Note 24: Analogy based Learning

Note Taker: Yi-an Huang
November 21, 2001

Difficulty on analogical reasoning:

What, how, (when) to transfer?

Method: Structure Mapping

What?--Correspondence

• Generate all local maps as much as possible

  In Example:

  1. mapping for GREATER

     temperature->pressure

     or

     temperature->dismeter ?

     There is a conflict on which local mapping is correct.

  2. Another conflict from mapping for coffee:

     from flow:	from flat_top:
     coffee->beaker ice cube->vial heat->water bar/spoon->pipe	coffee->water

     Again, conflict exists. So we don't know what is the correct.

     Heuristics?
     Maybe vocabulary to vocabulary, string to string.

• Global relations

  "principle of systematicity": When multiple matching choices exist, always pick the more nested match (i.e, inside a deeper structure).

  So, temperature->pressure and coffee->beaker are correct, because the first GREATER--pressure is more nested than the second GREATER--diameter.

  Q: Why does the principle work?
  A: Human intelligence from cognitive science discovery.

  Q: Why doesn't the principle work?

  What if the GREATER--diameter are deeper? Like this:

  

  The answer is simple, the principle doesn't work. Think others.

  Q:Why we are not confused in such a situation?
  A: We have more background knowledge.

How? Once a match is found, build the tree for heat flow:

Not only relation mapping exists, there are some other mappings

Example (metaphor): John runs like a hale. -- speed fast

Where: not the relation, but the object descriptions are mapped.

Q:What is not so good about this method?
A: Too much conflict, systematicity doesn't always work.

One alternative:Model-based Solution

Example: Create an electronic circuit that gives some X amount of light 6 lm(lumen)(Figure 1).

Figure 1	Figure 2

Create another circuit which gives n*X amount of light 18 lm(Figure 2).

We can give a generic model like this:

f1 ← s1, b1 (function, structure, behavior)

f2 = n*f1 ← n*s1, n*b1

Now, given a new domain: heat exchange that can cool up to ΔT. Design another heat exchange that can cool up to mΔT.

We need to abstract problem first.

f' ← s', b'

f" = m*f' ← ? (m*s'?)

Q: What is analogy after all?
"Only global agreement"
Definition: Always deal with two problems from different domains.
Always transfer some relations ("cause->cause", f ← s,b)

Diagram Representation

f1: input: electricity of voltage 1.5V output: light of 6lm	f2: input: electricity output: light of 18lm
b1:	b2:

Focus on difference:

1. First abstract for problem's number, 1.5V->V, so instead of 1.5V, 3V, 4.5V, we have 1*V, 2*V, 3*V, etc..
2. Then abstract substance and components
3. Generalize 3 to n

Finally we have:

Apply to heat exchange:

Becomes:

Q: Failure helps?

Problem: b(attery)→l(ight) → 3b →3l are given separately.

One is present with failure with reasoning out.

Same failure can be applied.

Partitioning

Big Problem P may not easily do analogical reasoning. But it can be partitioned into small problems.

Small problems can do analogy.

Q: Can structure mapping scheme be converted to model-based learning, and how?

For example:

Becomes:

Reference

Gentner, D. (1983). Structure-mapping: A theoretical framework for analogy. Cognitive Science, 7, pp 155-170.