Inspired by Solomonoffs theory of inductive inference, we propose a prior based on circuit complexity. There are several advantages to this approach. First, it relies on a complexity measure that does not depend on the choice of UTM. There is one universal definition for Boolean circuits involving an universal operation such as nand with simple conversions to alternative definitions such as and, or, and not. Second, there is no analogue of the halting problem. The output value of a circuit can be calculated recursively by computer in time proportional to the number of gates, while a short program may run for a very long time. Our prior assumes that a Boolean function, or equivalently, Boolean string of fixed length, is generated by some Bayesian mixture of circuits. This model is appropriate for learning Boolean functions from partial information, a problem often encountered within machine learning as "binary classification." We argue that an inductive bias towards simple explanations as measured by circuit complexity is appropriate for this problem.

翻译：受所罗门诺夫归纳推理理论的启发，我们提出了一种基于电路复杂性的先验分布。该方法具有若干优势。首先，它不依赖于通用图灵机（UTM）的选择，采用了一种通用的复杂性度量。布尔电路存在一种通用定义（例如使用与非门作为基本操作），且可简便地转换为其他等价定义（如与门、或门、非门）。其次，该方法不存在类似停机问题的困境：电路的输出值可通过计算机递归计算，耗时正比于门电路数量，而短程序却可能运行极长时间。我们的先验假设布尔函数（等价于固定长度的布尔字符串）由某种电路的贝叶斯混合模型生成。该模型适用于从部分信息中学习布尔函数的问题，即机器学习中常见的“二分类”问题。我们论证了以电路复杂性为测量标准的简约性归纳偏置对此类问题的适用性。