Representing meaning Is there a red shape above a circle? 57
Representing meaning Is there a red shape above a circle? 58
Sets encode meaning Is there a red shape above a circle? 59
Sets encode meaning Is there a red shape above a circle? 60
Set transformations encode meaning Is there a red shape above a circle? 61
Set transformations encode meaning Is there a red shape above a circle? 62
Sentence meanings are computations Is there a red shape above a circle? exists and red above circle 63
Sentence meanings are computations Is there a red shape above a circle? exists and red above circle 64
Computations are built from set functions exists ↦ red and ↦ true exists ↦ red above above circle 65
…or relaxed to vector functions 0.0 0.9 1.0 exists ↦ red and ↦ true exists ↦ red above above circle 66
Composing vector functions exists ↦ red and ↦ true exists ↦ red above above circle 67
Composing vector functions exists ↦ red and ↦ true exists ↦ red above above circle 68
Composing vector functions ↦ exists red and ↦ true red above exists ↦ circle above 69
Compositions of vector functions are neural nets ↦ ↦ true ↦ 70
Compositions of vector functions are neural nets ↦ exists red and ↦ true red above exists ↦ circle above 71
Outline yes Is there a red shape above a circle? exists and red above ↦ circle red ↦ true exists ↦ above 72
Outline yes Is there a red shape above a circle? exists and red above ↦ circle red ↦ true exists ↦ above 73
Outline yes Is there a red shape above a circle? exists and red above ↦ circle red ↦ true exists ↦ above 74
Outline yes Is there a red shape above a circle? exists and red above ↦ circle red ↦ true exists ↦ above 75
Outline yes Is there a red shape above a circle? exists and red above ↦ circle red ↦ true exists ↦ above 76
Anatomy of a module above 77
Anatomy of a module red color 78
The [find] module red 79
The [find] module necktie [Xu et al. 2015] 80
The [find] module 0.9 Columbia 0.1 Cooper 0.8 Myrtle Beach city nam ame typ ype coast co astal al Co Columbia ci city no no Cooper Co rive ver yes ye Myr yrtle ci city ye yes Beach ach 81
The [find] module red 82
The [find] module red 83
The [find] module red red 84
The [find] module 0.9 red red 85
The [find] module 0.9 red red 86
The [find] module 0.1 red red 87
The [describe] module red color 88
The [describe] module necktie what 89
The [describe] module red color 90
The [describe] module red . . . color 91
The [describe] module red . . . color 92
What modules do we need? Is there a red shape above a circle? What color is the triangle? Who is running in the grass? What cities are south of San Diego? 93
A module for predicates Is there a red shape above a circle? [find] What color is the triangle? Who is running in the grass? What cities are south of San Diego? 94
A module for relations Is there a red shape above a circle? [relate] What color is the triangle? Who is running in the grass? What cities are south of San Diego? [find] 95
Module inventory Is there a red shape above a circle? What color is the triangle? Who is running in the grass? [and] [describe] What cities are south of San Diego? [find] [relate] [exists] 96
Outline yes Is there a red shape above a circle? exists and red above ↦ circle red ↦ true exists ↦ above 97
Learning yes blue exists color and right_of red above circle circle What color is the shape right of a Is there a red shape above a circle? circle? 98
Learning yes blue What color is the shape right of a Is there a red shape above a circle? circle? 99
Parameter tying yes blue circle circle What color is the shape right of a Is there a red shape above a circle? circle? 100
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