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This paper introduces Strict Partial Order Networks (SPON), a novel neural network architecture designed to enforce asymmetry and transitive properties as soft constraints. We apply it to induce hypernymy relations by training with is-a…

Recent advances to combine structured regression models and deep neural networks for better interpretability, more expressiveness, and statistically valid uncertainty quantification demonstrate the versatility of semi-structured neural…

Randomized smoothing provides strong, model-agnostic robustness certificates, but existing guarantees are limited to single modalities, treating continuous and discrete inputs in isolation. This limitation becomes critical in multimodal…

The main aim of the ESS$\nu$SB proposal is the discovery of the leptonic CP phase $\delta_{CP}$ with a high significance ($5\sigma$ for 50% values of $\delta_{CP}$) by utilizing the physics at the second oscillation maxima of the $P_{\mu…

We construct an efficient class of increasingly high-order (up to 17th-order) essentially non-oscillatory schemes with multi-resolution (ENO-MR) for solving hyperbolic conservation laws. The candidate stencils for constructing ENO-MR…

Spectral functions of large matrices contains important structural information about the underlying data, and is thus becoming increasingly important. Many times, large matrices representing real-world data are \emph{sparse} or \emph{doubly…

We present algorithms for checking and enforcing robustness of concurrent programs against the Total Store Ordering (TSO) memory model. A program is robust if all its TSO computations correspond to computations under the Sequential…

Einstein's field equation of General Relativity (GR) has been known for over 100 years, yet it remains challenging to solve analytically in strongly relativistic regimes, particularly where there is a lack of a priori symmetry. Numerical…

Hyperspectral unmixing (HU) is a critical yet challenging task in remote sensing. However, existing nonnegative matrix factorization (NMF) methods with graph learning mostly focus on first-order or second-order nearest neighbor…

Under the assumption of a CSW generalization to loop amplitudes in N=4 SYM, (1) We prove that, formally the S-matrix is superconformal invariant to any loop order, and (2) We argue that superconformal symmetry survives regularization. More…

Chemical short-range order (SRO) provides new opportunities for tuning alloy properties, but conventional computational thermodynamics frameworks such as CALPHAD, based on Bragg-Williams mean-field approximations, cannot properly describe…

We introduce ordered transfer hyperparameter optimisation (OTHPO), a version of transfer learning for hyperparameter optimisation (HPO) where the tasks follow a sequential order. Unlike for state-of-the-art transfer HPO, the assumption is…

We consider a new hierarchy of semidefinite relaxations for the general polynomial optimization problem $(P):\:f^{\ast}=\min \{\,f(x):x\in K\,\}$ on a compact basic semi-algebraic set $K\subset\R^n$. This hierarchy combines some advantages…

The advantage of WENO-JS5 scheme [ J. Comput. Phys. 1996] over the WENO-LOC scheme [J. Comput. Phys.1994] is that the WENO-LOC nonlinear weights do not achieve the desired order of convergence in smooth monotone regions and at critical…

The performance of basis sets made of numerical atomic orbitals is explored in density-functional calculations of solids and molecules. With the aim of optimizing basis quality while maintaining strict localization of the orbitals, as…

The authors present SHarmonic, a new implementation of the spherical harmonics targeted for electronic-structure calculations. Their approach is to use explicit formulas for the harmonics written in terms of normalized Cartesian…

Set representations are the foundation of various set-based approaches in state estimation, reachability analysis and fault diagnosis. In this paper, we investigate spectrahedral shadows, a class of nonlinear geometric objects previously…

We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…

In this work we propose a new neural network architecture that efficiently implements and learns general purpose set-equivariant functions. Such a function f maps a set of entities x = {x1, . . . , xn} from one domain to a set of same…

We consider accelerated versions of the operator Sinkhorn iteration (OSI) for solving scaling problems for completely positive maps. Based on the interpretation of OSI as alternating fixed point iteration, it has been recently proposed to…