38 problems

Fisher information rank conjecture. The rank is

Improved eta-expanded theorem. The thesis of Theorem …

Consider the causal model $\mathcal{M}=(\{X,Y\},E,f,X\rightarrow Y,p_{X,E})$, where the discrete random variables $X$ and $Y$ have $n$ states, $E$ is independent of $X$ and has…

For a fixed ReLU-network architecture, let $\mathcal{P}$ denote the parameter space obtained from the space of weights by taking into account the trivial scaling and permutation sy…

Width-one identifiability conjecture. 1. There exist architectures $\mathcal{A}=(n_0,\ldots,n_{L+1})$ with $n_\ell=1$ for some $\ell\leq L$ for which no identifiable parameters exi…

MHA weak identifiability conjecture. For every parameter $\theta\in\Theta$ of an MHA model, the parameter $\theta$ is weakly identifiable with respect to the symmetry group

Weak identifiability conjecture. With mild assumptions on the activation function $\sigma$, for every parameter $\theta \in \Theta$ of an MLP, there exists a parameter…

Let $G=(V \cup \mathcal{H},D)$ be a factor analysis graph. M-identifiability and extended M-identifiability are the two identifiability properties defined by the matching criterion…

Let $n \geq 3$, and let $\mathcal{M} = (G, \textit{In}, \textit{Out}, \textit{Leak})$ be an $n$-compartment directed-cycle model with $\textit{In}=\{1\}$ and $\textit{Out}=\{p\}$,…

Two-orthogonal uniqueness and stabilization conjecture. A generic two-orthogonal tensor in $\mathbb{R}^{n_1}\otimes\cdots\otimes\mathbb{R}^{n_d}$ has a unique two-orthogonal decomp…

Let normalized deep self-attention networks be parametrized via $(\mathbf{M},L)$, where these parameters encode the network as defined in the paper. The normalization removes layer…

General-dimensional characterization conjecture. The following conditions are equivalent:

Let $\mathcal{G}$ be any family of non-complete graphs, and let $M_G$ denote the homoscedastic linear structural equation model associated with $G\in\mathcal{G}$. Generic identifia…

Let $p$ be an even positive integer with $p\neq 2$, let $n\geq 3$, and let $G$ be a connected graph with $n$ vertices. Write ${\cal CM}_n^p$ for the relevant $\ell_p$-configuration…

Let $X\subset\mathbb{P}^{N}$ be an irreducible and non-degenerate variety with non-degenerate Gauss map. The variety $X$ is $h$-identifiable if a general fiber of its $(h+1)$-secan…

Non-degenerate Gauss-map conjecture. The variety $X$ is $h$-identifiable if and only if a general $(h-1)$-tangential projection

Modified Bronowski conjecture. If a general $(h-1)$-tangential projection of $X$ is birational and its image is a variety of minimal degree, then $X$ is $h$-identifiable and

Bronowski's conjecture. The variety $X$ is $h$-identifiable if and only if a general $(h-1)$-tangential projection

Factorization conjecture. The determinant of $A(\Sigma)_{\cdot,E}$ factorizes as

Let $N$ be a metric semidirected network on taxon set $X$, let $d_N$ denote its average distances on $X$, and let $T$ be the distance split tree reconstructed from $d_N$. Distance-…

Let $\widetilde{\mathcal{M}}=(G,In,Out,Leak)$ be a strongly connected linear compartmental model with at least one input and at least one leak. A singular-locus equation $f$ is the…

Let $\mathcal{M}$ be an unidentifiable linear compartmental model. Leak-addition conjecture. If one leak is added, the resulting model $\widetilde{\mathcal{M}}$ is also unidentifia…

Let $\mathcal{M}$ be a strongly connected linear compartmental model that is generically locally identifiable, with singular-locus equation $f$. An edge $j\to i$ is dividing if its…

Let $\widetilde{\mathcal{M}}$ be a strongly connected linear compartmental model with at least one input and exactly one leak. A model is generically locally identifiable if its pa…

Let $\mathcal{M}=(G,In,Out,V)$ be a linear compartmental model. Suppose either that $G$ is strongly input-output connected and $|Out|=1$, or that $G$ is strongly connected and…