Teaching Machines to Learn by
Metaphors
Omer Levy & Shaul Markovitch
Technion – Israel Institute of Technology
Concept Learning by Induction
Few Examples
Transfer Learning
Target
(New)
Source
(Original)
Define: Related Concept
Transfer Learning Approaches
• Common Inductive Bias
• Common Instances
• Common Features
Different Feature Space
Example
-3 -2
0
2 3
Example
-3 -2
0
0
2 3
4
9
Example
-3 -2
0
𝑥𝑠 =
0
2 3
2
𝑥𝑡
4
9
Common Inductive Bias
-3 -2
0
0
2 3
4
9
Common Inductive Bias
-3 -2
0
0
2 3
4
9
Common Instances
-3 -2
0
0
2 3
4
9
Common Features
3
2
4
-2
-3
𝑥𝑠 =
2
𝑦𝑡
9
New Approach to Transfer Learning
Our Solution: Metaphors
Metaphors
Target
(New)
Source
(Original)
Source
Concept
Learner
Target
Metaphor
Learner
𝑥𝑡
𝜇
𝑥𝑠
ℎ𝑠
+/-
ℎ𝑡 𝑥𝑡 = ℎ𝑠 𝜇 𝑥𝑡
𝜇 is a perfect metaphor if:
1. 𝜇 is label preserving
𝑓𝑡 𝑥𝑡 = 𝑓𝑠 𝜇 𝑥𝑡
2. 𝜇 is distribution preserving
𝑥𝑡 ~𝑃𝑡 ⇒ 𝜇 𝑥𝑡 ~𝑃𝑠
Theorem
If 𝜇 is a perfect metaphor
- and ℎ𝑠 is a source hypothesis with 𝜀𝑠 error
- then ℎ𝑡 𝑥𝑡 = ℎ𝑠 𝜇 𝑥𝑡
is a target hypothesis with 𝜀𝑠 error
The Metaphor Theorem
If 𝜇 is an 𝜀-perfect metaphor
- and ℎ𝑠 is a source hypothesis with 𝜀𝑠 error
- then ℎ𝑡 𝑥𝑡 = ℎ𝑠 𝜇 𝑥𝑡
is a target hypothesis with 𝜀 + 𝜀𝑠 error
Redefine Transfer Learning
Given source and target datasets,
find a target hypothesis ℎ𝑡
such that 𝜀𝑡 is as small as possible.
Redefine Transfer Learning
Given source and target datasets,
find an 𝜀-perfect metaphor 𝜇
such that 𝜀 is as small as possible.
Metaphor Learning Framework
Concept Learning Framework
Search
Algorithm
Hypothesis
Space
ℎ
Evaluation
Function
Data
Metaphor Learning Framework
Source
Search
Algorithm
Metaphor
Space
𝜇
Evaluation
Function
Target
Metaphor Evaluation
Metaphor Evaluation
1. 𝜇 is label preserving
𝑓𝑡 𝑥𝑡 = 𝑓𝑠 𝜇 𝑥𝑡
2. 𝜇 is distribution preserving
𝑥𝑡 ~𝑃𝑡 ⇒ 𝜇 𝑥𝑡 ~𝑃𝑠
Metaphor Evaluation
1. 𝜇 is label preserving
Empirical error over target dataset
2. 𝜇 is distribution preserving
Statistical distance between 𝜇 𝑥𝑡 and 𝑥𝑠
Metaphor Evaluation
𝑆𝐷 𝜇 𝑥𝑡 , 𝑥𝑠
Metaphor Evaluation
𝑆𝐷 𝜇
+
𝑥𝑡
+
, 𝑥𝑠
Metaphor Evaluation
𝑆𝐷 𝜇
−
𝑥𝑡
−
, 𝑥𝑠
Metaphor Evaluation
𝑆𝐷 𝜇
+
𝑥𝑡
+
, 𝑥𝑠
+ 𝑆𝐷 𝜇
−
𝑥𝑡
−
, 𝑥𝑠
Metaphor Spaces
Metaphor Spaces
• General
• Few Degrees of Freedom
• Representation-Specific Bias
Geometric Transformations
Dictionary-Based Metaphors
cheese
queso
Linear Transformations
𝜇 𝑥 =𝑤 ⋅𝑥 +𝑣
Which metaphor space should I use?
Which metaphor space should I use?
Automatic Selection of Metaphor Spaces
Which metaphor space should I use?
Automatic Selection of Metaphor Spaces
Occam’s Razor
Which metaphor space should I use?
Automatic Selection of Metaphor Spaces
Occam’s Razor
Structural Risk Minimization
Automatic Selection of Metaphor Spaces
ℳ1
ℳ2
ℳ3
ℳ4
Automatic Selection of Metaphor Spaces
ℳ1
𝜇1
ℳ2
𝜇2
ℳ3
𝜇3
ℳ4
𝜇4
Automatic Selection of Metaphor Spaces
ℳ1
𝜇1
60%
ℳ2
𝜇2
90%
ℳ3
𝜇3
91%
ℳ4
𝜇4
70%
Empirical Evaluation
Reference Methods
Baseline
• Target Only
• Identity Metaphor
• Merge
State-of-the-Art
• Frustratingly Easy Domain Adaptation
– Daumé, 2007
• MultiTask Learning
– Caruana, 1997; Silver et al, 2010
• TrAdaBoost
– Dai et al, 2007
Digits: Negative Image
Digits: Negative Image
𝜇 𝑥𝑡 = 1 − 𝑥𝑡
Digits: Negative Image
Digits: Higher Resolution
Digits: Higher Resolution
→
Digits: Higher Resolution
Wine
Wine
Qualitative Results
Transfer Learning Target
Task
Instance
Digits:
Negative Image
Digits: Higher
Resolution
Target Sample Size
1
2
5
10
Discussion
Recap
• Problem: Concept learning with few examples
• Solution: Metaphors
Recap
• Problem: Concept learning with few examples
• Solution: Metaphors
• Target → Source
Recap
• Problem: Concept learning with few examples
• Solution: Metaphors
• Target → Source
• Generic framework
Recap
• Problem: Concept learning with few examples
• Solution: Metaphors
• Target → Source
• Generic framework
• Wide range of relations
Recap
• Problem: Concept learning with few examples
• Solution: Metaphors
•
•
•
•
Target → Source
Generic framework
Wide range of relations
Learn the difference
What if the concepts are not related?
What if the concepts are not related?
Metaphors are not a measure of relatedness
Metaphors are not a measure of relatedness
Metaphors explain how concepts are related
Vision
M E TAPH O R S
Explaining how concepts are related since 2012.