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by svantana
3571 days ago
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> Fun fact: any algorithmic process that "renders" something given a set of inputs can be "run in reverse" Now wait a minute, most algorithms cannot be run in reverse! The only general way to reverse an algo is to try all possible inputs, which has exponential complexity. That's the basis of RSA encryption. Maybe you're thinking about automatic differentiation, a general algo to get the gradient of the output w.r.t. the inputs. That allows you to search for a matching input using gradient descent, but that won't give you an exact match for most interesting cases (due to local minima). I'm not trying to nitpick -- in fact I believe that IF algos were reversible then human-level AI would have been solved a long time ago. Just write a generative function that is capable of outputting all possible outputs, reverse, and inference is solved. |
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E.g. a forward problem might be to solve some PDE to simulate the state of a system from some known initial conditions.
The inverse problem could be to try to reverse engineer what the initial conditions were given the observed state of the system.
Inverse problems are typically much harder to deal with, and much harder to solve. E.g. perhaps they don't have a unique solution, or the solution is a highly discontinuous function of the inputs, which amplifies any measurement errors. In practice this can be addressed by regularisation aka introducing strong structural assumptions about what the expected solution should be like. This can be quite reasonable from a Bayesian perspective.
https://en.wikipedia.org/wiki/Inverse_problem#Mathematical_c...