Related papers: CORN: Correlation-Driven Nonparametric Learning Ap…
Conformal prediction is a powerful distribution-free framework for constructing prediction sets with coverage guarantees. Classical methods, such as split conformal prediction, provide marginal coverage, ensuring that the prediction set…
Recent works have introduced input-convex neural networks (ICNNs) as learning models with advantageous training, inference, and generalization properties linked to their convex structure. In this paper, we propose a novel feature-convex…
Group symmetry is inherent in a wide variety of data distributions. Data processing that preserves symmetry is described as an equivariant map and often effective in achieving high performance. Convolutional neural networks (CNNs) have been…
We prove the so-called second case of the fractional Korn inequality for uniform domains. We obtain this result as an application of a novel fractional Korn-type inequality formulated in terms of truncated seminorms, which turns out to be…
In this note, we study the distribution of the rational canonical form of a random matrix over the finite field $\mathbb{F}_p$, whose entries are independent and $\epsilon$-balanced with $\epsilon\in(0,1-1/p]$. We show that, as the matrix…
An elementary proof is given to show that a parametrised algebraic curve in the plane may be traced out, in the sense of A. B. Kempe, by a finite pinned linkage. Additionally it is shown that any parametrised continuous curve \gamma: [0,1]…
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…
We have developed an Uncertainty Quantification process for multistep pipelines and applied it to the ACORN particle tracking pipeline. All our experiments are made using the TrackML open dataset. Using the Monte Carlo Dropout method, we…
The paper demonstrates that falsifiability is fundamental to learning. We prove the following theorem for statistical learning and sequential prediction: If a theory is falsifiable then it is learnable -- i.e. admits a strategy that…
Let $\mathscr{A}$ be a nonempty set of infinite matrices of linear operators between two topological vector spaces. We show that a sequence is uniformly $\mathscr{A}$-summable if and only if it is $B$-summable for all matrices $B$ of linear…
The Regular Post Embedding Problem extended with partial (co)directness is shown decidable. This extends to universal and/or counting versions. It is also shown that combining directness and codirectness in Post Embedding problems leads to…
We establish a family of coercive Korn-type inequalities for generalised incompatible fields in the superlinear growth regime under sharp criteria. This extends and unifies several previously known inequalities that are pivotal to the…
A celebrated unresolved conjecture of Peter Frankl states that every finite collection of sets, with finite universe, admits an abundant element. In this paper, we prove Frankl's union-closed conjecture(FC). We provide an induction proof…
This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the…
Sun proposed a list of congruence and quadratic-residue conjectures for determinants and permanents over residue classes modulo a prime. This article gives a uniform treatment of Conjectures 4.6, 4.7, 4.8(ii), 4.9, 4.10(ii), 4.11 and 4.12…
Motivation: Drug discovery demands rapid quantification of compound-protein interaction (CPI). However, there is a lack of methods that can predict compound-protein affinity from sequences alone with high applicability, accuracy, and…
Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap.…
This paper provides a rigorous and gap-free proof of the index theorem used in the theory of regular economy. In the index theorem that is the subject of this paper, the assumptions for the excess demand function are only several usual…
Uncertainty quantification (UQ) for foundation models is essential to identify and mitigate potential hallucinations in automatically generated text. However, heuristic UQ approaches lack formal guarantees for key metrics such as the false…