Course manual 2019/2020

Course content

Conceptual spaces are a way of representing concepts geometrically that can be used in AI, psychology, and language representations. Conceptual spaces lie between neural and symbolic models and therefore form a bridge between these two levels of representation. The course covers understanding what conceptual spaces are and how they can be formalized, how they can be used in AI applications, and how they are used for language representation. The course will involve theoretical work, programming in Python, and discussion of difficulties and areas for research in conceptual spaces.

The field of conceptual spaces is relatively new and an area of active research with many open questions. This course would particularly suit students who would potentially be interested to apply some of their learning in a summer project.

Study materials

Literature

Objectives

Give the definition of a conceptual space and explain how concepts are represented within a conceptual space.
Understand basic fuzzy set theory and why this is used in concept representations
Use a conceptual space representation to categorize objects and calculate combined concepts
Explain how conceptual spaces can be used for language representation including vector spaces semantics and how formal semantics can be applied.
Represent data within a conceptual space and build concepts within the space

Teaching methods

Lecture
Seminar
Self-study

The lectures will provide the theoretical background to the course, and lay out the techniques to be used in the assignments. Guest lecturers will provide the students with an insight into the latest research in conceptual spaces

The seminars will provide practice in using the techniques and theory described in the lectures. Teaching assistants will demonstrate techniques and be on hand to help with homework questions.

Assignments will be completed in self-study time and serve to consolidate the ideas introduced in lectures and seminars.

Learning activities

Activity	Hours
Hoorcollege	24
Tentamen	2
Tussentoets	2
Werkcollege	24
Self study	116
Total	168	(6 EC x 28 uur)

Attendance

Programme's requirements concerning attendance (OER-B):

For practical trainings and tutorials with assignments attendance is obligatory. The requirements for attendance might differ between courses and are stated in the course manual. When students do not meet the requirements for attendance, he or she cannot finish the course with a pass mark.

Assessment

Item and weight	Details
Final grade
20% Tussentoets
15% Homework 1
10 (67%) Homework 1 - Programming
5 (33%) Homework 1 - Written
15% Homework 2
10 (67%) Homework 2 - Programming
5 (33%) Homework 2 - Written
15% Homework 3
10 (67%) Homework 3 - Programming
5 (33%) Homework 3 - Written
15% Homework 4
10 (67%) Homework 4 - Programming
5 (33%) Homework 4 - Written
20% Tentamen

Students must obtain a grade of 12/20 in at least one exam. The exams will be open-book: access to study materials is allowed. Computers may be used to look at slides, practice exercises, homeworks etc, and any printed material. Either a computer or a calculator is needed to do some of the calculations. Internet and phones may not be used.

The tussentoets will be based on weeks 1-3 and the tentamen will be based on weeks 5-7. The resit will consist of two exam papers, students can choose whether to resit the tussentoets or the tentamen, but not both.

Deadlines for the homeworks are strict: failure to meet the deadline will result in a score of 0 for that homework.

Students must obtain an overall grade in line with the UvA minimal passing grade to pass the course.

Inspection of assessed work

Students will be notified by email in DataNose or Canvas.

Assignments

There are 4 homework assignments. Each of these carries 15% of the final grade and is scored out of 15. Each homework will consist of a programming element (10 points) and a calculation and discussion element (5 points). Homeworks should be completed in groups of 2-3. Homework assignments are graded and count towards the final exam. Feedback will be given by TAs in the werkcolleges.

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Weeknummer	Onderwerpen	Studiestof
1	Week 1: Introduction Why conceptual spaces? Categorization; similarity; route from neural to symbolic representations What is a conceptual space? Quality dimensions; domains; integral and separable dimensions Concept representation: Properties; Concepts; Prototype theory; Voronoi tessellations and other approaches	Lecture notes, Practice exercises, Homework 1
2	Week 2: Vagueness and Computing with Conceptual Spaces Introduction to fuzzy set theory: Membership and similarity; connectives; links to prototype theory Difficulties: ‘Pet fish’ problem; psychological evidence for overextension and underextension; stereotypes/extremes Formalizations of conceptual spaces: Aisbett and Gibbon, Lawry and Tang, Adams and Raubal, Bechberger Computing combinations of concepts: Fuzzy intersections, contrast classes	Lecture notes, Practice exercises, Homework 2
3	Week 3: Computing with Conceptual Spaces cont’d Building conceptual spaces: Building a conceptual space from data, clustering points in a space, extracting meaningful dimensions from data Combining concepts in conceptual spaces: examples from Schockaert/Bechberger	Lecture notes, Mock exam paper
4	Week 4: Tussentoets covering weeks 1-3	Lecture notes from previous weeks, Mock exam paper
5	Week 5: Conceptual Spaces and Language Introduction to formal semantics: Set-theoretic meaning, computing truth values of sentences Semantic spaces: vector representations of words, relevance of space dimensions, methods of computing meaning vectors Beyond nouns: Adjectives and verbs in conceptual spaces	Lecture notes, Practice exercises, Homework 3
6	Week 6: Formal semantics and vectors Type-logical grammars: Looking at categorial grammar and pregroup grammar Mapping grammar to vector spaces: Representing adjectives and verbs as matrices and tensors Applying grammar: Using tensor contraction to compute meanings of phrases and sentences Building adjectives and verbs: Linear regression, modified skip-gram, extensional models	Lecture notes, Practice exercises, Homework 4
7	Week 7: Grammar in Conceptual Spaces Mapping grammar onto conceptual spaces: Another look at adjectives and verbs in conceptual spaces Combining words in conceptual spaces: type reductions, examples.	Lecture notes, Mock exam paper
8	Week 8: Tentamen covering weeks 5-7	Lecture notes from previous weeks, Mock exam paper

Timetable

The schedule for this course is published on DataNose.

Processed course evaluations

Below you will find the adjustments in the course design in response to the course evaluations.

Feedback from the course evaluations mostly concerned the homeworks. Feedback suggested that the homeworks could give the students more freedom in the programming tasks, rather than a step-by-step guide, and also that homeworks could be more project-based. Feedback also said that the homework questions were sometimes too vague. The homeworks are updated to reflect these comments.

Other feedback was that the course did not have a clear enough structure. The lectures are updated to give more of a structure to the course.

Contact information

Coordinator

Martha Lewis

Owner	Bachelor Kunstmatige Intelligentie
Coordinator	Martha Lewis
Part of	Minor Kunstmatige Intelligentie, year 1 Minor Logic and Computation, year 1 Exchange Programme Faculty of Science, specialisation BSc Artificial Intelligence, year 1 Bachelor Kunstmatige Intelligentie, year 3 Bachelor Bèta-gamma, major Kunstmatige Intelligentie, year 3

Conceptual Spaces for Artificial Intelligence