[kdmytro]

The dataset Z is a collection of facts. The output Y captures the patterns from Z. The LLM can generate novel insights (facts) that satisfy Y without violating the data processing inequality if we consider the patterns to be a part of the information of Z.

[rassibassi]

If I understand you correctly, you basically mean some interpolation of knowledge within Z, that was not known to humans before, but can be synthesized by recombination of information within Z.

Yet, that still means, knowledge of O cannot be synthesized.