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by manthideaal
2270 days ago
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You are right. Also the Universal Approximation theorem (1) for neural networks guarantees that neural networks can approximate continuous function on compact subsets of R^n, in this case max(x,y). argmax([x,y]) = (sign(x[0]-x[1])+1)/2 Going beyond continuous functions, can deep learning be used for primality test? (1) https://en.wikipedia.org/wiki/Universal_approximation_theore... |
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> A long-standing difficulty for connectionism has been to implement compositionality, the idea of building a knowledge representation out of components such that the meaning arises from the meanings of the individual components and how they are combined. Here we show how a neural-learning algorithm, knowledge-based cascade-correlation (KBCC), creates a compositional representation of the prime-number concept and uses this representation to decide whether its input n is a prime number or not. KBCC conformed to a basic prime-number testing algorithm by recruiting source networks representing division by prime numbers in order from smallest to largest prime divisor up to √n. KBCC learned how to test prime numbers faster and generalized better to untrained numbers than did similar knowledge-free neural learners. The results demonstrate that neural networks can learn to perform in a compositional manner and underscore the importance of basing learning on existing knowledge.
But again, I think things such as prime number tests are the exact kind of edge cases where one needs too many heuristics built into the model for it to be practical to use.
But I think something like a prime test is not included under the definition I gave anyway, because the idea of "prime" actually implies a lot of context.
You can take a baby and he will be able to classify images, you can take a human that speaks a language with no concept of numbers and he will be able to play or sing music and distinguish patterns in it.
You can't talk about "prime" without a mathematical apparatus that takes years for humans to understand. However, since we learn it as such an early age, it ends up in the background.
Granted, that could be said about almost any cognitive ability (the fact that there's a lot of "subconscious context" required to use it).... so I don't know.