4 problems

Let a normalized data manifold be a closed orientable hypersurface in $\mathbb{R}^d$ with non-trivial top homology, and distinguish this global condition from local curvature of th…

Per-layer RLCT reduction conjecture. The same RLCT reduction holds for each normalized weight matrix $W_l$ in a deep network under the wrLLC isolation protocol: freezing all parame…

Because the outputs are constrained by $\mathbf{1}^T x=1$, let $x'=x-\frac{1}{d}\mathbf{1}$, so that $\mathbf{1}^T x'=0$, and let $W\in\mathbb{R}^{m\times d}$ act on the input. Def…

Tightness conjecture. The bound from Theorem bound-alternate is tight for all such $p$, $k$, and $r$; equivalently,