学习的热力学：记忆、拟合与价值的四分量类型核算
Thermodynamics of Learning: A Typed Four-Component Accounting of Memory, Fit, and Value
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中文总结 AI 辅助
该研究构建有限状态学习设备的四分量类型核算框架，分离记录相关与资本增益，推导资本化效率界，给出任务分布偏移下价值保留的两层对齐域及相关汇率结论。
中文摘要 AI 辅助
有限学习设备所记录的内容与其在未来任务中具有价值的内容并非同一量。我们为有限状态学习设备构建了一种类型化核算方法，将其分为四个分量：训练侧拟合泛函Φ_fit、记录相关存量J_D=I(M;D)、更新侧搜索总账σ_M以及操作资本价值V(M;T,b)。该价值是知情协议类与盲协议类之间的功差，盲协议类通过删除记忆读取端口并从头重新优化得到。（I）分离性：对于每个n，存在一类设备，其记录相关度和世界相关度增长n ln2，而资本增益恰好为零。在flat* regime中，无数据更新绝不会增加V。（II）资本化总账：一个精确的flat*提取恒等式和一个通用总账恒等式，给出了在无丢弃记录相关条件(f)下(F5')稳定的M局部更新的资本化效率η_cap=ΔV/(k T σ_M)的界η_cap≤1，以及等式成立的充要条件。（III）价值保留：对于保留差距L_gen（无符号约束）和保留比率ρ_gen（定义为正训练侧价值，不限于[0,1]区间），我们给出了两层对齐域：价值与经侧信息调整的记录拟合I(M';D|Y)之间的精确汇率（无任何记录侧信息独立性假设），以及在联合侧信息中性条件(M,D)⊥Y下的原始记录存量汇率，其边界由显式一次性密码本见证标记。这些是关于任务分布偏移下有限设备价值保留的陈述，而非统计泛化理论。
英文摘要
What a finite learning device has recorded and what will hold value for it on future tasks are not the same quantity. We develop a typed accounting for finite-state learning devices that separates four components: a training-side fit functional $Φ_{\mathrm{fit}}$, the record-correlation stock $J_{D}=I(M;D)$, an update-side search ledger $σ_{M}$, and an operational capital value $V(M;T,b)$. This value is the work gap between an informed protocol class and a blind class obtained by deleting the memory-read port and re-optimizing from scratch. (I) Separation: for every $n$, there is a device family on which record correlation and world correlation grow by $n\ln 2$ while the capital gain is exactly zero. In the $\mathrm{flat}^{*}$ regime, data-free updates never increase $V$. (II) Capitalization ledger: an exact $\mathrm{flat}^{*}$ extraction identity and a universal ledger identity give, for (F5$'$)-stable $M$-local updates under a no-discarded-record-correlation condition (f), the bound $η_{\mathrm{cap}}\le 1$ for the capitalization efficiency $η_{\mathrm{cap}}=ΔV/(k T\,σ_{M})$, together with necessary and sufficient conditions for equality. (III) Value retention: for the retention gap $L_{\mathrm{gen}}$ and retention ratio $ρ_{\mathrm{gen}}$ (the former carries no sign constraint; the latter is defined for positive training-side value and is not confined to $[0,1]$) we give a two-layer alignment domain: an exact exchange rate between value and the side-information-adjusted record fit $I(M';D\mid Y)$ without any record-side-information independence assumption, and a raw record-stock exchange rate under a joint side-information neutrality condition $(M,D)\perp Y$, whose boundary is marked by an explicit one-time-pad witness. These are statements about finite-device value retention under task-distribution shift, not a theory of statistical generalization.
发表机构
- ZeroStruct Inc.（ZeroStruct公司）
机构由 AI 辅助整理，请以论文原文为准。
