Systematic Human Learning and Generalization From a Brief Tutorial With Explanatory Feedback

We investigate human adults' ability to learn an abstract reasoning task quickly and to generalize outside of the range of training examples. Using a task based on a solution strategy in Sudoku, we provide Sudoku-naive participants with a brief instructional tutorial with explanatory feedback using a narrow range of training examples. We find that most participants who master the task do so within 10 practice trials and generalize well to puzzles outside of the training range. We also find that most of those who master the task can describe a valid solution strategy, and such participants perform better on transfer puzzles than those whose strategy descriptions are vague or incomplete. Interestingly, fewer than half of our human participants were successful in acquiring a valid solution strategy, and this ability was associated with completion of high school algebra and geometry. We consider the implications of these findings for understanding human systematic reasoning, as well as the challenges these findings pose for building computational models that capture all aspects of our findings, and we point toward a role for learning from instructions and explanations to support rapid learning and generalization.

Dual-Routes and the Cost of Determining Least-Costs

Theories of cognition that posit complementary dual-route processes afford better fits to the data when each route explains a part of the data not explained by the other route. However, such theories must also explain why each route is invoked, lest one can fit any data set with enough alternatives. One possible explanation is that route selection is based on a least-cost principle: the route that requires fewer cognitive resources (including time) relative to the goal at hand. We investigated this explanation with a dual-display version of visual search, where the target could be identified via opposing (easy or hard forms of) feature and conjunction search conditions. The data support a contextualized version of the least-cost principle in that the cost of computing least-cost also influences route selection: participants assessed alternatives, but only when the cost of that assessment was relatively low.

Beyond Psychometrics: The Difference between Difficult Problem Solving and Complex Problem Solving

In this paper we argue that a synthesis of findings across the various sub-areas of research in complex problem solving and consequently progress in theory building is hampered by an insufficient differentiation of complexity and difficulty. In the proposed framework of person, task, and situation (PTS), complexity is conceptualized as a quality that is determined by the cognitive demands that the characteristics of the task and the situation impose. Difficulty represents the quantifiable level of a person's success in dealing with such demands. We use the well-documented "semantic effect" as an exemplar for testing some of the conceptual assumptions derived from the PTS framework. We demonstrate how a differentiation between complexity and difficulty can help take beyond a potentially too narrowly defined psychometric perspective and subsequently gain a better understanding of the cognitive mechanisms behind this effect. In an empirical study a total of 240 university students were randomly allocated to one of four conditions. The four conditions resulted from contrasting the semanticity level of the variable labels used in the CPS system (high vs. low) and two instruction conditions for how to explore the CPS system's causal structure (starting with the assumption that all relationships between variables existed vs. starting with the assumption that none of the relationships existed). The variation in the instruction aimed at inducing knowledge acquisition processes of either (1) systematic elimination of presumptions, or (2) systematic compilation of a mental representation of the causal structure underpinning the system. Results indicate that (a) it is more complex to adopt a "blank slate" perspective under high semanticity as it requires processes of inhibiting prior assumptions, and (b) it seems more difficult to employ a systematic heuristic when testing against presumptions. In combination, situational characteristics, such as the semanticity of variable labels, have the potential to trigger qualitatively different tasks. Failing to differentiate between 'task' and 'situation' as independent sources of complexity and treating complexity and difficulty synonymously threaten the validity of performance scores obtained in CPS research.

Why Are There Failures of Systematicity? The Empirical Costs and Benefits of Inducing Universal Constructions

Systematicity is a property of cognition where capacity for certain cognitive abilities implies capacity for certain other (structurally related) cognitive abilities. This property is thought to derive from a capacity to represent/process common structural relations between constituents of cognizable entities, however, systematicity may not always materialize in such admissible contexts. A theoretical challenge is to explain why systematicity fails to materialize in contexts that allow the realization (e.g., by induction) of common structure (universal construction). We hypothesize that one cause of failure arises when the potential gain afforded by induction of common structure is overshadowed by the immediate benefit of learning the task as independent stimulus-response associations. This hypothesis was tested in an experiment that required learning two series of pair maps that involved products (universal construction), or non-products (control) of varied size: the number of unique cue/target elements (three to six) constituting pairs. Each series was learned in either ascending or descending order of size. Only performance on the product series was affected by order: systematicity was obtained universally in the descend group, but only on large sets in the ascend group, as revealed by the significant order × size interaction for errors in the product condition, F (3, 87) = 3.38, p < 0.05. Smaller maps are more easily learned without inducing the common product structure, which is more readily observable with larger maps: larger maps provide more evidence for relationships between stimulus dimensions that facilitate the discovery of the common structure. The new challenge, then, is to explain the systematic learnability of stimulus-response maps, i.e., second-order systematicity.

Systematicity and a Categorical Theory of Cognitive Architecture: Universal Construction in Context

Why does the capacity to think certain thoughts imply the capacity to think certain other, structurally related, thoughts? Despite decades of intensive debate, cognitive scientists have yet to reach a consensus on an explanation for this property of cognitive architecture—the basic processes and modes of composition that together afford cognitive capacity—called systematicity. Systematicity is generally considered to involve a capacity to represent/process common structural relations among the equivalently cognizable entities. However, the predominant theoretical approaches to the systematicity problem, i.e., classical (symbolic) and connectionist (subsymbolic), require arbitrary (ad hoc) assumptions to derive systematicity. That is, their core principles and assumptions do not provide the necessary and sufficient conditions from which systematicity follows, as required of a causal theory. Hence, these approaches fail to fully explain why systematicity is a (near) universal property of human cognition, albeit in restricted contexts. We review an alternative, category theory approach to the systematicity problem. As a mathematical theory of structure, category theory provides necessary and sufficient conditions for systematicity in the form of universal construction: each systematically related cognitive capacity is composed of a common component and a unique component. Moreover, every universal construction can be viewed as the optimal construction in the given context (category). From this view, universal constructions are derived from learning, as an optimization. The ultimate challenge, then, is to explain the determination of context. If context is a category, then a natural extension toward addressing this question is higher-order category theory, where categories themselves are the objects of construction.

Arbitrariness, Iconicity, and Systematicity in Language

The notion that the form of a word bears an arbitrary relation to its meaning accounts only partly for the attested relations between form and meaning in the languages of the world. Recent research suggests a more textured view of vocabulary structure, in which arbitrariness is complemented by iconicity (aspects of form resemble aspects of meaning) and systematicity (statistical regularities in forms predict function). Experimental evidence suggests these form-to-meaning correspondences serve different functions in language processing, development, and communication: systematicity facilitates category learning by means of phonological cues, iconicity facilitates word learning and communication by means of perceptuomotor analogies, and arbitrariness facilitates meaning individuation through distinctive forms. Processes of cultural evolution help to explain how these competing motivations shape vocabulary structure.

Commonalities between Perception and Cognition

Perception and cognition are highly interrelated. Given the influence that these systems exert on one another, it is important to explain how perceptual representations and cognitive representations interact. In this paper, I analyze the similarities between visual perceptual representations and cognitive representations in terms of their structural properties and content. Specifically, I argue that the spatial structure underlying visual object representation displays systematicity – a property that is considered to be characteristic of propositional cognitive representations. To this end, I propose a logical characterization of visual feature binding as described by Treisman’s Feature Integration Theory and argue that systematicity is not only a property of language-like representations, but also of spatially organized visual representations. Furthermore, I argue that if systematicity is taken to be a criterion to distinguish between conceptual and non-conceptual representations, then visual representations, that display systematicity, might count as an early type of conceptual representations. Showing these analogies between visual perception and cognition is an important step toward understanding the interface between the two systems. The ideas here presented might also set the stage for new empirical studies that directly compare binding (and other relational operations) in visual perception and higher cognition.