Generative AI has transformed the economics of information production, making explanations, proofs, examples, and analyses available at very low cost. Yet the value of information still depends on whether downstream users can absorb and act on it. A signal conveys meaning only to a learner with the structural capacity to decode it: an explanation that clarifies a concept for one user may be indistinguishable from noise to another who lacks the relevant prerequisites. This paper develops a mathematical model of that learner-side bottleneck. We model the learner as a mind, an abstract learning system characterized by a prerequisite structure over concepts. A mind may represent a human learner, an artificial learner such as a neural network, or any agent whose ability to interpret signals depends on previously acquired concepts. Teaching is modeled as sequential communication with a latent target. Because instructional signals are usable only when the learner has acquired the prerequisites needed to parse them, the effective communication channel depends on the learner's current state of knowledge and becomes more informative as learning progresses. The model yields two limits on the speed of learning and adoption: a structural limit determined by prerequisite reachability and an epistemic limit determined by uncertainty about the target. The framework implies threshold effects in training and capability acquisition. When the teaching horizon lies below the prerequisite depth of the target, additional instruction cannot produce successful completion of teaching; once that depth is reached, completion becomes feasible. Across heterogeneous learners, a common broadcast curriculum can be slower than personalized instruction by a factor linear in the number of learner types.

翻译：生成式人工智能已经改变了信息生产的经济学，使得解释、证明、示例和分析能够以极低的成本获取。然而，信息的价值仍然取决于下游用户能否吸收并据此采取行动。一个信号只有在具备解码其结构性能力的学习者那里才能传达意义：对一个用户来说能澄清某个概念的解释，对另一个缺乏相关先验知识的用户而言可能无异于噪声。本文针对学习者这一端存在的瓶颈开发了一个数学模型。我们将学习者建模为一个"心智"，即一个抽象的学习系统，其特征是概念之间具有先决条件结构。一个心智可以代表人类学习者、神经网络这样的机器学习者，或者任何其解释信号的能力依赖于先前习得概念的智能体。教学被建模为带有隐式目标的序贯通信过程。由于教学信号只有在学习者已掌握解析所需的前置知识时才可使用，有效通信信道取决于学习者的当前知识状态，并随着学习进程的推进而变得更加信息丰富。该模型得出了学习和采纳速度的两个极限：由先决条件可达性决定的结构极限，以及由目标不确定性决定的认知极限。这一框架暗示了训练和能力获取中的阈值效应。当教学时域低于目标概念的先决条件深度时，额外的教学无法成功完成教学目标；一旦达到该深度，教学完成就变得可行。对于异质性学习者群体，统一的广播式教学进度可能比个性化教学慢一个因子，该因子与学习者类型的数量呈线性关系。