Shape representations play a central role in our interaction with the world [1]. Nevertheless, we have only a vague understanding of how shape knowledge is represented.
In this paper, we use the framework of conceptual spaces [2] as a modeling tool for representing complex shapes. In this framework, each object is represented as a point in the conceptual space whose coordinates represent the object specific values of the employed quality dimensions. The geometric distance between two points represents the similarity between two objects (the smaller the distance, the more similar the objects). Higher-order concepts can be identified as convex, non-overlapping regions.
Our study aims at discovering structural characteristics of a shape space that can explain human perception and categorizations of complex shapes. This can contribute to new insights and a deeper understanding of perceptual processes but also allows for constructive uses, e.g. in the context of cognitive AI.
Based on human similarity ratings for pictures of common objects, shape spaces of varying dimensionality were constructed and validated by considering how well the similarities are reflected in the distances. Moreover, the conceptual regions for example categories were analyzed. In a second analysis step, we tested whether primitive shape features are detectable as quality dimensions in the shape spaces. The analysis scripts used in our study are available at https://github.com/lbechberger/LearningPsychologicalSpaces.

Representing Complex Shapes with Conceptual Spaces

The ability to flexibly route information between brain regions is crucial to perform new multi-step tasks. The mechanisms postulated by the global neuronal workspace theory of consciousness are thought to underlie this ability. We developed a spiking neural architecture based on the theory, which is able to route concepts in order to perform a cognitive task composed of chained operations.

Flexibly chaining mental operations with spiking neurons

Semantic analyses [1,2,5] of reciprocal verbs like kiss, date, collide, hug
and talk often assume a strong logical connection between the unary entry and their
binary alternate

Reciprocal predicates: a conceptual prototype model

A brief description of Semiotic-Conceptual Analysis (SCA) as an extension of FCA and its use as a framework for a qualitative analysis of the initial steps of data analysis

A Semiotic-Conceptual Analysis Framework as a Qualitative Method

This note concentrates on the notion of agents' behavior, as understood today, and suggests expanding it to study future socio-technical systems. The proposal is to take an ontological viewpoint to discuss anew topics like: how to understand behavior, how to connect behavior to an agents' type, how to structure a broader framework for behavior studies.

Agents’ behavior and its conceptual framework

This paper studies whether a perceptual visual system can simulate human-like cognitive capabilities by training a computational model to predict the output of an action using language instruction. The aim is to ground action words such that an AI is able to generate an output image that outputs the effect of a certain action on an given object. The output of the model is a synthetic generated image that demonstrates the effect that the action has on the scene. This work combines an image encoder, language encoder, relational network, and image generator to ground action words, and then visualize the effect an action would have on a simulated scene. The focus in this work is to learn meaningful shared image and text representations for relational learning and object manipulation.

Learning Generative Image Manipulations from Language Instructions

An intelligent agent in a complex environment will face a great number of diverse tasks. Instead of learning task-specific representations, we aim to re-use learned aspects in order to jump-start the acquisition of new tasks by building on available, abstract knowledge. This knowledge is meant to be grounded in the agents experience and acquired in a bottom-up process that is guided by intrinsic motivation. In short, our goal is not to make a robot understand human knowledge, but rather enabling it to accumulate and store its own generic concepts. For this purpose, we investigate the capabilities and limitations of current architectures to learn and represent bottom up relational concepts as one subtype of generic concepts. Using a powerful computation cluster with state of the art methods for distributed deep reinforcement learning, we are running large scale experiments to investigate the representations that are formed as well as the conditions that lead to them.

Relational Concepts in Deep Reinforcement Learning: Emergence and Representation

Embodied and situated approaches to concept acquisition have made a lot of progress in explaining where concepts come from and how they might be acquired initially. However, so far this progress is mostly restricted to (a) empirical concepts which might be derived directly from a combination of basic perceptual dimensions (e.g. shapes, colours, etc.), or (b) abstract concepts which might be linked to the aforementioned empirical ones by mechanisms such as conceptual metaphor (e.g. affection is warmth, mood is elevation, arithmetic is object collection, etc.). More complex abstract concepts can then be derived from those basic ones, resulting in a kind of bottom-up bootstrapping of ever more abstract concepts [2].

In this contribution, I want to demonstrate by example that in reality the acquisition of complex concepts is more convoluted than this picture implies. In an exploratory case study, I investigated how pairs of participants slowly acquaint themselves with a complex task domain over the course of three days. Specifically, they had to work on a complex spatial transformation and problem solving task in the domain of iterated mental paper folding [1]. In this task participants have to understand the geometry of edges which occurs when repeatedly mentally folding a sheet of paper in alternating directions without being allowed the use of external aids. Faced with the difficulty of handling increasingly complex folds (Fig. 1), participants are forced to look for regularities in the folding process, such as repeating configurations of edges, common transformations between folds, etc. which help them represent folds more efficiently. In a qualitative analysis of video recordings of the participants’ behaviour I have traced the de velopment of their conceptualisation of the task domain over the course of the study, focussing especially on the use of gesture and the spontaneous occurrence and use of idiosyncratic metaphors in the construction of new representations.

Presenting an in-depth analysis of one particular case (which was selected for its participants communicating particularly well and thus having generated more verbal descriptions than other pairs), I will show how this pair’s conceptualisation of the task domain developed, ranging from the use of iconic and deictic gestures in the beginning, over the emergence of figurative verbal descriptions, to finally re-representing the whole domain by use of a mnemonic metaphor and coining precise terminology (Fig. 2). While many aspects of this case are clearly idiosyncratic and cannot be generalised to derive a fully-fledged theory of concept acquisition, the case can still provide many interesting pointers for theory development.

Regarding such pointers, I will in particular discuss several potential extensions and directions for development for theories of problem-solving, metaphor production, and analogy-making – mainly focussing on: (a) The embedding of the memory retrieval process for potential source domains in its pragmatic, environmental, bodily, and social contexts, (b) the role of routine behaviour as a form of epistemic action, (c) the role of flawed (e.g. ambivalent) metaphors in the iterative refinement of target conceptualisations, and finally (d) the resultant weakening of the notion of static and encapsulated problem spaces.

References

1. Angerer, B., Schreiber, C.: Representational dynamics in the domain of iterated mental paper folding. Cognitive Systems  Research 54, 217–231 (2019)
2. Lakoff, G., Núñez, R.E.: Where Mathematics Comes from: How the Embodied Mind Brings Mathematics into Being. New York: Basic Books (2000)

Observing the conceptualisation of a complex task domain: The role of metaphors, gestures, and routine behaviour

In real world scenarios, there are many cases where collaborating participants have to identify a single entity or even a small subset of entities from a large information collection (e.g. a team of astrophysicists tries together to find all exoplanets close to our solar system). Supporting interactive systems use shared cognitive representation models as a key component of collaboration. Such models are beneficial since the abstract nature of relevant concepts is represented in a shared space visible to all team participants. In order to use shared cognitive representation models the participants' conceptions have to be synchronized continuously. This process of semantic co-creation occurs during communication between two or more people, when human cognitive representation models of the topic of discussion converge.

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