发表机构
Kyoto University; Kyoto MPI Inc.（京都大学; 京都MPI株式会社）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明在噪声置换网络中，期望自由能相等不蕴含修订后IIT系统整合信息相等，揭示局部自由能对应与全局非等价性共存，强调综合IIT与FEP需保留反事实因果信息。
AI 中文摘要
自由能原理（FEP）和主动推断通过概率生成模型和自由能泛函描述自适应系统，而整合信息理论（IIT）则刻画内在因果-效应组织。我们区分两个问题：修订后的IIT量是否允许局部的自由能类表示，以及标量期望自由能是否能决定系统整合信息。我们证明，2026年IIT的内在分化项和特化项允许精确的惊讶（surprisal）表示，因此在精确推断下允许变分自由能表示。随后，我们构建了噪声二元置换网络，其因果拓扑变化而局部转移可靠性固定。在均匀状态下，所有置换在共同偏好和观测模型下产生相同的一步预测分布和状态风险期望自由能，但修订后的IIT能区分它们：多周期置换具有零全系统整合，而单个噪声周期在中等可靠性下具有正整合。对于n单元噪声单周期，我们推导了修订后系统整合信息的闭式表达式，证明了最小信息划分恰好切割两条因果边，并表明随着n增长，最优可靠性趋近于1，联合特化状态概率趋近于1/2，最大整合趋近于1 ibit。针对n=2-5的数值IIT计算以及通过n=8的穷举划分枚举重现了解析结果。因此，局部惊讶/自由能对应与全局非等价性共存：相等的期望自由能并不意味着相等的修订后IIT系统整合信息。任何IIT与FEP/主动推断的综合都必须保留超越标量自由能值的反事实因果信息。
英文摘要
The free-energy principle (FEP) and active inference describe adaptive systems through probabilistic generative models and free-energy functionals, whereas integrated information theory (IIT) characterizes intrinsic cause-effect organization. We separate two questions: whether revised IIT quantities admit local free-energy-like representations and whether scalar expected free energy can determine system integrated information. We show that the 2026 IIT intrinsic-differentiation and specification terms admit exact surprisal representations, and hence variational-free-energy representations under exact inference. We then construct noisy binary permutation networks whose causal topology varies while local transition reliability is fixed. In a homogeneous state, all permutations yield the same one-step predictive distribution and state-risk expected free energy under common preferences and observation models, yet revised IIT distinguishes them: multicycle permutations have zero whole-system integration, whereas a single noisy cycle has positive integration at intermediate reliability. For an n-unit noisy single cycle, we derive a closed-form expression for revised system integrated information, prove that the minimum-information partition cuts exactly two causal edges, and show that as n grows the optimal reliability approaches unity, the joint specified-state probability approaches one half, and the maximum integration approaches one ibit. Numerical IIT calculations for n = 2-5 and exhaustive partition enumeration through n = 8 reproduce the analytical results. Thus, local surprisal/free-energy correspondence coexists with global non-equivalence: equal expected free energy does not imply equal revised IIT system integrated information. Any synthesis of IIT with FEP/active inference must retain counterfactual causal information beyond a scalar free-energy value.
Comments14 pages, 4 figures
