AI 中文总结
本研究提出PLDR-LLM训练与推理的统一理论，通过精确恒等式、预测重整化和算子约简分析行映射动力学，实验支持有限条件预测并揭示观测者依赖性。
AI 中文摘要
本专著对幂律解码器表示语言模型（PLDR-LLM）的训练与推理发展了一个统一的理论框架。精确的有限功恒等式将行中心化学习映射的绝对能量变化分解为参数贡献、符号交互作用和数值观测缺陷。正仿射分块在行常数面上保留重启，而增广的AdamW状态提供了完整的动力学描述。预测重整化作用于对不同的语料目标块进行单次遍历的完整条件训练法则，保留优化器记忆、剩余数据、调度和数值策略。自主约简需要闭合性；近似约简会带来后继误差和发射误差。有限总体协方差、匹配的物理时钟、矩阵通量和符号时间能量将行动力学与模型范围的观测联系起来。绝对行坍缩、相对行集中、算子稳定化和预测准确性被区分开来。实验揭示了观测者和优化器的依赖性，拒绝了所测试的自主行状态候选，并支持有限条件预测和状态特定的算子约简。独立的单遍族表现出移动的有限涨落区域，而未建立热力学临界类。条件对称性、头限制、协方差流和读出误差预算指定了将缩放定律迁移到推理所需的假设。该理论区分了精确恒等式、条件动力学主张和有限经验发现，并附有证明、选定的形式化检查和紧凑的数值证据。
英文摘要
This monograph develops a unified account of training and inference in Power Law Decoder Representation language models (PLDR-LLMs). Exact finite work identities decompose changes in the absolute energy of the row-centered learned map into parameter contributions, signed interactions, and numerical observation defects. Positive affine blocking retains restarts at the row-constant face, while the augmented AdamW state supplies the complete dynamical description. Predictive renormalization acts on the complete conditional training law for a single pass over distinct corpus target blocks, retaining optimizer memory, remaining data, schedule, and numerical policy. Autonomous reductions require closure; approximate reductions carry successor and emission errors. Finite-population covariance, matched physical clocks, matrix fluxes, and signed temporal energy connect row dynamics to model-wide observations. Absolute row collapse, relative row concentration, operator stabilization, and predictive accuracy are distinguished. Experiments reveal observer and optimizer dependence, reject the tested autonomous row-state candidates, and support finite conditional prediction and state-specific operator reduction. Independent single-pass families exhibit moving finite fluctuation regions without establishing a thermodynamic critical class. Conditional symmetry, head limits, covariance flows, and readout error budgets specify assumptions needed to transfer scaling laws to inference. The theory separates exact identities, conditional dynamical claims, and finite empirical findings, with proofs, selected formal checks, and compact numerical evidence.
CommentsMonograph; 655 pages, 76 figures, 311 tables
