Solving geometric analogy problems through two-stage analogical mapping

Evans' 1968 ANALOGY system was the first computer model of analogy. This paper demonstrates that the structure mapping model of analogy, when combined with high-level visual processing and qualitative representations, can solve the same kinds of geometric analogy problems as were solved by ANALOGY. Importantly, the bulk of the computations are not particular to the model of this task but are general purpose: We use our existing sketch understanding system, CogSketch, to compute visual structure that is used by our existing analogical matcher, Structure Mapping Engine (SME). We show how SME can be used to facilitate high-level visual matching, proposing a role for structural alignment in mental rotation. We show how second-order analogies over differences computed via analogies between pictures provide a more elegant model of the geometric analogy task. We compare our model against human data on a set of problems, showing that the model aligns well with both the answers chosen by people and the reaction times required to choose the answers.     

Extending SME to Handle Large‐Scale Cognitive Modeling

Analogy and similarity are central phenomena in human cognition, involved in processes ranging from visual perception to conceptual change. To capture this centrality requires that a model of comparison must be able to integrate with other processes and handle the size and complexity of the representations required by the tasks being modeled. This paper describes extensions to Structure‐Mapping Engine (SME) since its inception in 1986 that have increased its scope of operation. We first review the basic SME algorithm, describe psychological evidence for SME as a process model, and summarize its role in simulating similarity‐based retrieval and generalization. Then we describe five techniques now incorporated into the SME that have enabled it to tackle large‐scale modeling tasks: (a) Greedy merging rapidly constructs one or more best interpretations of a match in polynomial time: O(n²log(n)); (b) Incremental operation enables mappings to be extended as new information is retrieved or derived about the base or target, to model situations where information in a task is updated over time; (c) Ubiquitous predicates model the varying degrees to which items may suggest alignment; (d) Structural evaluation of analogical inferences models aspects of plausibility judgments; (e) Match filters enable large‐scale task models to communicate constraints to SME to influence the mapping process. We illustrate via examples from published studies how these enable it to capture a broader range of psychological phenomena than before.     

Structural constraints and object similarity in analogical mapping and inference

Theories of analogical reasoning have viewed relational structure as the dominant determinant of analogical mapping and inference, while assigning lesser importance to similarity between individual objects. An experiment is reported in which these two sources of constraints on analogy are placed in competition under conditions of high relational complexity. Results demonstrate equal importance for relational structure and object similarity, both in analogical mapping and in inference generation. The human data were successfully simulated using a computational analogy model (LISA) that treats both relational correspondences and object similarity as soft constraints that operate within a limited-capacity working memory; but not with a model (SME) that treats relational structure as pre-eminent.     

Category-based induction from similarity of neural activation

The idea that similarity might be an engine of inductive inference dates back at least as far as David Hume. However, Hume’s thesis is difficult to test without begging the question, since judgments of similarity may be infected by inferential processes. We present a one-parameter model of category-based induction that generates predictions about arbitrary statements of conditional probability over a predicate and a set of items. The prediction is based on the unconditional probabilities and similarities that characterize that predicate and those items. To test Hume’s thesis, we collected brain activation from various regions of the ventral visual stream during a categorization task that did not invite comparison of categories. We then calculated the similarity of those activation patterns using a simple measure of vectorwise similarity and supplied those similarities to the model. The model’s outputs correlated well with subjects’ judgments of conditional probability. Our results represent a promising first step toward confirming Hume’s thesis; similarity, assessed without reference to induction, may well drive inductive inference.     

The time course of similarity effects in visual search

It is well established that visual search becomes harder when the similarity between target and distractors is increased and the similarity between distractors is decreased. However, in models of visual search, similarity is typically treated as a static, time-invariant property of the relation between objects. Data from other perceptual tasks (e.g., categorization) demonstrate that similarity is dynamic and changes as perceptual information is accumulated (Lamberts, 1998). In three visual search experiments, the time course of target-distractor similarity effects and distractor-distractor similarity effects was examined. A version of the extended generalized context model (EGCM; Lamberts, 1998) provided a good account of the time course of the observed similarity effects, supporting the notion that similarity in search is dynamic. Modeling also indicated that increasing distractor homogeneity influences both perceptual and decision processes by (respectively) increasing the rate at which stimulus features are processed and enabling strategic weighting of stimulus information.     

Visual comparison processes: Identity and similarity decisions

In the first experiment, in which two successively presented free-form visual patterns varied in their similarity to each other, subjects had to decide, in one condition, if the patterns were “identical” and in two other conditions if the patterns were “similar.” Qualitative individual differences in the effect of similarity on the time required to make a decision were found in the “identity” condition, and these differences interacted with the “similarity” conditions. The individual differences and the experimental effects are interpreted in terms of a two-process model of the visual comparison process—a holistic matching process that is sometimes accompanied by an analytic difference detection process. In the second experiment, the same subjects repeatedly categorized subsets of the free-form visual patterns on the basis of similarity. There appeared to be no individual differences in the subjects’ perceptions of similarity, but subjects’ perceptions did differ from the assumptions made by the experimenters when they established the response criteria for the first experiment.     

A comparison of methods for measuring the interletter similarity between capital letters

Measures of interletter similarity are often required in perception experiments. The most reliable and valid of the available measures appears to be Townsend’s (1971) set of similarity parameters based on the Luce choice model. A simple mechanical measure offered a fairly strong prediction of the Luce choice-model similarity measure, as did a subjective rating measure based on the 10-point visual similarity ratings of eight subjects. By comparison, Gibson et al.’s (1963) matching-confusion matrix faired poorly, as did Gibson’s (1969) distinctive feature analysis based on a letter pair’s number of shared features. Distinctive feature analysis was significantly improved by substituting the feature set proposed by Geyer and DeWald (1973) or by weighting the features optimally via regression analysis. Such analyses suggested that figural curvature may be a particularly important perceptual feature, but in no case did these feature-analytic models predict the Luce measure as well as the mechanical or subjective rating measures.     

Analogy in a general-purpose reasoning system

This paper introduces the various forms of analogy in NARS, a general-purpose reasoning system. NARS is an AI system designed to be adaptive and to work with insufficient knowledge and resources. In the system, multiple types of inference, including analogy, deduction, induction, abduction, comparison, and revision, are unified both in syntax and in semantics. The system can also carry out relational and structural analogy, in ways comparable to (though different from) that in some other models of analogy, such as Copycat and SME. The paper addresses several theoretical issues in the study of analogy, including the specification and justification of analogy, the context sensitivity of analogy, as well as the role analogy plays in intelligence and cognition.     

Alignment to visual speech information

Speech alignment is the tendency for interlocutors to unconsciously imitate one another’s speaking style. Alignment also occurs when a talker is asked to shadow recorded words (e.g., Shockley, Sabadini, & Fowler, 2004). In two experiments, we examined whether alignment could be induced with visual (lipread) speech and with auditory speech. In Experiment 1, we asked subjects to lipread and shadow out loud a model silently uttering words. The results indicate that shadowed utterances sounded more similar to the model’s utterances than did subjects’ nonshadowed read utterances. This suggests that speech alignment can be based on visual speech. In Experiment 2, we tested whether raters could perceive alignment across modalities. Raters were asked to judge the relative similarity between a model’s visual (silent video) utterance and subjects’ audio utterances. The subjects’ shadowed utterances were again judged as more similar to the model’s than were read utterances, suggesting that raters are sensitive to cross-modal similarity between aligned words.     

Finding similarity in a model of relational reasoning

Similarity plays a central role in the study of perception and cognition. Previous attempts to model similarity have captured effects of either featural or structural similarity, but typically not both. We simulated both by fitting similarity data with the LISA model of relational reasoning [Hummel, J. E., & Holyoak, K. J. (1997). Distributed representations of structure: A theory of analogical access and mapping. Psychological Review, 104, 427–466, Hummel, J. E., & Holyoak, K. J. (2003a). A symbolic-connectionist theory of relational inference and generalization. Psychological Review, 110, 220–264]. The same mechanisms LISA uses to simulate analogy also provide a natural account of feature-based similarity effects (e.g., violations of symmetry), structural effects (e.g., the advantage of alignable over non-alignable differences), and the combined effects of featural and structured information (i.e., MIPs and MOPs; “Matches In/Out of Place”) on similarity judgments. Our approach differs from most models of similarity in that LISA was not originally designed to simulate similarity judgments, but rather analogical reasoning. LISA’s incidental ability to simulate diverse similarity effects speaks to the plausibility of the model’s account of human knowledge representation.     

Gaze behavior when approaching an intersection: Dwell time distribution and comparison with a quantitative prediction

The allocation of overt visual attention is investigated in a multi-task and dynamical situation: driving. The Expectancy–Value model of attention allocation stipulates that visual exploration depends on the expectancy and the value of the task-related information available in each Area Of Interest (AOI). We consider the approach to an intersection as a multi-task situation where two subtasks are involved: vehicle control and interactions with other drivers. Each of these subtasks is associated with some specific visual information present in the associated AOIs: the driver’s lane and the intersecting road at the intersection. An experiment was conducted in a driving simulator, coupled with a head-mounted eye-tracker. The intersecting road’s AOI’s Expectancy was manipulated with the traffic density, and its Value was manipulated with the priority rule before the intersection (stop, yield, and priority). The distribution of visual attention and the dynamics of visual exploration were analyzed on 20 participants, taking into account the dwell time in the AOIs associated to the driving subtasks, and the gaze transitions between the AOIs. The results suggest that visual attention to intersecting roads varied with the priority rule, and impacted the visual attention associated with the vehicle control subtask. In addition, a quantitative model was used to improve the understanding of the Expectancy and Value factors. The comparison of the data with the model’s predictions enables quantifying the observed differences between the experimental factors. Finally, the results associated with the traffic density are discussed in relation to the nature of the relevant information while approaching the intersection.     

Minding gaps on the skin: Opposite bisection biases on forehead and back of one’s head

Humans perceive the world from an egocentric perspective, while being able to mentally take a third person’s perspective. Graphesthesia tasks revealed that letters written on the back of one’s own head are consistently perceived from an embodied perspective, while the perspective on one’s front is less consistent and often disembodied. We developed a cutaneous gap bisection task as a more discrete measure of the perspective on the body. In analogy to a visual pseudoneglect, we expected bisections to deviate toward the left ear when perceived from an embodied perspective. While this hypothesis was confirmed for gap bisections on the back, the results on the front suggest overall a disembodied perspective. Contrary to our expectation, this pattern was not predicted by the spontaneous perspective participants took in a graphesthesia task, indicating different cognitive mechanisms. We discuss these findings in the frame of the current literature on spatial attention and perspective taking.     

Integrating structure and meaning: a distributed model of analogical mapping

In this paper we present Drama , a distributed model of analogical mapping that integrates semantic and structural constraints on constructing analogies. Specifically, Drama uses holographic reduced representations (Plate, 1994), a distributed representation scheme, to model the effects of structure and meaning on human performance of analogical mapping. Drama is compared to three symbolic models of analogy (SME, Copycat, and ACME) and one partially distributed model (LISA). We describe Drama's performance on a number of example analogies and assess the model in terms of neurological and psychological plausibility. We argue that Drama's successes are due largely to integrating structural and semantic constraints throughout the mapping process. We also claim that Drama is an existence proof of using distributed representations to model high-level cognitive phenomena.     

A computational model of visual analogies in design

We present an analysis of the work of human participants in addressing design problems by analogy. We describe a computer program, called Galatea, that simulates the visual input and output of four experimental participants. Since Galatea is an operational computer program, it makes specific commitments about the visual representations and reasoning it uses for analogical transfer. In particular, Galatea provides a computational model of how human designers might be generating new designs by incremental transfer of the problem-solving procedure used in previous design cases.     

Post-Established Harmony: Kant and Analogy Reconsidered

This essay is a response to John Milbank’s comparison of Kant and Aquinas’ theories of analogy in ‘A Critique of the Theology of Right’. A critique of Milbank’s essay forms the point of departure for my reconstruction of Kant’s actual theory of analogy. I show that the usual focus on the Prolegomena for this end is insufficient; in fact, the full extent of Kant’s theory of analogy only becomes clear in the Critique of Judgment. I also consider the significance of the Analogies of Experience in the Critique of Pure Reason. In conclusion, I draw on the work of Michel Guérin to designate Kantian analogy, ‘post-established harmony’.     

Visual similarity is stronger than semantic similarity in guiding visual search for numbers

Using a visual search task, we explored how behavior is influenced by both visual and semantic information. We recorded participants’ eye movements as they searched for a single target number in a search array of single-digit numbers (0–9). We examined the probability of fixating the various distractors as a function of two key dimensions: the visual similarity between the target and each distractor, and the semantic similarity (i.e., the numerical distance) between the target and each distractor. Visual similarity estimates were obtained using multidimensional scaling based on the independent observer similarity ratings. A linear mixed-effects model demonstrated that both visual and semantic similarity influenced the probability that distractors would be fixated. However, the visual similarity effect was substantially larger than the semantic similarity effect. We close by discussing the potential value of using this novel methodological approach and the implications for both simple and complex visual search displays.     

CAB: Connectionist Analogy Builder

The ability to make informative comparisons is central to human cognition. Comparison involves aligning two representations and placing their elements into correspondence. Detecting correspondences is a necessary component of analogical inference, recognition, categorization, schema formation, and similarity judgment. Connectionist Analogy Builder (CAB) determines correspondences through a simple iterative computation that matches elements in one representation with elements playing compatible roles in the other representation while simultaneously enforcing structural constraints. CAB shows promise as a process model of comparison as its performance can be related to human performance (e.g., solution trajectory, error patterns, time‐on‐task). Furthermore, CAB's bounded working memory allows it to account for the inherent capacity limitations of human processing. CAB's strengths are its parsimony, transparency of operations, and ability to generate performance predictions. In this paper, CAB is evaluated against benchmark phenomena from the analogy literature.     

Structure mapping in the comparison process

Carrying out similarity and analogy comparisons can be modeled as the alignment and mapping of structured representations. In this article we focus on three aspects of comparison that are central in structure-mapping theory. All three are controversial. First, comparison involves structured representations. Second, the comparison process is driven by a preference for connected relational structure. Third, the mapping between domains is rooted in semantic similarity between the relations that characterize the domains. For each of these points, we review supporting evidence and discuss some challenges raised by other researchers. We end with a discussion of the role of structure mapping in other cognitive processes.     

Paired comparison scaling of reaction potential in two different experiments on habituation

Thurstone’s method of paired comparisons was employed to obtain scaled values of reaction potential from two completely different experimental situations involving response decrement. The first was one in which the GSR was measured on 10 repeated presentations of a visual stimulus (N= 89). The second involved 80 presentations of ordinary visual scenes; the S looked at each scene as long as he wished before switching to the next (i.e., looking time was measured. N=80). Scaling reaction potential by Thurstone’s method provided a common operational definition for both sets of data and permitted their direct comparison in identical units. Both measures showed substantial decrement in reaction potential across stages, with the GSR scale values dropping steeply from the first to the second trial and. thereafter, following a course of decline similar to the looking time scale values. Tlie correlation of the two sets of scale values was essentially linear and equalled 0.90.     

Dynamics of activation of semantically similar concepts during spoken word recognition

Semantic similarity effects provide critical insight into the organization of semantic knowledge and the nature of semantic processing. In the present study, we examined the dynamics of semantic similarity effects by using the visual world eyetracking paradigm. Four objects were shown on a computer monitor, and participants were instructed to click on a named object, during which time their gaze position was recorded. The likelihood of fixating competitor objects was predicted by the degree of semantic similarity to the target concept. We found reliable, graded competition that depended on degree of target-competitor similarity, even for distantly related items for which priming has not been found in previous priming studies. Time course measures revealed a consistently earlier fixation peak for near semantic neighbors relative to targets. Computational investigations with an attractor dynamical model, a spreading activation model, and a decision model revealed that a combination of excitatory and inhibitory mechanisms is required to obtain such peak timing, providing new constraints on models of semantic processing.