Towards Grounding Conceptual Spaces in Neural Representations - PowerPoint PPT Presentation

Towards Grounding Conceptual Spaces in Neural Representations Lucas Bechberger and Kai-Uwe Kühnberger https://www.lucas-bechberger.de

The Different Layers of Representation ∀ x :apple ( x )⇒ red ( x ) Symbolic Layer Formal Logics Geometric ? Conceptual Layer Representation Sensor Values, Subsymbolic Layer [0.42; -1.337] Machine Learning Towards Grounding Conceptual Spaces in Neural Representations / Lucas Bechberger 2

Dimensions & Domains  Quality dimensions  Different ways stimuli are judged to be similar or different  Interpretable by a human  E.g., temperature, weight, brightness, pitch  Domain  Set of dimensions that inherently belong together  Color: hue, saturation, and brightness  Distance in this space is inversely related to similarity  Geometric betweenness represents semantic betweenness  Concepts: regions in this space Towards Grounding Conceptual Spaces in Neural Representations / Lucas Bechberger 3

Example: The Color Domain https://en.wikipedia.org/wiki/HSL_and_HSV#/media/File:HSL_color_solid_dblcone_chroma_gray.png Towards Grounding Conceptual Spaces in Neural Representations / Lucas Bechberger 4

Towards A Thorough Implementation Symbolic Layer Manually define regions Conceptual Layer Manually define dimensions representation learning Subsymbolic Layer Towards Grounding Conceptual Spaces in Neural Representations / Lucas Bechberger 5

InfoGAN – Architecture  Information Maximizing Generative Adversarial Networks x ? D z c G G(z) c X. Chen et al., “InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets”, Advances in Neural Information Processing Systems, 2016 Towards Grounding Conceptual Spaces in Neural Representations / Lucas Bechberger 6

InfoGAN – MNIST Results  Three latent variables  Categorical (10 classes)  Continuous (uniform)  Continuous (uniform) X. Chen et al., “InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets”, Advances in Neural Information Processing Systems, 2016 Towards Grounding Conceptual Spaces in Neural Representations / Lucas Bechberger 7

Domains and InfoGAN Domains in CS framework Latent Space of InfoGAN  Interpretable dimensions  Tends to be the case  Distance-based notion of  Smoothness assumption semantic similarity  Geometric betweenness  Interpolations in latent represents semantic space describe a betweenness meaningful morph Towards Grounding Conceptual Spaces in Neural Representations / Lucas Bechberger 8

Our Proposal  Use InfoGAN to learn dimensions of “difficult” domains  For starters: shape domain  Hyperparameters  Number of latent variables → as few as possible, as much as necessary  Type of latent variables → continuous (i.e., uniform or Gaussian)  Make sure that we learn new dimensions  Pre-select training data (if possible)  Additional term in loss function: correlation to other dimensions Towards Grounding Conceptual Spaces in Neural Representations / Lucas Bechberger 9

First Preliminary Results  Data set of right-angled triangles, rectangles, and ellipses  2 continuous varibles (uniform distribution), 500 epochs Towards Grounding Conceptual Spaces in Neural Representations / Lucas Bechberger 10

Towards A Thorough Implementation Symbolic Layer Manually define regions clustering Conceptual Layer Manually define dimensions representation learning Subsymbolic Layer Towards Grounding Conceptual Spaces in Neural Representations / Lucas Bechberger 11

Overall Envisioned System Subsymbolic layer Conceptual layer Symbolic layer HSB apple color domain banana ANN shape domain Towards Grounding Conceptual Spaces in Neural Representations / Lucas Bechberger 12

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