Abductive Symbolic Solver on Abstraction and Reasoning Corpus

TL;DR

This paper proposes a novel framework that symbolically represents the observed data into a knowledge graph and extracts core knowledge that can be used for solution generation and effectively narrowing the solution space and providing logical solutions grounded in core knowledge extraction.

Abstract

This paper addresses the challenge of enhancing artificial intelligence reasoning capabilities, focusing on logicality within the Abstraction and Reasoning Corpus (ARC). Humans solve such visual reasoning tasks based on their observations and hypotheses, and they can explain their solutions with a proper reason. However, many previous approaches focused only on the grid transition and it is not enough for AI to provide reasonable and human-like solutions. By considering the human process of solving visual reasoning tasks, we have concluded that the thinking process is likely the abductive reasoning process. Thus, we propose a novel framework that symbolically represents the observed data into a knowledge graph and extracts core knowledge that can be used for solution generation. This information limits the solution search space and helps provide a reasonable mid-process. Our approach holds promise for improving AI performance on ARC tasks by effectively narrowing the solution space and providing logical solutions grounded in core knowledge extraction.

Figures (9)

• Figure 1: Example ARC task. Solvers are supposed to formulate a pattern that applies to all the given example pairs and then construct an answer with the given test input grid.
• Figure 2: Overall framework of Symbolic ARC Solver. To tackle ARC tasks from the symbolic perspective, the first step involves generating a corresponding knowledge graph using a construction program based on defined Domain Specific Languages (DSL). (Step 1, Chapter \ref{['chap:ARCKG']}) Then, extract core knowledge from the knowledge graph using Specifier. (Step 2, Chapter 3.2) Since all the ARC tasks consist of multiples of example pairs and a test pair, we define Specifier to hold only the repeated conditions that appeared in all example pairs. Lastly, search solutions under given constraints using Synthesizer. (Step 3, Chapter 3.3) The information gained from the examples and proposing Transformation DSLs limits the solution search space and makes the search feasible.
• Figure 3: Overview of Domain-Specific Languages (DSLs) and their category tag.
• Figure 4: The taxonomy of the Domain-Specific Language (DSL). The terms Transformation DSL and Property DSL are equivalent to the DSL used in Synthesizer and ARCKG construction respectively. In particular, Transformation DSLs do not follow the traditional ones, such as move, flip, or rotate due to the experimental setup of this research. Transformation Selection 10 (TS10) contains a selection of suitable DSLs for the experiment and TS5 is a subset of it. General DSL takes the majority of the Property DSL and represents the characteristics of the object. Similarly, Pnode-layer DSL only appears in Pnode-layer and forms the fundamental feature of object forming. Syntax DSL contains node and edge list generation functions to store the information in the form of NodeList and EdgeList.
• Figure 5: An example of a straightforward, and almost backbone-structured knowledge graph of the first pair of Figure \ref{['fig:task']}. In practice, the ARCKG generated by Algorithm \ref{['alg:KgConstruction']} can contain up to millions of edges. The graph consists of four layers, with edges freely drawn between layers as well as between input and output by the Property DSL. The yellow edges represent connections between two nodes at the same position. The other (black, blue, green) indicate edges signify that nodes in the lower layer constitute nodes in the upper layer.