Commit Graph

5 Commits

Author SHA1 Message Date
gaojie b70161f4e5 feat(JEPA/math): 新增专题 VII & VIII,更新 README 与项目分析
Sync to site1 / sync (push) Has been cancelled
专题 VII — SIGReg 正则化(07_sigreg_regularization.md,760 行)
- 特征函数匹配损失 L_SIG 完整数学推导
- Cramér-Wold 定理证明:切片投影 → 联合高斯
- 切片技巧:256 个随机方向 + 梯形积分(17 节点)
- losses.py:SIGReg 逐行代码解析,张量形状追踪 (V,B,N)→scalar
- vs VICReg 对比:SIGReg 约束全分布,VICReg 仅约束二阶矩

专题 VIII — 线性 ICA:FastICA 与 JADE(08_linear_ica_fastica_jade.md,701 行)
- 盲源分离模型 x=As,非高斯性度量(峰度/负熵/互信息)
- FastICA 不动点迭代推导(三次收敛)
- JADE 四阶累积量张量 + Jacobi 联合对角化(二次收敛)
- Darmois-Skitovich 定理:ICA 可识别性充要条件
- ICA vs LeJEPA 对偶反转:高斯在 ICA 失败,在 LeJEPA 成功

其他变更:
- JEPA/math/README.md:专题表格新增 VII、VIII 行
- project_analysis.md:Session Log 补充 2026-06-05 工作记录
- lejepa-identifiability 子模块:.gitignore 新增 .venv/
2026-06-05 17:06:09 +08:00
gaojie b5499c7ea0 Add detailed lecture plan and summary for LeJEPA four theorems
- Introduced a comprehensive lecture plan for the four main theorems in LeJEPA, including knowledge dependency graphs, detailed outlines for each topic, and corresponding Lean 4 files for formal verification.
- Created a summary document encapsulating the core insights and mathematical structures of the four theorems, emphasizing their interdependencies and implications in the context of LeJEPA.
2026-06-05 16:30:24 +08:00
gaojie 5de86388db Add interactive HTML pages for planning explainer and spectral explainer
Sync to site1 / sync (push) Has been cancelled
- Created planning_explainer.html to demonstrate orthogonal invariance and optimal planning with interactive controls and visualizations.
- Created spectral_explainer.html to illustrate spectral decomposition and linear identifiability, featuring adjustable spectral weights and real-time correlation calculations.
2026-06-02 05:05:39 +08:00
gaojie 3df832ac6b Add new research papers to JEPA repository
Sync to site1 / sync (push) Has been cancelled
- Added 2506.09985_vjepa2.pdf (19.8 MB)
- Added 2511.08544_lejepa.pdf (8.5 MB)
- Added 2602.11389_causal_jepa.pdf (2.9 MB)
- Added 2603.19312_leworldmodel.pdf (5.5 MB)
2026-06-02 04:27:06 +08:00
gaojie c55f47b287 Add multiple research papers in PDF format to the repository, including recent works on AI and physics, with file sizes ranging from 1.7 MB to 32.3 MB.
Sync to site1 / sync (push) Has been cancelled
2026-06-02 04:12:38 +08:00