5 problems

Let $f:\mathbb{R}^m\rightarrow\mathbb{R}$ be a $C^1$ function that is $C^2$ near its critical points, and let $\{z_n\}$ be the sequence generated by the Backtracking GD method from…

Let $F$ be the loss function of a neural network, and distinguish local minima from saddle points, where a saddle point is a critical point that is neither a local minimum nor a lo…

Let $f:\mathbb{R}^k\rightarrow\mathbb{R}$ be a $C^1$ function and $C^2$ near its generalised saddle points. For an initial point $x_0\in\mathbb{R}^k$, let $\{x_n\}$ be the sequence…

Consider manifold gradient descent (MGD) applied to the paper's objective function on the sphere, and let its iterates start from the initialization used in the analysis. The objec…

Let $f_\beta(u)$ be the function whose saddle-point equation is … and let $u^*(\beta)$ be the branch of solutions defined in the source, satisfying $u^*(1)=0$ for…