There's an amazing and very large list of Open University courses by T. K. Finchley here https://tkfinchley.com/ou-maths-courses/. I particular recommend their course OU M335/M386/M435 Metric and Topological Spaces and Geometric Topology. Just wonderful pedagogy
via u/dnrlk at https://www.reddit.com/r/math/comments/1shlljv/20th_century_math_explainers/
we use the distance preference characterized by these centers to score keys according to their positions, and also leverage Q/K norms as an additional signal for importance estimation
大多数人认为KV缓存压缩主要基于注意力分数或内容相似性，但作者提出使用向量中心决定的距离偏好和Q/K范数作为重要性估计的信号。这一方法将注意力机制从传统的基于内容相似性转向基于几何特征，是一种全新的压缩思路。
AI turns semantic relationships into geometric relationships
here's a trivial example of why the "standard" geometric mean is not a good estimate of central tendency when you have values near zero.
Data that combine multiplicatively, like rates, are actually very common outside of economics too. The key is to recognize when a measured variables is affected by many (semi) independent forces, each of which scales that variable up or down — rather than simply adding or subtracting a fixed amount to it. This is often true in the natural sciences.
Ortiz, E., & Serrano, M. Á. (2021). Multiscale opinion dynamics on real networks. ArXiv:2107.06656 [Physics]. http://arxiv.org/abs/2107.06656
Ortiz, E., García-Pérez, G., & Serrano, M. Á. (2020). Geometric detection of hierarchical backbones in real networks. ArXiv:2006.03207 [Physics]. http://arxiv.org/abs/2006.03207
Distance from a point to a line segment
Lines and Distance of point to line
point: P
line_seg_start_point: P0
line_seg_end_point: P1
