13 problems

Let $c$ denote the collinearity parameter, $\Delta$ the correlation parameter, and $p$ the number of variables in the latent linear-regression framework described above. Proposed f…

Let $f,g:\mathbb{R}^d\to\mathbb{R}$ be two continuous functions, and let $\Gamma,\Gamma^\prime$ be their respective graphs. Write…

For a partition $\lambda=(\lambda_1,\ldots,\lambda_r)$, let $E_\lambda^U$ be the set of $\lambda$-Escher tuples, let $\tau_\lambda:E_\lambda^U\to\mathbb{Q}^{\xi(\lambda)}$ be the c…

Let the SUCPA-map be $\mathbf{f}=[f_1,\ldots,f_K]:\mathbb{R}^K\to\mathbb{R}^K$, and let $\omega(\boldsymbol{\beta}^{[0]})$ denote the $\omega$-limit set of an initial condition…

Neural Channel capacity conjecture. The capacity of a Neural Channel increases with the size of the spare subnetwork.

Neural-channel universality conjecture. Every overparameterized neural network is a Neural Channel.

Let $G(n-d,n)$ denote the Grassmannian of $(n-d)$-dimensional subspaces of an $n$-dimensional space, and let $\bm{p}$ be a Plücker-coordinate vector in $\bigcup\limits_n G(n-d,n)$.…

Let $\mathcal{D}_{train}$ and $\mathcal{D}_{test}$ be the training and test subsets of the dataset, and let $D_{model}\circ E_{model}$ be a trained autoencoder. Near each training…

Let $\{\boldsymbol{x}^{\mu}\}_{\mu=1}^{n}$ be independent samples from a data distribution on $\mathcal{X}\subset\mathbb{R}^{D}$, and let the centred teacher and student features b…

Consider the subcategory of $\mathbf{BayesLens}$ spanned by finite-dimensional smooth manifolds, with morphisms generated under sequential and parallel composition by the generaliz…

Let $\mathcal{D}$ be a natural distribution over examples, let $n$ be the number of samples, let $\mathcal{F}$ be a family of interpolating models, and let $\varepsilon\geq0$. A pa…

Let $\mathcal{F}$ be a classifier family and let $\mathcal{D}$ be a distribution. For independent train sets $S_1,S_2\sim\mathcal{D}^n$, let $f_1,f_2$ be classifiers trained on…

Lacasse's conjecture. For every $m\in\mathbb{N}$,