עלות ההקטנה: גבול תפיסה-קיפול על הלקאי-מעשי

תקציר מקורי באנגליתarXiv:2609.12111v1 Announce Type: new Abstract: Factual hallucination in closed-book question answering is often treated as a coverage problem: a model fails because the relevant fact is absent from its internal memory. This view misses a second source of error. Even when a fact has been observed, finite memory may force it to be stored only approximately. We study this effect through a simple coverage--compression model of factual recall. We consider an unstructured question-answering task with $N$ possible queries and $K$ possible answers. A learner observes $M$ training facts, compresses them into at most $B$ bits, and answers uniformly drawn test queries without retrieval. For a uniformly random ground-truth mapping, we prove $\mathcal{E} \geq \frac{M}{N}\delta^\star\!\left(\frac{B}{M}