Hallucinations are the space-optimal behavior for limited-capacity models performing membership testing on sparse facts, as shown by a rate-distortion theorem that equates optimal memory use to minimum KL divergence between fact and non-fact score distributions.
For p∈ (0, 1), let ν := µK + µN and write fK := dµK dν , fN := dµN dν , so that the mixtureµp =pµ K + (1−p)µ N has density mp := dµp dν =pf K + (1−p)f N
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Hallucination is a Consequence of Space-Optimality: A Rate-Distortion Theorem for Membership Testing
Hallucinations are the space-optimal behavior for limited-capacity models performing membership testing on sparse facts, as shown by a rate-distortion theorem that equates optimal memory use to minimum KL divergence between fact and non-fact score distributions.