发表机构
Fudan University（复旦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明仅凭互信息阈值不足以确定物理分类代价，通过构造有界速率协议和传输边界，揭示精度约束下熵产生存在信息论无法捕捉的额外物理成本。
AI 中文摘要
一个物理分类器要达到规定的精度，必须产生多少熵？率失真理论规定了所需的最小信息量，但该信息阈值是否足以确定物理代价？我们证明并非如此，即使对于二分类任务和两态记忆也是如此。对于通过有限对称实验观测到的均匀二值目标，在共同操作时间、积分迁移率预算和足够大的有限跃迁率上限下，用其必要的互信息阈值替换分类误差约束会严格降低熵产生的下确界。当目标误差严格介于观测的贝叶斯误差和随机猜测之间时，这种分离成立。两个结果确立了这一物理差距。首先，按后验置信度对观测排序可得到精确的传输-风险边界和传输-信息边界。具有相同贝叶斯误差的观测可以有不同的代价边界。其次，我们构造了有界速率协议，从精确重置开始，以低于1的写入概率实现规定的编码器，并给出高于传输边界的显式超额代价。一个可实现的信息约束代价随后低于对每个任务可行协议均有效的下界。重复噪声观测的示例说明了这种分离。这些结果指出了仅基于信息的基准在物理分类中的局限性：任务精度和动力学约束必须被明确保留。所分析的代价是记忆写入期间的总熵产生，不包括数据获取、控制器操作和后续重置。
英文摘要
How much entropy must a physical classifier produce to achieve a prescribed accuracy? Rate--distortion theory specifies the minimum information required, but does that information threshold suffice to determine the physical cost? We show that it does not, even for a binary task and a two-state memory. For a uniform binary target observed through a finite symmetric experiment, replacing the classification-error constraint with its necessary mutual-information threshold strictly lowers the infimum of entropy production under a common operation time, integrated mobility budget, and sufficiently large finite transition-rate cap. The separation holds whenever the target error lies strictly between the Bayes error of the observations and chance. Two results establish this physical gap. First, ordering observations by posterior confidence gives exact transport--risk and transport--information frontiers. Observations with the same Bayes error can have different cost frontiers. Second, we construct bounded-rate protocols that realize prescribed encoders with write probabilities below one, starting from exact reset, with an explicit excess cost above the transport bound. An achievable information-constrained cost then falls below a lower bound valid for every task-feasible protocol. Examples with repeated noisy observations illustrate the separation. The results identify a limitation of information-only benchmarks for physical classification: task accuracy and kinetic constraints must be retained explicitly. The cost analyzed is total entropy production during memory writing, excluding data acquisition, controller operation, and subsequent reset.
