5 problems

Let $n\geq 1$, $L\geq 1$, and let $f:[0,1]^n\to\mathbb{R}$ or $f:[0,1]^n\to\mathbb{R}^m$ be continuous. Consider a Sprecher Network with architecture $n\to[d_1,\dots,d_L]\to 1$ or…

Let a neural operator have adjustable capacity, for example through its number of layers or neurons, and consider the non-convex optimization landscape of its training loss. Overpa…

Asymptotic covariance approximation conjecture. The population covariances can be asymptotically approximated by the last iterates of the corresponding linear recursions, with the…

Consider linear neural networks trained on $m$ data points. The results referred to as Proposition … , Corollary … are observed computationally to hold when $m=2$. Extension conjec…

Assume that $X X^T$ has full rank. Let $N$ be the depth, let $W(t)=W_N(t)\cdots W_1(t)$ denote the product along the gradient flow, and let $\mathcal{M}_k$ denote the rank-constrai…