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

Using Conceptual Spaces for Cognitive AI

https://www.lucas-bechberger.de Lucas Bechberger

Institute of Cognitive Science Osnabrück University

Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 2

Conceptual Spaces

Symbolic Layer Subsymbolic Layer [0.42; -1.337, ...] ∀ x:apple( x)⇒red(x) Formal Logics Sensor Values, Machine Learning

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Conceptual Layer Geometric Representation

Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 3

My PhD Project / Outline

Symbolic Layer Subsymbolic Layer Conceptual Layer

Manually define regions Manually define dimensions

3.) Learning Concepts 2.) Learning Dimensions 1.) Mathematical Formalization

Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 4

My PhD Project / Outline

Symbolic Layer Subsymbolic Layer Conceptual Layer

Manually define regions Manually define dimensions

3.) Learning Concepts 2.) Learning Dimensions

1.) Mathematical Formalization

Representing Correlations in Conceptual Spaces / Lucas Bechberger 5

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 6

The Color Domain

https://en.wikipedia.org/wiki/HSL_and_HSV#/media/File:HSL_color_solid_dblcone_chroma_gray.png

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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 8

Betweenness and Distance

B C A A C B

hue hue brightness size

Euclidean distance Manhattan distance B(x,y,z) :↔ d(x,y) + d(y,z) = d(x,z)

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Convexity and Manhattan Distance

height age adult child

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

• Convex region C:
• Star-shaped region S:

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Formalizing Star-Shaped Concepts

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Formalizing Star-Shaped Concepts

S = S1.0 ~ S0.5 S0.25 ~ ~

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Operations on Concepts

• Basic
• Membership
• Concept Creation
• Intersection
• Unification
• Projection
• Cut
• Relations Between Concepts
• Size
• Subsethood
• Implication
• Similarity
• Betweenness

S1 ~ x S2 ~ v S3 ~

https://github.com/lbechberger/ConceptualSpaces

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My PhD Project / Outline

Symbolic Layer Subsymbolic Layer Conceptual Layer

Manually define regions Manually define dimensions

3.) Learning Concepts 2.) Learning Dimensions 1.) Mathematical Formalization

Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 14

Learning Dimensions

https://www.pinclipart.com/downpngs/hmJhoT_hammer-saw- clipart-hammer-and-saw-png-transparent/ 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/

Handcrafting Psychology Machine Learning

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Learning Dimensions: MDS

Psychological grounding Dealing with unseen inputs 1) Psychological experiment 2) Average across participants 3) Multidimensional Scaling

space # dimensions matrix similarity judgments

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Learning Dimensions: ANNs

• Autoencoder (e.g., β-VAE): compress and reconstruct input
• Hidden neurons = dimensions in our conceptual space
• utput

hidden representation input

24 75 02 53 42 91 22 76 03 50

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

Dealing with unseen inputs Psychological grounding

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Learning Dimensions: Hybrid

Psychological Experiment

MDS

ANN

dog cat . . .

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

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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

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Feasibility Study: MDS

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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

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Feasibility Study: Experiment 1

Baseline Correct Targets Shuffled Targets 0,2 0,4 0,6 0,8 1 1,2 1,4 Training Test MSE

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Feasibility Study: Experiment 3

1 2 3 4 5 6 7 8 9 10 0,2 0,4 0,6 0,8 1 1,2 1,4

Baseline Regression

Number of Dimensions MSE

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My PhD Project / Outline

Symbolic Layer Subsymbolic Layer Conceptual Layer

Manually define regions Manually define dimensions

3.) Learning Concepts 2.) Learning Dimensions 1.) Mathematical Formalization

Using Conceptual Spaces for Cognitive AI / Lucas Bechberger 24

Learning Concepts: LTN

apple red sweet 0.99 0.75 0.31

Apple AND red IMPLIES sweet: 0.31 Symbolic Subsymbolic Conceptual

Serafini, L. & d'Avila Garcez, A. Logic Tensor Networks: Deep Learning and Logical Reasoning from Data and Knowledge. NeSy 2016

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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

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My PhD Project / Outline

Symbolic Layer Subsymbolic Layer Conceptual Layer

Manually define regions Manually define dimensions

3.) Learning Concepts 2.) Learning Dimensions 1.) Mathematical Formalization

Thank you for your attention!

Questions? Comments? Discussions? https://www.lucas-bechberger.de @LucasBechberger