Notes and writings by Feixiang Tao on physics, mathematics, and computer science.https://tensorfieldx.space/https://tensorfieldx.space/notes/rl-math04/https://tensorfieldx.space/notes/rl-math04/从随机近似出发，统一理解增量学习、TD(0)、SARSA 与 Q-learning 的收敛骨架。Mon, 13 Apr 2026 00:00:00 GMThttps://tensorfieldx.space/notes/rl-math05/https://tensorfieldx.space/notes/rl-math05/从轨迹分布出发推导策略梯度，并统一理解 baseline、reward-to-go 与 off-policy 校正。Mon, 13 Apr 2026 00:00:00 GMThttps://tensorfieldx.space/notes/ode03/https://tensorfieldx.space/notes/ode03/围绕常微分方程的初值问题，梳理局部存在唯一性、连续依赖、流映射、变分方程与延拓理论。Tue, 31 Mar 2026 00:00:00 GMThttps://tensorfieldx.space/notes/rl-math01/https://tensorfieldx.space/notes/rl-math01/在有限折扣 MDP 中建立值函数、贝尔曼期望方程及其矩阵与算子视角。Thu, 19 Mar 2026 00:00:00 GMThttps://tensorfieldx.space/notes/rl-math02/https://tensorfieldx.space/notes/rl-math02/从最优贝尔曼方程出发，推导值迭代、策略迭代及其收敛性。Thu, 19 Mar 2026 00:00:00 GMThttps://tensorfieldx.space/notes/minimind01-rmsnorm/https://tensorfieldx.space/notes/minimind01-rmsnorm/解释 RMSNorm 在 Transformer 中的作用、实现细节与张量形状流。Wed, 18 Mar 2026 00:00:00 GMThttps://tensorfieldx.space/notes/minimind02-rope-yarn/https://tensorfieldx.space/notes/minimind02-rope-yarn/从注意力几何出发梳理 RoPE 的位置编码机制与 YaRN 的长上下文扩展。Wed, 18 Mar 2026 00:00:00 GMThttps://tensorfieldx.space/notes/minimind03-gqa/https://tensorfieldx.space/notes/minimind03-gqa/围绕 KV cache 成本分析 GQA 的设计动机、张量形状与系统折中。Wed, 18 Mar 2026 00:00:00 GMThttps://tensorfieldx.space/notes/minimind04-ffn/https://tensorfieldx.space/notes/minimind04-ffn/拆解门控 FFN 在 Transformer block 中的角色、形状变化与工程设计。Wed, 18 Mar 2026 00:00:00 GMThttps://tensorfieldx.space/notes/minimind05-model/https://tensorfieldx.space/notes/minimind05-model/按数据流梳理 HollowStoneMindModel 从 token id 到 hidden states 的完整组装过程。Wed, 18 Mar 2026 00:00:00 GMThttps://tensorfieldx.space/notes/ode01/https://tensorfieldx.space/notes/ode01/从高阶线性微分方程出发，过渡到一阶自治系统与动力系统的核心问题。Wed, 18 Mar 2026 00:00:00 GMThttps://tensorfieldx.space/notes/ode02/https://tensorfieldx.space/notes/ode02/借助 Poincare 映射研究周期驱动 logistic 方程的周期解、稳定性与分岔结构。Wed, 18 Mar 2026 00:00:00 GMThttps://tensorfieldx.space/notes/minimind-architecture/https://tensorfieldx.space/notes/minimind-architecture/MiniMind / HollowStoneMind 的 Dense 与 MoE 两种模型主干结构总览与设计决策分析。Thu, 12 Mar 2026 00:00:00 GMThttps://tensorfieldx.space/notes/probability025/https://tensorfieldx.space/notes/probability025/梳理期望的三种等价写法、推前测度记号与条件期望的投影视角。Fri, 27 Feb 2026 00:00:00 GMThttps://tensorfieldx.space/notes/probability02/https://tensorfieldx.space/notes/probability02/从信息与投影视角梳理期望、条件期望和独立性的几何结构。Thu, 26 Feb 2026 00:00:00 GMThttps://tensorfieldx.space/notes/probability01/https://tensorfieldx.space/notes/probability01/从测度、sigma-代数与随机变量出发，重建现代概率论的基础框架。Sun, 08 Feb 2026 00:00:00 GMThttps://tensorfieldx.space/notes/eecs598-1/https://tensorfieldx.space/notes/eecs598-1/从信息论公理出发，推导熵、交叉熵与KL散度的数学关系，及其在深度学习损失函数中的物理意义。Thu, 22 Jan 2026 00:00:00 GMThttps://tensorfieldx.space/notes/mc05/https://tensorfieldx.space/notes/mc05/从几何不变量出发，推导相对论下的惯性运动与 E=mc²。Mon, 12 Jan 2026 00:00:00 GMThttps://tensorfieldx.space/notes/map01/https://tensorfieldx.space/notes/map01/从有限维欧几里得空间出发，到无穷维函数空间的结构：完备性、正交基、勒让德多项式以及狄拉克函数的诞生。Sun, 11 Jan 2026 00:00:00 GMThttps://tensorfieldx.space/notes/mc04/https://tensorfieldx.space/notes/mc04/直觉的危机与数学解答：从内蕴定义到嵌入视角。Fri, 09 Jan 2026 00:00:00 GMThttps://tensorfieldx.space/notes/mc03/https://tensorfieldx.space/notes/mc03/从微分流形的拉回度规到明可夫斯基时空的严谨构建：双曲旋转、四维速度与因果结构。Thu, 08 Jan 2026 00:00:00 GMThttps://tensorfieldx.space/notes/mechanics02/https://tensorfieldx.space/notes/mechanics02/从双摆的甜甜圈说起：流形、切空间的两种视角以及广义速度的几何本质。Thu, 08 Jan 2026 00:00:00 GMThttps://tensorfieldx.space/notes/machanics0/https://tensorfieldx.space/notes/machanics0/变分基础Tue, 06 Jan 2026 00:00:00 GMThttps://tensorfieldx.space/notes/cs61c-note1/https://tensorfieldx.space/notes/cs61c-note1/CS61C 中的数字表示、编译工具链、内存布局及栈帧结构。Fri, 02 Jan 2026 00:00:00 GMThttps://tensorfieldx.space/notes/mechanics01/https://tensorfieldx.space/notes/mechanics01/从广义坐标到变分法，推导惯性系下自由粒子的拉格朗日量。Fri, 02 Jan 2026 00:00:00 GMT