How should a machine intelligence perform unsupervised structure discovery over streams of sensory input? One approach to this problem is to cast it as an apperception task [1]. Here, the task is to construct an explicit interpretable theory that both explains the sensory sequence and also satisfies a set of unity conditions, designed to ensure that the constituents of the theory are connected in a relational structure.

However, the original formulation of the apperception task had one fundamental limitation: it assumed the raw sensory input had already been parsed using a set of discrete categories, so that all the system had to do was receive this already-digested symbolic input, and make sense of it. But what if we don't have access to pre-parsed input? What if our sensory sequence is raw unprocessed information?

The central contribution of this paper is a neuro-symbolic framework for distilling interpretable theories out of streams of raw, unprocessed sensory experience. First, we extend the definition of the apperception task to include ambiguous (but still symbolic) input: sequences of sets of disjunctions. Next, we use a neural network to map raw sensory input to disjunctive input. Our binary neural network is encoded as a logic program, so the weights of the network and the rules of the theory can be solved jointly as a single SAT problem. This way, we are able to jointly learn how to perceive (mapping raw sensory information to concepts) and apperceive (combining concepts into declarative rules).

机器智能应如何在感觉输入流上执行无监督的结构发现？解决此问题的一种方法是将其转换为感知任务[1]。在这里，任务是构建一个明确的可解释的理论，该理论既可以解释感官序列，又可以满足一组统一条件，旨在确保该理论的组成部分以关系结构连接。

但是，知觉任务的原始表述有一个基本局限性：它假定原始的感觉输入已经使用一组离散的类别进行了解析，因此所有系统要做的就是接收这个已经被消化的符号输入，然后感觉。但是，如果我们无权访问预先输入的内容怎么办？如果我们的感觉序列是未经处理的原始信息怎么办？

本文的主要贡献是一个神经符号框架，用于从原始的，未经处理的感官体验流中提炼出可解释的理论。首先，我们将感知任务的定义扩展到包括歧义（但仍是符号）输入：析取集的序列。接下来，我们使用神经网络将原始的感觉输入映射到析取输入。我们的二进制神经网络被编码为逻辑程序，因此网络的权重和理论规则可以作为一个SAT问题共同解决。这样，我们就可以共同学习如何感知（将原始的感官信息映射到概念）和感知（将概念合并为声明性规则）。