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1. Visual analogy: Deep learning versus compositional models

   Ichien, N.; Liu, Q.; Fu, S.; Holyoak, K. J.; Yuille, A. L.; Lu, H. (July 2021, Proceedings of the 43rd Annual Meeting of the Cognitive Science Society)

   Fitch, T.; Lamm, C.; Leder, H.; Teßmar-Raible, K. (Ed.)

   Is analogical reasoning a task that must be learned to solve from scratch by applying deep learning models to massive numbers of reasoning problems? Or are analogies solved by computing similarities between structured representations of analogs? We address this question by comparing human performance on visual analogies created using images of familiar three-dimensional objects (cars and their subregions) with the performance of alternative computational models. Human reasoners achieved above-chance accuracy for all problem types, but made more errors in several conditions (e.g., when relevant subregions were occluded). We compared human performance to that of two recent deep learning models (Siamese Network and Relation Network) directly trained to solve these analogy problems, as well as to that of a compositional model that assesses relational similarity between part-based representations. The compositional model based on part representations, but not the deep learning models, generated qualitative performance similar to that of human reasoners. 

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2. Not quite any way you slice it: How different analogical constructions affect Raven's Matrices performance

   Yang, Y.; McGreggor, K.; Kunda, M. (January 2020, Proceedings of the Eighth Annual Conference on Advances in Cognitive Systems (ACS))

   null (Ed.)

   Analogical reasoning fundamentally involves exploiting redundancy in a given task, but there are many different ways an intelligent agent can choose to define and exploit redundancy, often resulting in very different levels of task performance. We explore such variations in analogical reasoning within the domain of geometric matrix reasoning tasks, namely on the Raven’s Standard Progressive Matrices intelligence test. We show how different analogical constructions used by the same basic visual-imagery-based computational model—varying only in how they “slice” a matrix problem into parts and do search and optimization within/across these parts—achieve very different levels of test performance, ranging from 13/60 correct all the way up to 57/60 correct. Our findings suggest that the ability to select or build effective high-level analogical constructions can be as important as an agent’s competencies in low-level reasoning skills, which raises interesting open questions about the extent to which building the “right” analogies might contribute to individual differences in human matrix reasoning performance, and how intelligent agents might learn to build or select from among different analogical constructions in the first place. 

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3. Emergence of analogy from relation learning

   https://doi.org/10.1073/pnas.1814779116  

   Lu, Hongjing; Wu, Ying Nian; Holyoak, Keith J. (February 2019, Proceedings of the National Academy of Sciences)

   By middle childhood, humans are able to learn abstract semantic relations (e.g., antonym, synonym, category membership) and use them to reason by analogy. A deep theoretical challenge is to show how such abstract relations can arise from nonrelational inputs, thereby providing key elements of a protosymbolic representation system. We have developed a computational model that exploits the potential synergy between deep learning from “big data” (to create semantic features for individual words) and supervised learning from “small data” (to create representations of semantic relations between words). Given as inputs labeled pairs of lexical representations extracted by deep learning, the model creates augmented representations by remapping features according to the rank of differences between values for the two words in each pair. These augmented representations aid in coping with the feature alignment problem (e.g., matching those features that make “love-hate” an antonym with the different features that make “rich-poor” an antonym). The model extracts weight distributions that are used to estimate the probabilities that new word pairs instantiate each relation, capturing the pattern of human typicality judgments for a broad range of abstract semantic relations. A measure of relational similarity can be derived and used to solve simple verbal analogies with human-level accuracy. Because each acquired relation has a modular representation, basic symbolic operations are enabled (notably, the converse of any learned relation can be formed without additional training). Abstract semantic relations can be induced by bootstrapping from nonrelational inputs, thereby enabling relational generalization and analogical reasoning. 

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4. From Vision to Reasoning:Probabilistic Analogical Mapping Between 3D Objects

   Fu, S.; Holyoak, K. J.; Lu, H. (January 2022, Proceedings of the 44th Annual Meeting of the Cognitive Science Society)

   We see the external world as consisting not only of objects and their parts, but also of relations that hold between them. Visual analogy, which depends on similarities between relations, provides a clear example of how perception supports reasoning. Here we report an experiment in which we quantitatively measured the human ability to find analogical mappings between parts of different objects, where the objects to be compared were drawn either from the same category (e.g., images of two mammals, such as a dog and a horse), or from two dissimilar categories (e.g., a chair image mapped to a cat image). Humans showed systematic mapping patterns, but with greater variability in mapping responses when objects were drawn from dissimilar categories. We simulated the human response of analogical mapping using a computational model of mapping between 3D objects, visiPAM (visual Probabilistic Analogical Mapping). VisiPAM takes point-cloud representations of two 3D objects as inputs, and outputs the mapping between analogous parts of the two objects. VisiPAM consists of a visual module that constructs structural representations of individual objects, and a reasoning module that identifies a probabilistic mapping between parts of the two 3D objects. Model simulations not only capture the qualitative pattern of human mapping performance cross conditions, but also approach human-level reliability in solving visual analogy problems. 

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5. Impact of Semantic Representations on Analogical Mapping with Transitive Relations

   Linford, B.; Ichien, N.; Holyoak, K. J.; Lu, H. (January 2022, Proceedings of the 44th Annual Meeting of the Cognitive Science Society)

   Analogy problems involving multiple ordered relations of the same type create mapping ambiguity, requiring some mechanism for relational integration to achieve mapping accuracy. We address the question of whether the integration of ordered relations depends on their logical form alone, or on semantic representations that differ across relation types. We developed a triplet mapping task that provides a basic paradigm to investigate analogical reasoning with simple relational structures. Experimental results showed that mapping performance differed across orderings based on category, linear order, and causal relations, providing evidence that each transitive relation has its own semantic representation. Hence, human analogical mapping of ordered relations does not depend solely on their formal property of transitivity. Instead, human ability to solve mapping problems by integrating relations relies on the semantics of relation representations. We also compared human performance to the performance of several vector-based computational models of analogy. These models performed above chance but fell short of human performance for some relations, highlighting the need for further model development. 

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