通过分层梯度分解实现自证系统，让神经网络在损伤后仍能自我修复。
Self-Evidencing Through Hierarchical Gradient Decomposition: A Dissipative System That Maintains Non-Equilibrium Steady-State by Minimizing Variational Free Energy
- 用反馈对齐、资格迹和营养场图分层分配梯度，实现局部精确计算
- 营养场图与真实梯度相关性达0.9693，任务干扰后保留率98.6%
- 适合研究神经可塑性、自修复架构或生物启发学习的学者
自由能原理（FEP）指出，自组织系统必须最小化变分自由能才能持续存在，但该原理如何转化为可实施的算法长期未明。本文提出一种构造性证明，表明可通过精确的局部信用分配实现FEP。系统在层级上分解梯度计算：空间信用通过反馈对齐实现，时间信用通过资格迹实现，结构信用则通过营养场图（TFM）估计每条连接块的期望梯度大小。我们证明这些机制在其各自层级上是精确的，并实证验证核心主张：TFM与理想梯度的相关性达到0.9693。这种精确性催生出涌现能力：任务干扰后保留率达98.6%，可自主恢复75%结构损伤，实现自组织临界性（谱半径p ≈ 1.0），并在无需经验回放的连续控制任务中实现样本高效的强化学习。该架构统一了普里高津的耗散结构、弗里斯顿的自由能最小化与霍普菲尔德的吸引子动力学，表明对网络拓扑的精确层级推断可用局部、生物合理规则实现。
原文摘要 · Abstract (English)
The Free Energy Principle (FEP) states that self-organizing systems must minimize variational free energy to persist, but the path from principle to implementable algorithm has remained unclear. We present a constructive proof that the FEP can be realized through exact local credit assignment. The system decomposes gradient computation hierarchically: spatial credit via feedback alignment, temporal credit via eligibility traces, and structural credit via a Trophic Field Map (TFM) that estimates expected gradient magnitude for each connection block. We prove these mechanisms are exact at their respective levels and validate the central claim empirically: the TFM achieves 0.9693 Pearson correlation with oracle gradients. This exactness produces emergent capabilities including 98.6% retention after task interference, autonomous recovery from 75% structural damage, self-organized criticality (spectral radius p ~= 1.0$), and sample-efficient reinforcement learning on continuous control tasks without replay buffers. The architecture unifies Prigogine's dissipative structures, Friston's free energy minimization, and Hopfield's attractor dynamics, demonstrating that exact hierarchical inference over network topology can be implemented with local, biologically plausible rules.
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