skip to main content

Title: Not quite any way you slice it: How different analogical constructions affect Raven's Matrices performance
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.
Authors:
; ;
Award ID(s):
1730044
Publication Date:
NSF-PAR ID:
10209953
Journal Name:
Proceedings of the Eighth Annual Conference on Advances in Cognitive Systems (ACS)
Sponsoring Org:
National Science Foundation
More Like this
  1. 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).more »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.« less
  2. Design-by-analogy (DbA) is an important method for innovation that has gained much attention due to its history of leading to successful and novel design solutions. The method uses a repository of existing design solutions where designers can recognize and retrieve analogical inspirations. Yet, exploring for analogical inspiration has been a laborious task for designers. This work presents a computational methodology that is driven by a topic modeling technique called non-negative matrix factorization (NMF). NMF is widely used in the text mining field for its ability to discover topics within documents based on their semantic content. In the proposed methodology, NMFmore »is performed iteratively to build hierarchical repositories of design solutions, with which designers can explore clusters of analogical stimuli. This methodology has been applied to a repository of mechanical design-related patents, processed to contain only component-, behavior-, or material-based content to test if unique and valuable attribute-based analogical inspiration can be discovered from the different representations of patent data. The hierarchical repositories have been visualized, and a case study has been conducted to test the effectiveness of the analogical retrieval process of the proposed methodology. Overall, this paper demonstrates that the exploration-based computational methodology may provide designers an enhanced control over design repositories to retrieve analogical inspiration for DbA practice.« less
  3. 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 reasoningmore »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.

    « less
  4. In this paper, we present the Visuospatial Reasoning Environment for Experimentation (VREE). VREE provides a simulated environment where intelligent agents interact with virtual objects while solving different visuospatial reasoning tasks. This paper shows how VREE is valuable for studying the sufficiency of visual imagery approaches for a large number of visuospatial reasoning tasks as well as how diverse strategies can be represented and studied within a single task. We present results from computational experiments using VREE on the block design task and on numerous subtests from the Leiter-R test battery on nonverbal intelligence.
  5. Abstract

    Extracting an individual’s knowledge structure is a challenging task as it requires formalization of many concepts and their interrelationships. While there has been significant research on how to represent knowledge to support computational design tasks, there is limited understanding of the knowledge structures of human designers. This understanding is necessary for comprehension of cognitive tasks such as decision making and reasoning, and for improving educational programs. In this paper, we focus on quantifying theory-based causal knowledge, which is a specific type of knowledge held by human designers. We develop a probabilistic graph-based model for representing individuals’ concept-specific causal knowledgemore »for a given theory. We propose a methodology based on probabilistic directed acyclic graphs (DAGs) that uses logistic likelihood function for calculating the probability of a correct response. The approach involves a set of questions for gathering responses from 205 engineering students, and a hierarchical Bayesian approach for inferring individuals’ DAGs from the observed responses. We compare the proposed model to a baseline three-parameter logistic (3PL) model from the item response theory. The results suggest that the graph-based logistic model can estimate individual students’ knowledge graphs. Comparisons with the 3PL model indicate that knowledge assessment is more accurate when quantifying knowledge at the level of causal relations than quantifying it using a scalar ability parameter. The proposed model allows identification of parts of the curriculum that a student struggles with and parts they have already mastered which is essential for remediation.

    « less