teaching machines to learn by metaphors
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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Teaching Machines to Learn by Metaphors
Omer Levy & Shaul MarkovitchTechnion – Israel Institute of Technology
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Concept Learning by Induction
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Few Examples
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Transfer Learning
Target (New)
Source (Original)
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Define: Related Concept
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Transfer Learning Approaches
• Common Inductive Bias
• Common Instances
• Common Features
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Different Feature Space
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Example
0 2 3-3 -2
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Example
0 2 3-3 -2
0 4 9
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Example
0 2 3-3 -2
0 4 9
𝑥𝑠=𝑥𝑡2
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Common Inductive Bias
0 2 3-3 -2
0 4 9
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Common Inductive Bias
0 2 3-3 -2
0 4 9
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Common Instances
0 2 3-3 -2
0 4 9
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Common Features
23
-3-2
4 9
𝑥𝑠=𝑦𝑡2
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New Approach to Transfer Learning
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Our Solution: Metaphors
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Metaphors
Target (New)
Source (Original)
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Concept Learner
Metaphor Learner
𝜇 h𝑠
Source
Target
+/-𝑥𝑡 𝑥𝑠
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h𝑡 (𝑥𝑡 )=h𝑠 (𝜇 (𝑥𝑡 ))
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is a perfect metaphor if:
1. is label preserving
2. is distribution preserving
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Theorem
If is a perfect metaphor- and -
is a source hypothesis with error- then -
is a target hypothesis with error
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The Metaphor Theorem
If is an -perfect metaphor- and -
is a source hypothesis with error- then -
is a target hypothesis with error
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Redefine Transfer Learning
Given source and target datasets, find a target hypothesis such that is as small as possible.
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Redefine Transfer Learning
Given source and target datasets, find an -perfect metaphor such that is as small as possible.
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Metaphor Learning Framework
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h
Concept Learning Framework
Search Algorithm
Hypothesis Space
Evaluation Function
Data
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𝜇
Source
Target
Metaphor Learning Framework
Search Algorithm
Metaphor Space
Evaluation Function
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Metaphor Evaluation
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Metaphor Evaluation
1. is label preserving
2. is distribution preserving
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Metaphor Evaluation
1. is label preservingEmpirical error over target dataset
2. is distribution preservingStatistical distance between and
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Metaphor Evaluation
𝑆𝐷 (𝜇 (𝑥𝑡 ) ,𝑥𝑠 )
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Metaphor Evaluation
𝑆𝐷 ¿
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Metaphor Evaluation
𝑆𝐷 (𝜇 (𝑥𝑡− ) , 𝑥𝑠−)
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Metaphor Evaluation
𝑆𝐷 ¿
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Metaphor Spaces
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Metaphor Spaces
• General
• Few Degrees of Freedom
• Representation-Specific Bias
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Geometric Transformations
Я R
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Dictionary-Based Metaphors
cheese queso
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Linear Transformations
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Which metaphor space should I use?
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Automatic Selection of Metaphor Spaces
Which metaphor space should I use?
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Occam’s Razor
Automatic Selection of Metaphor Spaces
Which metaphor space should I use?
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Structural Risk Minimization
Occam’s Razor
Automatic Selection of Metaphor Spaces
Which metaphor space should I use?
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Automatic Selection of Metaphor Spaces
ℳ1
ℳ2
ℳ3
ℳ 4
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Automatic Selection of Metaphor Spaces
ℳ1
ℳ2
ℳ3
ℳ 4
𝜇1
𝜇2
𝜇3
𝜇4
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Automatic Selection of Metaphor Spaces
ℳ1
ℳ2
ℳ3
ℳ 4
𝜇1
𝜇2
𝜇3
𝜇4
60 %
9 0 %
91 %
7 0 %
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Empirical Evaluation
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Reference MethodsBaseline• 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
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Digits: Negative Image
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Digits: Negative Image
𝜇 (𝑥𝑡 )=1−𝑥𝑡
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Digits: Negative Image
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Digits: Higher Resolution
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Digits: Higher Resolution
→
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Digits: Higher Resolution
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Wine
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Wine
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Qualitative ResultsTransfer Learning
TaskTarget
InstanceTarget Sample Size
1 2 5 10
Digits: Negative Image
Digits: Higher Resolution
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Discussion
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Recap
• Problem: Concept learning with few examples• Solution: Metaphors
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Recap
• Problem: Concept learning with few examples• Solution: Metaphors
• Target Source
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Recap
• Problem: Concept learning with few examples• Solution: Metaphors
• Target Source• Generic framework
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Recap
• Problem: Concept learning with few examples• Solution: Metaphors
• Target Source• Generic framework• Wide range of relations
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Recap
• Problem: Concept learning with few examples• Solution: Metaphors
• Target Source• Generic framework• Wide range of relations• Learn the difference
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What if the concepts are not related?
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What if the concepts are not related?
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Metaphors are not a measure of relatedness
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Metaphors are not a measure of relatedness
Metaphors explain how concepts are related
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Vision
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Explaining how concepts are related since 2012.M E T A P H O R S