"The study, published on September 4 and led by OpenAI researchers Adam Tauman Kalai, Edwin Zhang, and Ofir Nachum alongside Georgia Tech's Santosh S. Vempala, provided a comprehensive mathematical framework explaining why AI systems must generate plausible but false information even when trained on perfect data. "Like students facing hard exam questions, large language models sometimes guess when uncertain, producing plausible yet incorrect statements instead of admitting uncertainty," the researchers wrote in the paper. "Such 'hallucinations' persist even in state-of-the-art systems and undermine trust.""
"The researchers demonstrated that hallucinations stemmed from statistical properties of language model training rather than implementation flaws. The study established that "the generative error rate is at least twice the IIV misclassification rate," where IIV referred to "Is-It-Valid" and demonstrated mathematical lower bounds that prove AI systems will always make a certain percentage of mistakes, no matter how much the technology improves."
Large language models necessarily produce plausible yet incorrect outputs because of fundamental statistical and computational constraints. Hallucinations arise from the statistical properties of language-model training rather than implementation mistakes. Mathematical lower bounds demonstrate a nonzero minimum error, with the generative error rate provably at least twice the IIV (Is-It-Valid) misclassification rate. State-of-the-art models from major providers exhibit these persistent errors even when trained on perfect data. These limits imply that improved engineering alone cannot eliminate hallucinations and that model outputs require explicit uncertainty measures and continued human oversight.
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