Visual Sequences IQ Tests 1 Dipendra Kumar Misra (Y9201) Mukul Singh (Y9350) Tags : Search, Pattern Recognition, Logic etc Advisor : Dr. Amitabh Mukherjee Dr. Sumit Gulwani

Sample Problem 2 Which Image logically follows the Input Sequence

Motivation Automate Manual Verification of Intelligence Problems Synthesis of IQ Problems Insights into cognitive studies Visual Problems combine both Logic and Geometry 3

Background Work IQ problems have been studied for a long time Fanya Montalvo [1986, 1993] discusses topics such as Diagram Understanding “It will be hard for a computer program to solve picture problems” – Sanghi & Dowe 4

Case Study No Formal Definition of IQ problems Separate Semantic Based problems from Syntax Based problems Case Study on over 100 problems from standard books and online tests 5

Our Intuition “A Transformation Language with few transformations like Rotation and Shading should be powerful enough to cover a large subset of problems” 6

Methodology Front End Back End Set of Images ( Test Set and Solution Set ) Solution 7

Front End L1 Set of Images (Test Set and solution set) Set of Lines, Circles and Special Objects detected in the image set L2 Polygons formed by combining suitable lines 8

Back End Transformation of P1 = T1 ∩ T3 U T2 ∩ (T4 U T5) 9 P1 P2 P3 P4 P6 P5 T2 T1 T3 T4 T5

Ranking Method Rank(P,Q) = MatchPrimitive(P,Q) + MatchPrimitive(Q,P) MatchPrimitive(P,Q) = Number of Primitive of P in Q 10

Lets Do Some Practice 11

Handling Ambiguity Multiple Transformations – Use Least Complex Formula (Kolmogorov) 12 P AB Q AB R 270R 90 R 270 Choosing Cross Terms (90,270) will give us wrong answer

Results Solve Visual Problems for a Large Subset Zero Human Intervention No restriction on type of primitives – apple, cap, chair etc. 13

References & Resources “IQ Tests to Keep You Sharp” by Philip Carter and Kenneth Russel “Check Your IQ” by Ken Russell and Philip Carter Spreadsheet Data Manipulation Using Examples S. Gulwani POPL 2011 A computer program capable of passing IQ tests, Sanghi, P. and Dowe 2003 Montalvo, Fanya S. Diagram understanding,