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Open Source Initiative tries to define Open Source AI
(www.theregister.com)
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In theory, if you have the inputs, you have reproducible outputs, modulo perhaps some small deviations due to non-deterministic parallelism. But if those effects are large enough to make your model perform differently you already have big issues, no different than if a piece of software performs differently each time it is compiled.
That's the theory for some paradigms that were specifically designed to have the property of determinism.
Most things in the world, even computers, are non-deterministic
Nondeterminism isn't necessarily a bad thing for systems like AI.