Canada

Distributed vector representations are a key bridging point between connectionist and symbolic representations of cognition. It is unclear how uncertainty should be modelled in systems using such representations. One may place vector-valued distributions over vector representations, although that may assign non-zero probabilities to vector symbols that cannot occur. In this paper we discuss how bundles of symbols in Vector Symbolic Architectures (VSAs) can be understood as defining an object that has a relationship to a probability distribution, and how statements in VSAs can be understood as being analogous to probabilistic statements. We sketch novel designs for networks that compute entropy and mutual information. In this paper we restrict ourselves to operators proposed for Holographic Reduced Representations, and representing real-valued data. However, we suggest that the methods presented in this paper should translate to any VSA where the dot product between fractionally bound symbols induces a valid kernel.

CogSci 2022

Fractional Binding in Vector Symbolic Architectures as Quasi-Probability Statements

technical paper

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The 44th Annual Meeting of the Cognitive Science Society highlighted research on the theme Cognitive Diversity in addition to the full breadth and diversity of research topics offered by the society’s membership. 





Models in cognitive science are often restricted for the sake of interpretability, and as a result may miss patterns in the data that are instead classified as noise. In contrast, deep neural networks can detect almost any pattern given sufficient data, but have only recently been applied to large-scale data sets and tasks for which there already exist process-level models to compare against. Here, we train deep neural networks to predict human play in 4-in-a-row, a combinatorial game of intermediate complexity, using a data set of 10,874,547 games. We compare these networks to a planning model based on a heuristic function and tree search, and make suggestions for model improvements based on this analysis. This work provides the foundation for estimating a noise ceiling on massive data sets as well as systematically investigating the processes underlying human sequential decision-making.

Improving a model of human planning via large-scale data and deep neural networks

“Slavery ended in the United States because slavery is morally wrong.” This explanation does not seem to fit the typical criteria for explaining an event, since it appeals to ethics rather than causal factors as the reason for this social change. But do people perceive these ethical claims as explanatory, and if so, why? In Study 1, we find that people accept ethical explanations for social change and that this is predicted by their meta-ethical beliefs in moral progress and moral objectivism, suggesting that they treat morality somewhat akin to a causal force. In Study 2, we find that people recognize this relationship between ethical explanations and meta-ethical commitments, using the former to make inferences about individuals’ beliefs in moral progress and objectivism. Together these studies demonstrate that our moral commitments shape our judgments of explanations and that explanations shape our moral inferences about others.

Ethical Explanations

To defend or burnish our moral reputation, we often tell moral narratives. Moral narratives describe morally relevant actions and explanations of those actions, detailing how people acted and why they did so. When and why does communication about moral events include descriptions of peoples’ actions and explanations? We hypothesize that informational, reputational, and presentational goals of narrators shape whether their communication contains clear actions and explanations. We asked a group of “narrators” to communicate with other people following a moral decision. Another group of “audience” members judged them based on their chosen statement. We find that the informational and reputational goals of narrators can explain what information they decide to reveal. Narrators choose what to say based on inferring the audience’s likely perceptions but underestimate how much audiences in fact expect answers to “what” and “why”. Audiences, however, do not always perceive the lack of expected information as indicative of deceit.

Narrating the "what" and "why" of our moral actions

One of the most influential modern theories of morality, Moral Foundations Theory, proposes that morality is formed on innate and shared modular foundations. Psychologists have studied the conceptual development of these moral foundations in childhood, but there exists no comprehensive effort on characterizing the early emergence of moral foundations in naturalistic settings. We explore the emerging order of moral foundations through child and caretaker speech. Using computational methods, we contribute an annotated dataset of moral utterances and find that the individualizing foundations emerge earlier than the binding foundations. Furthermore, caretakers tend to talk more about fairness and degradation, while children talk more about cheating. These results are robust across child gender, family's social class, and race.

The emergence of moral foundations in child language development

Rules undoubtedly guide our moral lives. Simple moral rules prohibit lying, cheating, and stealing, for instance. But the moral mind is more flexible than a theory based only on rule-adherence can account for. In this paper, we look at one particular kind of flexibility: the ability to figure out when it is okay to break a moral rule. We elicit judgments of the moral acceptability of breaking a simple rule: it's wrong to cut in line. We created a video game environment in which agents attempt to gather water -- and sometimes must stand in line behind others to do so. Subjects watch clips of the game being played and make judgments of the moral acceptability of cutting in line across a wide range of spatio-temporally varied and dynamic scenarios. Our data suggests that subjects make judgments by using a generative understanding of the underlying function of the rule about waiting in line. We further show that our data cannot be accounted for by either 1) simple rule adherence or 2) utility maximization.

Flexibility in Moral Cognition: When is it okay to break the rules?

Statistical descriptions of reaction times are central components of quantitative attention models. It is often assumed that total reaction time is comprised of various components, e.g. sensory delays, decision making and motor execution contributions. We use machine learning to decompose observed total reaction times into sensorimotor and decision components, and evaluate which model assumptions maximize approximate Bayesian model evidence (free energy or evidence lower bound). We find that an inverse Gaussian decision time distribution combined with a very narrow Gaussian sensorimotor distribution can best explain human reaction time data. We also model outliers explicitly by a uniform background distribution. We find that the model assigns a small fraction of datapoints to this outlier distribution.

Sensorimotor processes are not a source of much noise: Sensory-motor and decision components of reaction times

Beyond seemingly lower-level features such as color and motion, visual perception also recovers properties that are more commonly associated with higher-level thought — as when an upwardly accelerating object is seen as self-propelled, and resisting the force of gravity. Past work has explored how speed changes drive the perception of physical forces, but might the reverse also be true? Does seeing a speed change as resisting the force of gravity make us more likely to notice it in the first place? In four experiments, observers were more sensitive to objects’ accelerations when they moved upward (i.e. when those accelerations were opposite to gravity), and they were more sensitive to objects’ decelerations when they moved downward (i.e. when those decelerations appeared as ‘braking’ against gravity). We conclude that the perception of physical forces is not merely an outcome of visual processing, but also determines the perception of other, seemingly lower-level, features of how objects move.

May the Force be against you: Better sensitivity to speed changes opposite to gravity

According to the embodied cognition view, retrieving the meaning of action-related language requires the participation of sensorimotor processes. In consequence, an increasing number of neurostimulation (TMS and tDCS) studies have tried to test this idea. In the present study, we aim to evaluate the evidential value of this body of research (N = 43) by means of p-curve analyses. Our results suggest that the published studies so far do not yet allow to establish if they explore real effects beyond a reasonable doubt. We also found that these studies are quite underpowered (estimated power < 30%), which suggests that a large percentage of these findings are, in fact, false-positive results. In sum, our study suggests that the results derived from brain stimulation studies of embodied semantics are not as reliable as would be desirable. We give some recommendations that will be important for future research on this topic.

Grounding meaning in the motor system: A p-curve analysis of the TMS and tDCS evidence

Using space to think about time appears to be a human universal, but the specifics of people’s space-time mappings vary across individuals and groups. What determines how people spatialize time in their minds? Here we hypothesized that motor experience contributes to individuals’ space-time mappings, independent of linguistic and cultural factors. Many everyday motor actions require using the hands in a particular sequence (e.g., positioning a nail with the nondominant hand before swinging the hammer with the dominant hand), establishing a correlation between space (left hand, right hand) and time (earlier action, later action) that reverses with handedness. These action sequences reinforce Westerners’ typical left-to-right mental timeline for right-handers, but contradict this timeline for left-handers. Accordingly, we find that right-handers associate leftward space with earlier times and rightward space with later times more strongly than left-handers, for whom cultural and bodily experiences present contrasting relationships between space and time.

The le hand of time: Roles of cultural and bodily experience in constructing the mental timeline

The current work tests the hypothesis that the island status of clausal adjuncts, as determined by judgments on wh-questions, are predicted by the degree of “backgroundedness” of the adjuncts, as determined by a separate negation task. Results of two experiments support the hypothesis that acceptability of extraction from adjuncts in wh-questions is inversely correlated with the degree to which the adjunct is backgrounded in discourse. Taken together, results show that temporal clausal adjuncts (headed by before, after, while) are stronger islands than adjuncts that are causal (here, headed by to or by). This demonstrates that adjuncts differ in degree of island status, depending on their meaning, despite parallel syntactic structure.

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Fractional Binding in Vector Symbolic Architectures as Quasi-Probability Statements

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