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This paper proposes a time-domain analog calculations model based on a pulse-width modulation (PWM) approach for neural network calculations including weighted-sum or multiply-and-accumulate calculation and rectified-linear unit operation. We also propose very-large-scale integration (VLSI) circuits to implement the proposed model. Unlike the conventional analog voltage or current mode circuits, our circuits use transient operation in charging/discharging processes to capacitors through resistors. Since the circuits calculate multiple weighted-sums by charging a capacitance, they can be operated with extremely low energy consumption. However, because a relatively long time constant is required to guarantee calculation resolution in the time domain, they have to use very high-resistance devices, on the order of giga-ohms. We designed, fabricated, and tested a proof-of-concept complementary metal-oxide-semiconductor (CMOS) VLSI chip using a 250-nm fabrication technology to verify weighted-sum operation based on the proposed model with binary weights and PWM input signals, which realizes the BinaryConnect model. In the chip, memory cells of static-random-access memory (SRAM) are used for synaptic connection weights. High-resistance operation was realized by using the subthreshold operation region of MOS transistors, unlike in the ordinary in-memory-computing circuits. We evaluated the energy efficiency and temperature characteristics by measurement using the fabricated chip, where the highest energy efficiency for the weighted-sum calculation was 300 TOPS/W (Tera-Operations Per Second per Watt). The effects by a temperature change can be compensated for by adjusting the bias voltage. If state-of-the-art VLSI technology is used to implement the proposed model, an energy efficiency of more than 1,000 TOPS/W will be possible.

An Energy-Efficient Time-Domain Analog CMOS BinaryConnect Neural Network Processor Based on a Pulse-Width Modulation Approach