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Suppose you're training a language model by minimizing cross entropy, and the omniscient being is watching. In each step, your model instantiates some probability distribution, whose gradients are computed. That distribution exists, and is not deterministic to the omniscient entity.

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An LLM is given a definition of the macrostate which creates the probability distribution, but a different definition of the macrostate (such as would be known to the omniscient being) would create a different distribution. According to the omniscient entity, the vast majority of long combinations of tokens would have zero probability because nobody will ever write them down in that order. The infinite monkey theorem is misleading in this regard. The odds of producing Shakespeare's works completely randomly before the heat death of the universe are practically zero, even if all the computing power in the world were dedicated to the cause.

What’s non deterministic there?

That “probability distribution” is just a mathematical function assigning numbers to tokens, defined using a model that the person creating the model and the omniscent entity know, applying a set of deterministic mathematical functions to a sequence of observed inputs that the person creating the model and the omniscent entity also know.

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