训练、学习与推理：神经系统的统一动力学

摘要

我们定义原子生成事实f=(u,tau,omega,z;rho)，记录其起源、已实现变换、具体发生、生成结果与关系角色。将这些事实编译为生成事实图（GFG），可为AI原生、可编译的科学事实基底提供载体，并完整保留生成历史。我们建立了一种基于GFG的递归科学过程，其中分析、干预、回放与验证会为后续周期生成新事实。借助nanoGPT，我们确立了统一的训练-学习动力学。训练是带状态与记忆的参数-优化器系统的演化：每次实际训练动作进入接收状态，并产生一种由该状态及目标特异更新几何共同调控的有限振幅非线性函数响应。学习则是这些响应所引发的分布式功能支持的持续性重组；当目标特异状态对照其读出边界进行评估时，能力的形成、维持、衰退或恢复便成为可观测现象。三个主坐标——目标边界状态、目标特异更新几何以及参数-Adam接收状态——共同构成一个二阶预测器，可在更新后输出被读取之前进行预测。在留出运行中，该预测器在四种转变上达到了91.43%的准确率和91.49%的宏平均召回率。我们进一步将推理确立为训练-学习动力学的冻结投影。组件门控与回滚实验表明，训练期间形成的查询条件支持存在因果募集与非加性组合，并由此推导出由注意力实现的组织条件。受控反馈提示可能存在的双刃强化效应。ResNet/CIFAR-100与扩散模型/CIFAR-10实验进一步证实，在nanoGPT之外，接收状态条件响应、持续支持重组以及冻结推理投影同样成立。

English

We define an atomic generation fact f=(u,tau,omega,z;rho), recording the origin, realized transformation, concrete occurrence, generated result and relation role. Compiled into a Generation-Fact Graph (GFG), these facts provide an AI-native, compilable scientific fact substrate preserving generation histories. We establish a GFG-based recursive scientific process in which analysis, intervention, replay and validation form facts for later cycles. Using nanoGPT, we establish unified training-learning dynamics. Training is the evolution of a parameter-optimizer system with state and memory: each actual training action enters the receiving state and produces a finite-amplitude nonlinear functional response conditioned by that state and target-specific update geometry. Learning is the persistent reorganization of distributed functional support by these responses; capability formation, maintenance, decline or recovery becomes observable when target-specific states are evaluated against their readout boundaries. Three primary coordinates - target-boundary state, target-specific update geometry and parameter-Adam receiving state - yield a second-order predictor operating before post-update outputs are read. On held-out runs, it achieved 91.43% accuracy and 91.49% macro-averaged recall across four transitions. We further establish inference as a frozen projection of training-learning dynamics. Component gating and rollback show causal recruitment and non-additive combination of query-conditioned support formed during training, deriving organizational conditions realized by Attention. Controlled feedback indicates possible double-edged reinforcement effects. ResNet/CIFAR-100 and diffusion/CIFAR-10 experiments confirm receiving-state-conditioned responses, persistent support reorganization and frozen inference projection beyond nanoGPT.