Generalized Planning for the Abstraction and Reasoning Corpus

TL;DR

ARC poses a broad abstract-reasoning challenge that is difficult for pure learning approaches. The paper presents GPAR, which reframes ARC tasks as generalized planning problems and solves them via planning programs with pointers encoded in PDDL with external functions to capture object-centric abstractions. Key contributions include a novel ARC-domain encoding in PDDL, action-pruning constraints, and a GP-based synthesis pipeline that delivers state-of-the-art performance on object-centric ARC tasks with strong generalization. The work demonstrates the viability of planning-based methods for visual reasoning and suggests avenues for richer abstractions and cross-model connections to further improve performance.

Abstract

The Abstraction and Reasoning Corpus (ARC) is a general artificial intelligence benchmark that poses difficulties for pure machine learning methods due to its requirement for fluid intelligence with a focus on reasoning and abstraction. In this work, we introduce an ARC solver, Generalized Planning for Abstract Reasoning (GPAR). It casts an ARC problem as a generalized planning (GP) problem, where a solution is formalized as a planning program with pointers. We express each ARC problem using the standard Planning Domain Definition Language (PDDL) coupled with external functions representing object-centric abstractions. We show how to scale up GP solvers via domain knowledge specific to ARC in the form of restrictions over the actions model, predicates, arguments and valid structure of planning programs. Our experiments demonstrate that GPAR outperforms the state-of-the-art solvers on the object-centric tasks of the ARC, showing the effectiveness of GP and the expressiveness of PDDL to model ARC problems. The challenges provided by the ARC benchmark motivate research to advance existing GP solvers and understand new relations with other planning computational models. Code is available at github.com/you68681/GPAR.

Figures (11)

• Figure 1: Three example tasks from the ARC. For a given task, each row contains an input-output image pair as a training instance, and the bottom row is the test instance. The goal of the solver is to learn from the training instances how to generate the output for the test instance.
• Figure 2: A PDDL example for a fragment of an ARC task.
• Figure 3: A planning program $\Pi$ to alter size-1 nodes with different colors to black. Pointers $no$ indexes node objects $\{\textit{node$_1$}, \textit{node$_2$}, \textit{node$_3$}\}$, and $co$ indexes color objects $\{\textit{black}, \textit{green}, \textit{blue}, \textit{red}\}$.
• Figure 4: An example task for which the 4- vs. 8-connected abstractions produce different nodes (left), and an example task where identified nodes are the same (right).
• Figure 5: An illustration of the planning process with the application section and the looping section. Lines 0 and 1 ensure $no_1$ indexes the square node, and lines 2 and 3 constrain the $no_2$ to point to the single-pixel node, while $mo_1$ indexes the correct spatial relation between $no_1$ and $no_2$.