变组合子集的泛归纳法
Universal Induction with Varying Sets of Combinators
摘要：
泛归纳是AGI中的一个关键问题。它的实用性可以通过选择参考机器或表示与环境一致的算法来实现。这台机器应该是可更新的，以便更有效地解决后续任务。我们研究这个问题的组合逻辑的一个例子，非常简单的图灵完备参考机，它使修改程序表示引入不同的原始组合子。利用遗传编程系统搜索组合子表达式，将组合子表达式分解为子表达式，在交叉操作中进行重组。我们的实验表明，开发的系统可以解决低复杂度的归纳或预测任务（比使用蛮力更有效）;有用的组合子可以被揭示并包含在简化更困难的任务的表示中。然而，组合子的最佳集合取决于特定的任务，因此应该与搜索引擎协调地自适应地选择参考机。
英文摘要：
Universal induction is a crucial issue in AGI. Its practical applicability can be achieved by the choice of the reference machine or representation of algorithms agreed with the environment. This machine should be updatable for solving subsequent tasks more efficiently. We study this problem on an example of combinatory logic as the very simple Turing-complete reference machine, which enables modifying program representations by introducing different sets of primitive combinators. Genetic programming system is used to search for combinator expressions, which are easily decomposed into sub-expressions being recombined in crossover. Our experiments show that low-complexity induction or prediction tasks can be solved by the developed system (much more efficiently than using brute force); useful combinators can be revealed and included into the representation simplifying more difficult tasks. However, optimal sets of combinators depend on the specific task, so the reference machine should be adaptively chosen in coordination with the search engine.
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