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1. 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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2. AI, visual imagery, and a case study on the challenges posed by human intelligence tests

   https://doi.org/10.1073/pnas.1912335117  

   Kunda, Maithilee ( November 2020 , Proceedings of the National Academy of Sciences)

   Observations abound about the power of visual imagery in human intelligence, from how Nobel prize-winning physicists make their discoveries to how children understand bedtime stories. These observations raise an important question for cognitive science, which is, what are the computations taking place in someone’s mind when they use visual imagery? Answering this question is not easy and will require much continued research across the multiple disciplines of cognitive science. Here, we focus on a related and more circumscribed question from the perspective of artificial intelligence (AI): If you have an intelligent agent that uses visual imagery-based knowledge representations and reasoning operations, then what kinds of problem solving might be possible, and how would such problem solving work? We highlight recent progress in AI toward answering these questions in the domain of visuospatial reasoning, looking at a case study of how imagery-based artificial agents can solve visuospatial intelligence tests. In particular, we first examine several variations of imagery-based knowledge representations and problem-solving strategies that are sufficient for solving problems from the Raven’s Progressive Matrices intelligence test. We then look at how artificial agents, instead of being designed manually by AI researchers, might learn portions of their own knowledge and reasoning procedures from experience, including learning visuospatial domain knowledge, learning and generalizing problem-solving strategies, and learning the actual definition of the task in the first place.

    

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3. Learning algebraic representation for systematic generalization in abstract reasoning

   Zhang, C. ; Xie, S. ; Jia B. ; Wu, Y. N. ; Zhu, S.-C. ; Zhu, Y. ( January 2022 , European Conference on Computer Vision (ECCV 2022))

   Is intelligence realized by connectionist or classicist? While connectionist approaches have achieved superhuman performance, there has been growing evidence that such task-specific superiority is particularly fragile in systematic generalization. This observation lies in the central debate between connectionist and classicist, wherein the latter continually advocates an algebraic treatment in cognitive architectures. In this work, we follow the classicist’s call and propose a hybrid approach to improve systematic generalization in reasoning. Specifically, we showcase a prototype with algebraic representation for the abstract spatial-temporal reasoning task of Raven’s Progressive Matrices (RPM) and present the ALgebra-Aware Neuro-Semi-Symbolic (ALANS) learner. The ALANS learner is motivated by abstract algebra and the representation theory. It consists of a neural visual perception frontend and an algebraic abstract reasoning backend: the frontend summarizes the visual information from object-based representation, while the backend transforms it into an algebraic structure and induces the hidden operator on the fly. The induced operator is later executed to predict the answer’s representation, and the choice most similar to the prediction is selected as the solution. Extensive experiments show that by incorporating an algebraic treatment, the ALANS learner outperforms various pure connectionist models in domains requiring systematic generalization. We further show the generative nature of the learned algebraic representation; it can be decoded by isomorphism to generate an answer. 

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4. Two Computational Approaches to Visual Analogy: Task‐Specific Models Versus Domain‐General Mapping

   https://doi.org/10.1111/cogs.13347  

   Ichien, Nicholas ; Liu, Qing ; Fu, Shuhao ; Holyoak, Keith J. ; Yuille, Alan L. ; Lu, Hongjing ( September 2023 , Cognitive Science)

   Advances in artificial intelligence have raised a basic question about human intelligence: Is human reasoning best emulated by applying task‐specific knowledge acquired from a wealth of prior experience, or is it based on the domain‐general manipulation and comparison of mental representations? We address this question for the case of visual analogical reasoning. Using realistic images of familiar three‐dimensional objects (cars and their parts), we systematically manipulated viewpoints, part relations, and entity properties in visual analogy problems. We compared human performance to that of two recent deep learning models (Siamese Network and Relation Network) that were directly trained to solve these problems and to apply their task‐specific knowledge to analogical reasoning. We also developed a new model using part‐based comparison (PCM) by applying a domain‐general mapping procedure to learned representations of cars and their component parts. Across four‐term analogies (Experiment 1) and open‐ended analogies (Experiment 2), the domain‐general PCM model, but not the task‐specific deep learning models, generated performance similar in key aspects to that of human reasoners. These findings provide evidence that human‐like analogical reasoning is unlikely to be achieved by applying deep learning with big data to a specific type of analogy problem. Rather, humans do (and machines might) achieve analogical reasoning by learning representations that encode structural information useful for multiple tasks, coupled with efficient computation of relational similarity.

    

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5. Dynamic prompt learning via policy gradient for semi-structured mathematical reasoning

   Lu, P. ; Qiu, L. ; Chang, K. W. ; Wu, Y. N. ; Zhu, S. C. ; Rajpurohit, T. ; Clark, K. ; Kalyan, A. ( May 2023 , International Conference on Learning Representations (ICLR 2023))

   Mathematical reasoning, a core ability of human intelligence, presents unique challenges for machines in abstract thinking and logical reasoning. Recent large pre-trained language models such as GPT-3 have achieved remarkable progress on mathematical reasoning tasks written in text form, such as math word problems (MWP). However, it is unknown if the models can handle more complex problems that involve math reasoning over heterogeneous information, such as tabular data. To fill the gap, we present Tabular Math Word Problems (TABMWP), a new dataset containing 38,431 open-domain grade-level problems that require mathematical reasoning on both textual and tabular data. Each question in TABMWP is aligned with a tabular context, which is presented as an image, semi-structured text, and a structured table. There are two types of questions: free-text and multi-choice, and each problem is annotated with gold solutions to reveal the multi-step reasoning process. We evaluate different pre-trained models on TABMWP, including the GPT-3 model in a few-shot setting. As earlier studies suggest, since few-shot GPT-3 relies on the selection of in-context examples, its performance is unstable and can degrade to near chance. The unstable issue is more severe when handling complex problems like TABMWP. To mitigate this, we further propose a novel approach, PROMPTPG, which utilizes policy gradient to learn to select in-context examples from a small amount of training data and then constructs the corresponding prompt for the test example. Experimental results show that our method outperforms the best baseline by 5.31% on the accuracy metric and reduces the prediction variance significantly compared to random selection, which verifies its effectiveness in selecting in-context examples. 

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