訓練、學習與推論：神經系統的統一動力學

摘要

我們將原子生成事實 f=(u,tau,omega,z;rho) 定義為記錄來源、實現變換、具體發生、生成結果與關係角色的基本單元。這些事實被編譯為生成事實圖（Generation-Fact Graph, GFG），提供了一種AI原生、可編譯的科學事實基底，保存生成歷史。我們建立了一個基於GFG的遞歸科學過程，其中分析、干預、重放與驗證為後續循環形成事實。利用nanoGPT，我們建立了統一的訓練-學習動力學。訓練是帶有狀態與記憶的參數-優化器系統的演化：每個實際訓練動作進入接收狀態，並在該狀態與目標特定更新幾何的條件下產生有限幅度非線性函數響應。學習是這些響應對分佈式功能支援的持續重組；當目標特定狀態根據其讀出邊界進行評估時，能力形成、維持、衰退或恢復變得可觀測。三個主要坐標——目標邊界狀態、目標特定更新幾何與參數-Adam接收狀態——產生一個在更新後輸出被讀取之前運作的二階預測器。在留出運行中，它在四種轉換上達到了91.43%的準確率和91.49%的宏平均召回率。我們進一步將推理確立為訓練-學習動力學的凍結投影。組件門控與回滾顯示了訓練期間形成的查詢條件支援的因果募集與非加性組合，推導出由Attention實現的組織條件。受控反饋顯示可能的雙刃強化效應。ResNet/CIFAR-100與擴散模型/CIFAR-10實驗證實了nanoGPT之外的接收狀態條件響應、持續性支援重組與凍結推理投影。

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.