Universal law of generalization

The universal law of generalization is a theory of cognition originally posited in 1987 by Roger Shepard.[1] Shepard began researching mechanisms of generalization while he was still a graduate student at Yale:[2]

I was now convinced that the problem of generalization was the most fundamental problem confronting learning theory. Because we never encounter exactly the same total situation twice, no theory of learning can be complete without a law governing how what is learned in one situation generalizes to another.

Bird with earthworm: Shepard gives example of bird using "generalization," based on experience with one previous worm, to decide if another worm is edible.

According to the law, the probability that a response to one stimulus will be generalized to another will be a function of the "distance" between the two stimuli. (The 1987 paper gives a "generalization" example of a bird that has eaten one earthworm, and is presented with a slightly different-looking earthworm.[3]) The "distance" between two slightly different stimuli is an abstract measurement of their difference in an imagined psychological space (the latter concept being typical of Shepard's work.)[4]

Explaining the concept of "psychological space" in the abstract of his 1987 paper, Shepard wrote:[3]

A psychological space is established for any set of stimuli by determining metric distances between the stimuli such that the probability that a response learned to any stimulus will generalize to any other is an invariant [monotonic function] of the distance between them.

Using experimental evidence from both human and non-human subjects, Shepard hypothesized, more specifically, that the probability of generalization will fall off exponentially with the distance measured by one of two particular metrics. His analysis goes on to argue for the universality of this rule for all sentient organisms, due to evolutionary internalization.

References
  1. "What your cell phone camera tells you about your brain". ScienceDaily.com. September 19, 2018. Retrieved February 5, 2019. A canonical law of cognitive science -- the Universal Law of Generalization, introduced in a 1987 article also published in Science -- tells us that your brain makes perceptual decisions based on how similar the new stimulus is to previous experience. Specifically, the law states that the probability you will extend a past experience to new stimulus depends on the similarity between the two experiences, with an exponential decay in probability as similarity decreases. This empirical pattern has proven correct in hundreds of experiments across species including humans, pigeons, and even honeybees.
  2. Shepard, Roger (2004). "How a cognitive psychologist came to seek universal laws" (PDF). Psychonomic Bulletin & Review. 11 (1): 1–23. doi:10.3758/BF03206455. PMID 15116981. Retrieved February 5, 2019. I was now convinced that the problem of generalization was the most fundamental problem confronting learning theory. Because we never encounter exactly the same total situation twice, no theory of learning can be complete without a law governing how what is learned in one situation generalizes to another."
  3. Shepard, RN (September 11, 1987). "Toward a universal law of generalization for psychological science". Science (journal). Retrieved February 5, 2019. A psychological space is established for any set of stimuli by determining metric distances between the stimuli such that the probability that a response learned to any stimulus will generalize to any other is an invariant monotonic function of the distance between them. To a good approximation, this probability of generalization (i) decays exponentially with this distance, and (ii) does so in accordance with one of two metrics, depending on the relation between the dimensions along which the stimuli vary.
  4. Sims, Chris (May 11, 2018). "Efficient coding explains the universal law of generalization in human perception". Science (journal). Retrieved February 5, 2019. Perceptual generalization and discrimination are fundamental cognitive abilities. For example, if a bird eats a poisonous butterfly, it will learn to avoid preying on that species again by generalizing its past experience to new perceptual stimuli. In cognitive science, the “universal law of generalization” seeks to explain this ability and states that generalization between stimuli will follow an exponential function of their distance in “psychological space.”
  • Shepard, R. N. (1987); "Toward a universal law of generalization for psychological science." Science, 237, 1317–1323.


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