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A. Zaghår
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Efficient learning through programmatic representations
How can we better find the matches between input and output objects?
The Abstraction and Reasoning Corpus (ARC) serves as a challenging benchmark designed to measure human-like artificial intelligence by only providing a few training examples for each task. Program synthesis offers a new approach to solving this benchmark by generating rule-based transformation programs. A recent approach, BEN, tackles these tasks by making use of program synthesis in a Divide, Align and Conquer strategy. The Align component identifies correspondences between the input and output objects by using a Structure Mapping Engine (SME) rooted in analogical reasoning. Despite its success, each individual part of the algorithm can be further improved, in particular the features of objects used in Align.
We present an enhanced object-matching methodology of the Align component to improve the quality of the correspondences found. First, the BEN algorithm is re-implemented in Julia, making use of an Answer Set Programming (ASP) solver using Clingo and Prolog for the SME to offer better efficiency. Second, we augment the structural representation of the objects by introducing features that capture the spatial relations between them, specifically through forms of ranked coordinates. Furthermore, we refine how multi-coloured objects are propositionally encoded. Finally, we introduce a weighting heuristic for the features: the significance of individual visual attributes is minimized when the input and output grids contain the same number of objects, and simple coordinates are eliminated when the input and output grids have different sizes.
The proposed changes were evaluated by isolating the Align component across subsets of the ARC-AGI-1 benchmark. In a sample of 25 manually selected tasks, the number of perfectly matched tasks improved significantly from 11 to 23. In a randomly selected sample of 25 tasks, the modifications give better or identical matches in 22 tasks, with only 3 showing degradations. When running the entire benchmark with the full BEN algorithm, one extra task is solved and two no longer are. Average times are similar and the number of searched transformations decreases. These findings suggest that including spatial relations and contextual weighting of the features improves the accuracy of finding correct correspondences for the ARC benchmark. ...
We present an enhanced object-matching methodology of the Align component to improve the quality of the correspondences found. First, the BEN algorithm is re-implemented in Julia, making use of an Answer Set Programming (ASP) solver using Clingo and Prolog for the SME to offer better efficiency. Second, we augment the structural representation of the objects by introducing features that capture the spatial relations between them, specifically through forms of ranked coordinates. Furthermore, we refine how multi-coloured objects are propositionally encoded. Finally, we introduce a weighting heuristic for the features: the significance of individual visual attributes is minimized when the input and output grids contain the same number of objects, and simple coordinates are eliminated when the input and output grids have different sizes.
The proposed changes were evaluated by isolating the Align component across subsets of the ARC-AGI-1 benchmark. In a sample of 25 manually selected tasks, the number of perfectly matched tasks improved significantly from 11 to 23. In a randomly selected sample of 25 tasks, the modifications give better or identical matches in 22 tasks, with only 3 showing degradations. When running the entire benchmark with the full BEN algorithm, one extra task is solved and two no longer are. Average times are similar and the number of searched transformations decreases. These findings suggest that including spatial relations and contextual weighting of the features improves the accuracy of finding correct correspondences for the ARC benchmark. ...
The Abstraction and Reasoning Corpus (ARC) serves as a challenging benchmark designed to measure human-like artificial intelligence by only providing a few training examples for each task. Program synthesis offers a new approach to solving this benchmark by generating rule-based transformation programs. A recent approach, BEN, tackles these tasks by making use of program synthesis in a Divide, Align and Conquer strategy. The Align component identifies correspondences between the input and output objects by using a Structure Mapping Engine (SME) rooted in analogical reasoning. Despite its success, each individual part of the algorithm can be further improved, in particular the features of objects used in Align.
We present an enhanced object-matching methodology of the Align component to improve the quality of the correspondences found. First, the BEN algorithm is re-implemented in Julia, making use of an Answer Set Programming (ASP) solver using Clingo and Prolog for the SME to offer better efficiency. Second, we augment the structural representation of the objects by introducing features that capture the spatial relations between them, specifically through forms of ranked coordinates. Furthermore, we refine how multi-coloured objects are propositionally encoded. Finally, we introduce a weighting heuristic for the features: the significance of individual visual attributes is minimized when the input and output grids contain the same number of objects, and simple coordinates are eliminated when the input and output grids have different sizes.
The proposed changes were evaluated by isolating the Align component across subsets of the ARC-AGI-1 benchmark. In a sample of 25 manually selected tasks, the number of perfectly matched tasks improved significantly from 11 to 23. In a randomly selected sample of 25 tasks, the modifications give better or identical matches in 22 tasks, with only 3 showing degradations. When running the entire benchmark with the full BEN algorithm, one extra task is solved and two no longer are. Average times are similar and the number of searched transformations decreases. These findings suggest that including spatial relations and contextual weighting of the features improves the accuracy of finding correct correspondences for the ARC benchmark.
We present an enhanced object-matching methodology of the Align component to improve the quality of the correspondences found. First, the BEN algorithm is re-implemented in Julia, making use of an Answer Set Programming (ASP) solver using Clingo and Prolog for the SME to offer better efficiency. Second, we augment the structural representation of the objects by introducing features that capture the spatial relations between them, specifically through forms of ranked coordinates. Furthermore, we refine how multi-coloured objects are propositionally encoded. Finally, we introduce a weighting heuristic for the features: the significance of individual visual attributes is minimized when the input and output grids contain the same number of objects, and simple coordinates are eliminated when the input and output grids have different sizes.
The proposed changes were evaluated by isolating the Align component across subsets of the ARC-AGI-1 benchmark. In a sample of 25 manually selected tasks, the number of perfectly matched tasks improved significantly from 11 to 23. In a randomly selected sample of 25 tasks, the modifications give better or identical matches in 22 tasks, with only 3 showing degradations. When running the entire benchmark with the full BEN algorithm, one extra task is solved and two no longer are. Average times are similar and the number of searched transformations decreases. These findings suggest that including spatial relations and contextual weighting of the features improves the accuracy of finding correct correspondences for the ARC benchmark.