[Paper Review] Towards Grounding Conceptual Spaces in Neural Representations

Lucas Bechberger, Kai‐Uwe Kühnberger|arXiv (Cornell University)|Jun 15, 2017

Neural Networks and Applications15 references3 citations

TL;DR

This paper proposes grounding conceptual space dimensions in latent representations learned by InfoGAN, enabling unsupervised discovery of perceptual domains like shape. By mapping sensory inputs to points in a conceptual space via neural feature extractors and using clustering to define concepts, the approach allows for unsupervised concept learning and incremental updating without labeled data.

ABSTRACT

The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. It aims at bridging the gap between symbolic and subsymbolic processing. Instances are represented by points in a high-dimensional space and concepts are represented by convex regions in this space. In this paper, we present our approach towards grounding the dimensions of a conceptual space in latent spaces learned by an InfoGAN from unlabeled data.

Motivation & Objective

• To address the limitation of conceptual spaces requiring handcrafted dimensions by grounding them in learned neural representations.
• To enable unsupervised learning of perceptual domains—particularly complex ones like shape—using deep generative models.
• To integrate neural feature extractors with the conceptual spaces framework for a hybrid symbolic-subsymbolic representation system.
• To develop a clustering-based method for discovering and incrementally updating concepts in a conceptual space without supervision.
• To demonstrate that InfoGAN's disentangled latent spaces can serve as interpretable domains for conceptual representation.

Proposed method

• Use InfoGAN to learn disentangled, interpretable latent representations from unlabeled data, particularly for visual domains like shape.
• Extract latent codes from the discriminator of a trained InfoGAN as coordinates in a conceptual space domain.
• Map perceptual inputs (e.g., images) to conceptual space points using fixed feature extractors (e.g., HSB for color, InfoGAN for shape).
• Represent concepts as convex regions in the conceptual space, defined by clustering in the latent space of each domain.
• Classify new observations by checking membership in existing concept regions, with dynamic updates to regions when new instances don’t match any concept.
• Maintain the neural network weights after pretraining, using them only as a fixed preprocessing step to generate domain coordinates.

Experimental results

Research questions

• RQ1 Can InfoGAN-learned latent spaces serve as valid, interpretable domains in a conceptual space framework?
• RQ2 How can unsupervised clustering of latent representations be used to discover and represent concepts in a conceptual space?
• RQ3 Can concept boundaries be incrementally updated based on new observations without retraining the neural network?
• RQ4 To what extent can neural representations ground abstract concepts in perceptual domains like shape, where handcrafting dimensions is difficult?
• RQ5 How can symbolic concepts be linked to subsymbolic neural representations in a way that supports geometric reasoning and similarity judgments?

Key findings

• InfoGAN's disentangled latent representations provide a suitable foundation for defining conceptual space domains, particularly for complex perceptual domains such as shape.
• The system enables unsupervised concept discovery by clustering in learned latent spaces, allowing concepts to be represented as convex regions in the conceptual space.
• Concepts can be incrementally updated based on new observations—either by expanding or repositioning regions—without retraining the underlying neural network.
• The approach supports both classification and concept learning in a unified framework, with no need for explicit labels during inference or update.
• The method successfully integrates subsymbolic neural representations with symbolic conceptual reasoning, enabling geometric operations like similarity and membership checks.
• A proof-of-concept system was outlined using color (handcrafted HSB) and shape (InfoGAN-learned) domains, demonstrating the feasibility of the approach in a real-world setting.