![]() The sequence game is part of the amazing Fluid Concepts and Creative Analogies (fun fact: it was the first book sold on Amazon!), a 1995 book by A.I. Our interest in PP lies in the ability to reason explicitly about structures and deal well with uncertainty even without lots of data: good luck with “machine-learning-your-way” out of this: f(1) = 1 f(2) = 4 f(3) = ? The sequence game came to my mind, serendipitously, while exploring probabilistic programming ( PP), which is often explained as an attempt to unify general purpose programming with probabilistic modeling. ![]() We won’t spoil the surprise (see the very end for the solution), but use this nice puzzle to discuss a more general problem: given the universe of integers and functions built out of arithmetical operations (addition, subtraction, multiplications, etc.), how can we learn the “generator function” of a sequence given that the number of possibilities is infinite? Īs it turns out, this is not the function generating this sequence. It does not seem that hard, does it? 3 will be our obvious answer as we would assume the “generator function” could be something as simple as f(x) = x: f(0) = 0 f(1) = 1 f(2) = 2 f(3) = ? -> 3. Imagine someone came to you with the following puzzle: given the sequence of integers 0, 1, 2, …, guess the next item. (…) Luckily, a new term was just then coming into currency - ‘cognitive science’ - and I started to favor that way of describing my research interests, since it clearly stresses the idea of fidelity to what actually goes on in the human mind/brain.” - Douglas Hofstadter (before 2000, just to be clear) “Then slid down the slope that ends up in meaningless buzzwords and empty hype. Back to the future: concepts in the time of the great A.I. Concept learning through probabilistic programming.
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