An abstraction is a compact, reusable idea drawn from experience. Instead of storing every situation separately, you identify what several situations have in common. When something unfamiliar appears, you can combine those ideas to make sense of it. A jet plane, for example, might initially look like a large metal bird that does not flap its wings. section 19.3.2 section 19.3.1
Recognizing a new beetle
Suppose you have seen many beetles. You can group similar ones and form a prototype for each group: a representation of shared features, not a copy of any individual beetle. A new beetle can then be compared with the prototypes rather than every beetle you have encountered. section 19.4.1
Two kinds of comparison produce different abstractions:
- Value-centric abstraction groups instances by degrees of similarity, as with the beetle prototypes. It supports approximate recognition and intuition. section 19.4.1 section 19.4.2
- Program-centric abstraction looks for exact structural matches across instances. It isolates shared structures and supports more exact reasoning and planning. section 19.4.1 section 19.4.2
Table 19.1 The two poles of abstraction
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Value-centric abstraction
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Program-centric abstraction
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|---|---|
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Relates things by distance
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Relates things by exact structural match
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Continuous, grounded in geometry
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Discrete, grounded in topology
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Produces abstractions by “averaging” instances into “prototypes”
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Produces abstractions by isolating isomorphic substructures across instances
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Underlies perception and intuition
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Underlies reasoning and planning
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Immediate, fuzzy, approximative
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Slow, exact, rigorous
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Requires a lot of experience to produce reliable results
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Experience-efficient; can operate on as few as two instances
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Compare the two poles side by side: their matching rules, resulting abstractions, and roles in perception or reasoning differ, but the two work together. section 19.4.2
Acquiring abstractions is only half the job. Recombining them for a new problem helps explain extreme generalization: dealing with situations far from past experience, sometimes with little new data. Classic deep learning can acquire useful patterns during training, but its trained mapping mainly supports local generalization near familiar inputs; it does not recombine what it knows on the fly at test time. section 19.3.2 section 19.2.2
