Using Conceptual Spaces for Cognitive AI Lucas Bechberger - PowerPoint PPT Presentation

Using Conceptual Spaces for Cognitive AI Lucas Bechberger Institute of Cognitive Science Osnabrück University https://www.lucas-bechberger.de

Conceptual Spaces ∀ x :apple ( x )⇒ red ( x ) Symbolic Layer Formal Logics Geometric ? Conceptual Layer Representation Sensor Values, Subsymbolic Layer [0.42; -1.337, ...] Machine Learning Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 2

My PhD Project / Outline Symbolic Layer Manually define 3.) Learning Concepts regions Conceptual Layer 1.) Mathematical Formalization Manually define 2.) Learning Dimensions dimensions Subsymbolic Layer Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 3

My PhD Project / Outline Symbolic Layer Manually define 3.) Learning Concepts regions Conceptual Layer 1.) Mathematical Formalization Manually define 2.) Learning Dimensions dimensions Subsymbolic Layer Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 4

Conceptual Spaces  Quality dimensions  Interpretable ways of judging the similarity of two instances  E.g., temperature, weight, brightness, pitch  Domain  Set of dimensions that inherently belong together  Color: hue, saturation, and brightness Gärdenfors, P. Conceptual Spaces: The Geometry of Thought. MIT press, 2000 Representing Correlations in Conceptual Spaces / Lucas Bechberger 5

The Color Domain https://en.wikipedia.org/wiki/HSL_and_HSV#/media/File:HSL_color_solid_dblcone_chroma_gray.png Representing Correlations in Conceptual Spaces / Lucas Bechberger 6

Concepts  Property  Region within a single domain  Examples: “white”, “baby blue”, “hot”, “sour”, “round”  Concept  Spans multiple domains  Examples: “apple”, “dog”, “chair”  Components of a concept  One region per domain  Salience weights for the domains  Correlations between the domains Representing Correlations in Conceptual Spaces / Lucas Bechberger 7

Betweenness and Distance B(x,y,z) :↔ d(x,y) + d(y,z) = d(x,z) Euclidean distance Manhattan distance A A C C brightness size B B hue hue Representing Correlations in Conceptual Spaces / Lucas Bechberger 8

Convexity and Manhattan Distance  Convex region C:  Star-shaped region S: height adult child age Bechberger, L. & Kühnberger, K.-U. Formalized Conceptual Spaces with a Geometric Representation of Correlations. In: Kaipainen, M.; Zenker, F.; Hautamäki, A. & Gärdenfors, P. (Ed.). Conceptual Spaces: Elaborations and Applications, Springer International Publishing, 2019, 29-58 Representing Correlations in Conceptual Spaces / Lucas Bechberger 9

Formalizing Star-Shaped Concepts Representing Correlations in Conceptual Spaces / Lucas Bechberger 10

Formalizing Star-Shaped Concepts ~ S = S 1.0 ~ S 0.5 ~ S 0.25 Representing Correlations in Conceptual Spaces / Lucas Bechberger 11

Operations on Concepts  Basic x  Membership  Concept Creation ~ S 1  Intersection v  Unification  Projection ~ S 2  Cut  Relations Between Concepts ~ S 3  Size  Subsethood  Implication  Similarity  Betweenness https://github.com/lbechberger/ConceptualSpaces Representing Correlations in Conceptual Spaces / Lucas Bechberger 12

My PhD Project / Outline Symbolic Layer Manually define 3.) Learning Concepts regions Conceptual Layer 1.) Mathematical Formalization Manually define 2.) Learning Dimensions dimensions Subsymbolic Layer Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 13

Learning Dimensions Handcrafting Psychology https://www.pinclipart.com/downpngs/hmJhoT_hammer-saw- clipart-hammer-and-saw-png-transparent/ Machine Learning https://www.pinclipart.com/downpngs/TJoTxi_brai n-symbol-of-psychology-clipart/ https://www.pinclipart.com/downpngs/hboiwb_ne ural-networks-set-out-to-replicate-the-brains/ Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 14

Learning Dimensions: MDS 1) Psychological experiment similarity judgments 2) Average across participants matrix # dimensions 3) Multidimensional Scaling space Psychological grounding Dealing with unseen inputs Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 15

Learning Dimensions: ANNs  Autoencoder (e.g., β-VAE): compress and reconstruct input 22 76 03 50 output 42 91 hidden representation Dealing with unseen inputs 24 75 02 53 input Psychological grounding  Hidden neurons = dimensions in our conceptual space Higgins, I.; Matthey, L.; Pal, A.; Burgess, C.; Glorot, X.; Botvinick, M.; Mohamed, S. & Lerchner, A. β-VAE: Learning Basic Visual Concepts with a Constrained Variational Framework, ICLR 2017 Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 16

Learning Dimensions: Hybrid dog cat . . . ANN Psychological MDS Experiment Psychological grounding Dealing with unseen inputs Bechberger, L. & Kypridemou, E. Mapping Images to Psychological Similarity Spaces Using Neural Networks. AIC 2018 Bechberger, L. & Kühnberger, K.-U. Generalizing Psychological Similarity Spaces to Unseen Stimuli. Preprint 2019 Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 17

Feasibility Study: Data Set  NOUN data set  64 images of novel objects  Pairwise similarity ratings Horst, J. S. & Hout, M. C. The Novel Object and Unusual Name (NOUN) Database: A Collection of Novel Images for Use in Experimental Research. Behavior Research Methods, 2016, 48, 1393-1409 Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 18

Feasibility Study: MDS Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 19

Feasibility Study: ANN Setup Szegedy, C.; Vanhoucke, V.; Ioffe, S.; Shlens, J. & Wojna, Z. Rethinking the Inception Architecture for Computer Vision. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2016, 2818-2826 Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 20

Feasibility Study: Experiment 1 1,4 1,2 1 0,8 MSE 0,6 0,4 0,2 0 Baseline Correct Targets Shuffled Targets Training Test Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 21

Feasibility Study: Experiment 3 1,4 1,2 1 0,8 MSE 0,6 Baseline Regression 0,4 0,2 0 1 2 3 4 5 6 7 8 9 10 Number of Dimensions Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 22

My PhD Project / Outline Symbolic Layer Manually define 3.) Learning Concepts regions Conceptual Layer 1.) Mathematical Formalization Manually define 2.) Learning Dimensions dimensions Subsymbolic Layer Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 23

Learning Concepts: LTN Apple AND red IMPLIES sweet: 0.31 0.99 0.75 0.31 apple red sweet Symbolic Conceptual Subsymbolic Serafini, L. & d'Avila Garcez, A. Logic Tensor Networks: Deep Learning and Logical Reasoning from Data and Knowledge. NeSy 2016 Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 24

Learning Concepts: LTN  Conceptual space of movies from Derrac and Schockaert  Extracted conceptual space from movie reviews  15.000 data points  Multi-label problem: genres, plot keywords, age restriction  Use LTN to learn concepts in that space  Extract rules with apriori algorithm  Vary size of training set and compare to other classifiers  Long run: align LTN with conceptual spaces theory  Convexity, domain structure, ... Joaquín Derrac and Steven Schockaert. Inducing semantic relations from conceptual spaces: a data-driven approach to commonsense reasoning, Artificial Intelligence, vol. 228, pages 66-94, 2015 Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 25

My PhD Project / Outline Symbolic Layer Manually define 3.) Learning Concepts regions Conceptual Layer 1.) Mathematical Formalization Manually define 2.) Learning Dimensions dimensions Subsymbolic Layer Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 26

Thank you for your attention! Questions? Comments? Discussions? https://www.lucas-bechberger.de @LucasBechberger