now become a hot topic in both academia and industry for achieving ultra-low-power circuits and systems. The ITRS report on emerging research devices identified themagnetic tunnel junction(MTJ) nanopillar (one of the Spintronics nanodevices) as one of the most promising technologies to be part of future micro-electronic circuits. In this review we will give an overview of the status and prospects of spin-based devices and circuits that are currently under intense investigation and development across the world, and address particularly their merits and challenges for practical applications. We will also show that, with a rapid development of Spintronics, some novel computing architectures and paradigms beyond classic Von-Neumann architecture have recently been emerging for next-generation ultra-low-power circuits and systems.