121 problems

Consider a model whose target spectral distribution is heavy-tailed, in contrast with the Marchenko–Pastur target distribution discussed above. Heavy-tailed target conjecture. A mo…

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

High-accuracy conjecture. High accuracy should still be achievable over the field of rational numbers when

Wasserstein distance superiority conjecture. For a very large training set, the Wasserstein distance will have better performance than each of the three tested distances.

The paper studies machine intelligence as a system whose capabilities may depend not only on representational structure but also on access structure. Capability convergence hypothe…

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 $S(r,q)$ be a binary softmax function with elements $S_1(r,q)$ and $S_2(r,q)$ that minimize the prevalence-weighted cross-entropy objective in the infinite-sample limit, where…

The [? Let Poseidon be a neural operator model pretrained on fluid-type datasets, and consider the INS-Tracer equation dataset, whose physical mechanisms include incompressible Nav…

EFS has a forward optimization step whose time complexity is quadratic in the number of training samples. Stochastic optimization conjecture. Stochastic optimization techniques cou…

CCA+LoRA one-step conjecture. The particularly poor prediction quality of CCA+LoRA when $t=1$ is caused by the absence of the action of Koopman matrices.

Let a Gaussian process be used to model an error, cost, or risk function in machine learning, and consider covariance kernels that are isotropic but non-stationary. Benning et al.'…

A cutting-plane learning problem considers candidate cuts evaluated by a gap-closed score, with attention restricted to cuts that cut off the current fractional solution. Gap-close…

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

Let $q\geq 1$ be an integer, let $\chi\colon \mathbb{Z}\to\mathbb{C}$ be a Dirichlet character modulo $q$, and let … be its Dirichlet $L$-function. Denote its initial non-trivial z…

Generic statistical-ensemble conjecture. All Attention schemes are variants of a generic, abstract statistical ensemble, with a more complete set of pairwise and/or higher-order in…

Consider convolutional neural networks used in inverse-scattering reconstruction, with convolution blocks providing local operations, and consider scatterers outside the training d…

Aligned multi-objective optimization (AMOO) considers multiple related loss functions whose feedback is aligned or approximately aligned during optimization. In this setting, algor…

Tuning-parameter conjecture. The observed differences in tuning bias may be due to the large number of parameters tuned in these methods.

Topological complexity conjecture. Since LSUN Kitchen is a much larger dataset containing diverse images, its underlying lower-dimensional submanifold has more complex topological…

Let CGL denote the paper’s coincidence-graph learning approach, applied to larger and more randomized graphs, and let the system’s recursive range measure how far graph interaction…

Consider an agent whose internal graph uses de-inforcement and which can enter a “rest” state with limited or no external stimuli. Rest-state de-inforcement conjecture. During such…

The model uses de-inforcement, meaning that plasticity reduces rather than amplifies signals in its internal graph representation. De-inforcement conjecture. The de-inforcement fun…

A flow is a family of maps with group properties, and neural conjugate flows represent dynamics by composing an invertible map, a flow, and its inverse. Training may either impose…

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…

For a partition $\lambda=(\lambda_1,\ldots,\lambda_r)$, let $E_\lambda^U$ be the set of $\lambda$-Escher tuples associated with $U$, let…