EAGER: Digital Yet Deliberately Random -- Synthesizing Logical Computation on Stochastic Bit Streams

大多数数字系统操作数据的位置表示，如二进制基数。该项目提倡一种替代表示：随机比特流，其中信号值由获得1与0的概率编码。这种表示比二进制基数的紧凑性要小得多。然而，复杂的操作可以用非常简单的逻辑来执行。特别是由加法和乘法等运算组成的算术函数，可以非常有效地实现。复函数，如指数函数和三角函数，可以通过多项式近似计算。因为随机表示是均匀的，所有比特的权重相等，所以它对软错误（即比特翻转）有很高的容忍度。随机比特流上的计算提供了可调的精度：随着随机比特流长度的增加，它所表示的值的精度也会增加。因此，无需重新设计硬件，就可以灵活地权衡精度和计算时间。相比之下，对于传统的二进制基数实现，当需要更高的精度时，底层硬件必须重新设计。该项目将开发和应用一个统一的框架，从电路级到架构级和系统级综合这些计算。将发展用组合逻辑转换概率值的技术。作为这项资助的一部分，欧洲经委会和明尼苏达大学新的生物医学信息学和计算生物学项目联合开设了一门关于“电路、计算和生物学”的新课程。研究人员将尝试将随机思想纳入计算机设计课程，pi将专注于建立目前的研究成果，包括女性和代表性不足的学生。

Most digital systems operate on a positional representation of data, such as binary radix. This project advocates an alternative representation: random bit streams where the signal value is encoded by the probability of obtaining a one versus a zero. This representation is much less compact than binary radix. However, complex operations can be performed with very simple logic. In particular, arithmetic functions, consisting of operations like addition and multiplication can be implemented very efficiently. Complex functions, such as exponentials and trigonometric functions, can be computed through polynomial approximations. Because a stochastic representation is uniform, with all bits weighted equally, it is highly tolerant of soft errors (i.e., bit flips). Computation on stochastic bit streams offers tunable precision: as the length of the stochastic bit stream increases, the precision of the value represented by it also increases. Thus, without hardware redesign, one has the flexibility to tradeoff precision and computation time. In contrast, with a conventional binary-radix implementation, when a higher precision is required, the underlying hardware has to be redesigned. This project will develop and apply a unified framework for synthesizing such computation from the circuit level to the architectural and system level. Techniques for transforming probability values with combinational logic will be developed. As part of this grant, a new course on "Circuits, Computation, and Biology" offered jointly through the ECE Department and the new Biomedical Informatics and Computational Biology Program at the University of Minnesota. The researchers will try to incorporate stochastic ideas in computer design curriculum, The PIs will focus on building upon current research efforts that include female and underrepresented students.