University of Minnesota

Kiarash Bazargan

David J Lilja

Marcus Riedel

Mohammadhassan Najafi

Sayed Abdolrasoul Faraji

Soheil Mohajer

Zhiheng Wang

Ramesh Harjani

Bingzhe Li

Shiva Jamalizavareh

Various implementations of sorting networks are described that utilize time-encoded data signals having encoded values. In some examples, an electrical circuit device includes a sorting network configured to receive a plurality of time-encoded signals. Each time-encoded signal of the plurality of time-encoded signals encodes a data value based on a duty cycle of the respective time-encoded signal or based on a proportion of data bits in the respective time-encoded signal that are high relative to the total data bits in the respective time-encoded signal. The sorting network is also configured to sort the plurality of time-encoded signals based on the encoded data values of the plurality of time-encoded signals.

Sorting networks using unary processing

Example devices are described that include a computational unit configured to process first set of data bits encoding a first numerical value and a second set of data bits encoding a second numerical value. The computational unit includes a bit-stream generator configured to generate bit combinations representing first and second bit sequences that encode the first and second numerical values, respectively, based on a proportion of the data bits in the sequence that are high relative to the total data bits. The first bit sequence is generated using a first Sobol sequence source, and the second bit sequence is generated using a second Sobol sequence source different from the first Sobol sequence source. The device also includes computation logic configured to perform a computational operation on the bit combinations and produce an output bit-stream having a set of data bits indicating a result of the computational operation.

Low-discrepancy deterministic bit-stream processing using Sobol sequences

In some examples, a device includes shuffling circuitry configured to receive an input unary bit stream and generate a shuffled bit stream by selecting n-tuple combinations of bits of the input unary bit stream. The device also includes stochastic logic circuitry having a plurality of stochastic computational units configured to perform operations on the shuffled bit stream in parallel to produce an output unary bit stream, each of the stochastic computational units operating on a different one of the n-tuple combinations of the bits.

Parallel computing using stochastic circuits and deterministic shuffling networks

This disclosure describes techniques for performing computational operations on input unary bit streams using one or more scaling networks. In some examples, a device is configured to perform a digital computational operation, where the device includes a plurality of input wires and a plurality of output wires. Each input wire is configured to receive a respective input bit of an encoded input value, and each output wire is configured to output a respective output bit of an encoded output value. The device also includes scaling network circuitry configured to apply a function to the encoded input value by electrically routing at least one input wire of the plurality of input wires to at least two output wires of the plurality of output wires. The device can also include hybrid binary/unary computations.

Computational devices using thermometer coding and scaling networks on unary encoded data

Devices and techniques are described in which stochastic computation is performed on analog periodic pulse signals instead of random, stochastic digital bit streams. Exploiting pulse width modulation (PWM), time-encoded signals corresponding to specific values are generated by adjusting the frequency (period) and duty cycles of PWM signals. With this approach, the latency, area, and energy consumption are all greatly reduced, as compared to prior stochastic approaches. Circuits synthesized with the proposed approach can work as fast and energy efficiently as a conventional binary design while retaining the fault-tolerance and low-cost advantages of conventional stochastic designs.

Stochastic computation using pulse-width modulated signals

In some examples, a device includes an integrated circuit and two or more computational units configured to process respective stochastic bit streams in accordance with respective input clocks. Each of the stochastic bit streams comprises sequential sets of data bits, each of the sets of data bits representing a numerical value based on a probability that any bit in the respective set of data bits is one. The respective input clocks for each of the two or more computational units are unsynchronized.

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Plymouth, MN, United States of America

Kiarash Bazargan