AI 中文总结
该研究定义原子生成事实并构建生成事实图，基于nanoGPT等建立训练-学习统一动力学，二阶预测器在四转换上获91.43%准确率等，还将推理确立为训练-学习动力学的冻结投影。
AI 中文摘要
我们定义了一个原子生成事实f=(u,τ,ω,z;ρ)，用于记录生成来源、已实现变换、具体发生情况、生成结果及关系角色。这些事实被编译为生成事实图（Generation-Fact Graph，GFG），提供了一种AI原生的、可编译的科学事实基底，可保留生成历史。我们建立了基于GFG的递归科学过程，其中分析、干预、重放和验证为后续循环生成事实。使用nanoGPT，我们建立了统一的训练-学习动力学：训练是带状态和记忆的参数-优化器系统的演化过程，每个实际训练动作进入接收状态，产生由该状态和目标特定更新几何条件决定的有限振幅非线性函数响应；学习是这些响应对分布式功能支持的持续重组，当根据目标特定状态的读出边界进行评估时，能力的形成、维持、下降或恢复变得可观测。三个主要坐标——目标边界状态、目标特定更新几何、参数-Adam接收状态——产生了在更新后输出被读取前运行的二阶预测器，在保留运行中，其在四个转换上达到了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，组件门控和回滚显示了训练期间形成的查询条件支持的因果招募和非加性组合，推导了注意力（Attention）实现的组织条件，受控反馈表明可能存在双刃剑式的强化效应。ResNet/CIFAR-100和扩散模型/CIFAR-10实验证实，除nanoGPT外，接收状态条件响应、持续支持重组和冻结推理投影也成立。
英文摘要
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.
Comments39 pages, 2 figures, 3 tables. Evidence spans 22 indexed experimental programmes: held-out prediction (91.43% accuracy), causal interventions, and cross-system validation in nanoGPT, ResNet/CIFAR-100 and diffusion/CIFAR-10. Code: https://github.com/wind342/gfg-training-learning-inference-experiments. Evidence: https://doi.org/10.5281/zenodo.22032772
