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Consider some compact Riemannian manifold $M$. Fix some point $p$. Consider a "sub-sphere of radius $r$" - i.e. set of points on distance $r$ from $p$. Consider growth function $g(r)$ to be ...

I know that mean curvature and diffusion-type flows are common in manifold learning because of their smoothing effects. I haven't seen Ricci flow used as much. Given that Ricci and diffusion-type ...

After seeing this article https://www.quantamagazine.org/an-idea-from-physics-helps-ai-see-in-higher-dimensions-20200109/ I wanted to ask myself how useful of an endeavor would it be if one goes ...

Disclaimer: This is a cross-post from a very similar question on math.SE. I allowed myself to post it here after reading this meta post about cross-posting between mathoverflow and math.SE, I did ...

Let $X \in \mathbb{R}^{n \times d}, w \in \mathbb{R}^d, y \in \{\pm 1\}^{n}, \alpha \in [0,1], \lambda \in \mathbb{R}$. I have an expression that looks as follows $\frac{1}{2}\|Xw -y \|_{2}^2 + \...