Title: Compositional-ARC: Assessing Systematic Generalization in Abstract Spatial Reasoning
Primary area: transfer learning, meta learning, and lifelong learning
Keywords: Systematic Generalization, Abstract Spatial Reasoning, ARC, Meta-Learning for Compositionality

Abstract: Systematic generalization refers to the capacity to understand and generate novel combinations from known components. Despite recent progress by large language models (LLMs) across various domains, these models often fail to extend their knowledge to novel compositional scenarios, revealing notable limitations in systematic generalization. There has been an ongoing debate about whether neural networks possess the capacity for systematic generalization, with recent studies suggesting that meta-learning approaches designed for compositionality can significantly enhance this ability. However, these insights have largely been confined to linguistic problems, leaving their applicability to other tasks an open question. In this study, we extend meta-learning for compositionality to the domain of abstract spatial reasoning. To this end, we introduce $\textit{Compositional-ARC}\textemdash{}$a dataset designed to evaluate the capacity of models to systematically generalize from known geometric transformations (e.g., translation, rotation) of abstract two-dimensional objects to novel combinations of these transformations (e.g., translation+rotation). Our results show that a small transformer-based encoder-decoder model, trained via meta-learning for compositionality, can systematically generalize to previously unseen transformation compositions. Notably, despite having only 5.7M parameters, this model significantly outperforms state-of-the-art LLMs$\textemdash{}$including o3-mini, GPT-4o, and Gemini 2.0 Flash, which fail to exhibit similar systematic behavior$\textemdash{}$and performs on par with the winning model of the ARC prize 2024, an 8B-parameter LLM trained via test-time training. Our findings highlight the effectiveness of meta-learning in promoting systematicity beyond linguistic tasks, suggesting a promising direction toward more robust and generalizable models.

TL;DR: In this study, we extend meta-learning for compositionality to the domain of abstract spatial reasoning, demonstrating that neural networks can systematically generalize from known geometric transformations to novel combinations.