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Memristive devices share remarkable similarities to biological synapses, dendrites, and neurons at both the physical mechanism level and unit functionality level, making the memristive approach to neuromorphic computing a promising technology for future artificial intelligence. However, these similarities do not directly transfer to the success of efficient computation without device and algorithm co-designs and optimizations. Contemporary deep learning algorithms demand the memristive artificial synapses to ideally possess analog weighting and linear weight-update behavior, requiring substantial device-level and circuit-level optimization. Such co-design and optimization have been the main focus of memristive neuromorphic engineering, which often abandons the "non-ideal" behaviors of memristive devices, although many of them resemble what have been observed in biological components. Novel brain …