大模型在语义模糊时无法同时保证准确、无偏和有用。
A CAP-like Trilemma for Large Language Models: Correctness, Non-bias, and Utility under Semantic Underdetermination
- 在语义不明确时，模型需自行选择判断标准，否则会引入偏见。
- 避免偏见会导致拒绝回答或含糊回应，降低实用性。
- 该理论解释了部分大模型失败的深层原因，适合关注AI伦理与可靠性者阅读。
CAP定理指出，在网络分区情况下，分布式系统无法同时满足一致性、可用性和分区容错性。受此启发，本文提出大语言模型（LLM）的类CAP猜想：在语义不明确的情况下，模型无法始终同时保证强正确性、严格无偏性和高实用性。当提示中的前提无法确定唯一答案时，即为语义不明确。此时，一个有用且明确的响应需要模型引入选择标准、偏好、先验或价值排序。若这些标准未由用户给出或无法从前提中合理推导，响应将在广义选择理论意义上产生偏见。反之，若模型避免使用未经证实的偏好，则可保持正确性和无偏性，但可能因拒绝、模糊或澄清而降低实用性。本文形式化了这一正确性-无偏性-实用性三难困境，构建了具体例子，并论证某些大模型失败并非仅源于模型能力限制，而是源自不确定决策请求的结构性问题。
原文摘要 · Abstract (English)
The CAP theorem states that a distributed system cannot simultaneously guarantee consistency, availability, and partition tolerance under network partition. Inspired by this result, this paper formulates a CAP-like conjecture for Large Language Models (LLMs). The proposed trilemma states that, under semantic underdetermination, an LLM cannot always simultaneously guarantee strong correctness, strict non-bias, and high utility. A prompt is semantically underdetermined when the given premises do not determine a unique answer. In such cases, a useful and decisive response requires the model to introduce a selection criterion, preference, prior, or value ordering. If this criterion is not supplied by the user or justified by the available premises, the response becomes biased in a broad selection-theoretic sense. Conversely, if the model avoids unsupported preferences, it may preserve correctness and non-bias but may reduce utility through refusal, hedging, or clarification. The paper formalizes this correctness--non-bias--utility trilemma, develops examples, and argues that certain LLM failures arise not merely from model limitations but from the structure of underdetermined decision requests.
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