# Physically-Equivalent Architectures for Reasoning under Uncertainty

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## Description:

Most real-world computation problems e.g., gene expression for uncovering genetic basis of diseases, macro finance, text classification, speech recognition, motion detection/processing, cyber threat detection, environment monitoring, and many others, require reasoning or decision-making in the presence of uncertainty: i.e., without the availability of complete information and/or well-characterized logic relationships. Bayesian Network (BN) is a widely successful formalism for such applications, capable of modeling causal relationships between random variables in an application domain. Conventional Von Neumann architectures built with CMOS technology are not well suited to implementing such applications because: i) their emulation of an inherently non-deterministic, non-logical computing model on a deterministic Boolean logic framework is inefficient, ii) BN’s structure and parameter learning is super-exponential in the number of variables, iii) conventional architectures incorporate a limited number of multiplication and division units (due to high complexity of CMOS logic implementation of multipliers and dividers), iv) the use of a rigid separation between logic and memory is undesirable, and v) use of a radix-based representation of data is inefficient for probabilistic information.

In this multi-disciplinary project, we propose an unconventional hardware architecture and nanoscale technology implementation of BNs based on unique magneto-electric computations that can efficiently address the aforementioned problems. This framework, extending from the physical layer to architecture, can potentially address causal inference and learning problems that are computationally infeasible today, and enable such capability at smaller scale in everyday embedded systems. Our overarching philosophy is finding and operating with physical equivalency, from the data representation to circuit and architectural components, which harnesses the direct synergy between the physical layer and conceptual framework. This mindset brings overall benefits beyond the sum of benefits of individual components.

At the bottom of the system stack, voltage-controlled straintronic magnetic tunnel junctions (S-MTJs) are employed that intrinsically support volatile and non-volatile behaviors with excellent energy-efficiency. Information representation is probabilistic with equivalence in the physical domain. A novel non-volatile mixed-signal magneto-electric probability composer circuit framework implements inference and learning related operations. In conjunction with a reconfigurable parallel architecture, this machine allows for direct physical realization of Bayesian nodes. Our preliminary evaluation shows up to four orders of magnitude performance improvement for Bayesian Networks with a million random variables vs. state-of-the-art 100 core microprocessors, which is truly game changing. Additionally, smaller causal inference problems (~100 variables) can be accommodated with very small area (about 0.1mm^{2}) and low power (~12mW) requirements.

**Acknowledgements:** This project is sponsored by NSF grant CCF-1407906.