Compositional-ARC: Assessing Systematic Generalization in Abstract Spatial Reasoning

Philipp Mondorf, Shijia Zhou, Monica Riedler, and Barbara Plank. (2026). Compositional-ARC: Assessing systematic generalization in abstract spatial reasoning. In The Fourteenth International Conference on Learning Representations.

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 Compositional-ARC—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—including o3-mini, GPT-4o, and Gemini 2.0 Flash, which fail to exhibit similar systematic behavior—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.

Data Structure

This repository contains the data for Compositional-ARC. It is structured as follows:

all/
│   └── all_episodes
├── split_seed_1860/
│   ├── train_episodes
│   ├── val_episodes
│   └── test_episodes
├── split_seed_1870/
│   ├── train_episodes
│   ├── val_episodes
│   └── test_episodes
├── split_seed_1880/
│   ├── train_episodes
│   ├── val_episodes
│   └── test_episodes
├── split_seed_1890/
│   ├── train_episodes
│   ├── val_episodes
│   └── test_episodes

As described in our paper, Compositional-ARC consists of 100,000 episodes. Each episode comprises three few-shot examples for the "3-Shot" task, 12 systematic study examples for the “Systematicity” setup, and ten query input-output grid pairs demonstrating the final level-2 transformation composition. Each episode is characterized by a unique visual interpretation grammar. For instance, in one episode, yellow objects are translated down by a single cell, while in another, yellow objects are reflected horizontally. All 100,000 episodes can be found in all/all_episodes.

Data Instances

Each data sample (episode) contains the following information:

{
    "primitive_functions": {
        "shape_transformation": list of input-output examples for shape-based transformation, 
        "color_transformation": list of input-output examples for color-based transformation,
        "indicator_transformation": list of input-output examples for neighbor-based transformation,
    },
    "function_compositions": {
        "shape_color_transformation": list of input-output examples for (shape+color)-based transformation,
        "shape_indicator_transformation": list of input-output examples for (shape+neighbor)-based transformation,
        "color_indicator_transformation": list of input-output examples for (color+neighbor)-based transformation,
    },
    "queries": list of input-output level-2 composition queries,
    "meta_data": {
        "shape_transformation": {
            "type": type of transformation,
            "kwargs": transformation argument dict,
        },
        "color_transformation": {
            "type": type of transformation,
            "kwargs": transformation argument dict,
        },
        "indicator_transformation": {
            "type": type of transformation,
            "kwargs": transformation argument dict,
        }
    }
}

Training Splits

As described in our paper, we split the data into training, validation, and test sets to train an encoder-decoder model via MLC. Importantly, the data splits are constructed such that the geometric transformations involved in the final query level-2 compositions differ between the training and evaluation sets. For instance, while the model is trained on basic transformations and a range of transformation compositions (e.g., translation + rotation + reflection), it is evaluated out of distribution on compositions not seen during training (e.g., translation + rotation + extension). We include four different data splits (based on seeds 1860, 1870, 1880, and 1890) in this repository.

Further Information

Details about the data generation process, dataset statistics, and evaluations are presented in the corresponding paper.

Citation

If you find our work helpful, you can cite this paper as:

@inproceedings{
mondorf2026compositionalarc,
title={Compositional-{ARC}: Assessing Systematic Generalization in Abstract Spatial Reasoning},
author={Philipp Mondorf and Shijia Zhou and Monica Riedler and Barbara Plank},
booktitle={The Fourteenth International Conference on Learning Representations},
year={2026},
url={https://openreview.net/forum?id=h497VpgFKd}
}