Related papers: Concentration Robustness in LP Kinetic Systems
In this paper, we consider the problem of constraint management in Linear Periodic (LP) systems using Reference Governors (RG). First, we present the periodic-invariant maximal output admissible sets for LP systems. We extend the earlier…
While the class of Polynomial Nets demonstrates comparable performance to neural networks (NN), it currently has neither theoretical generalization characterization nor robustness guarantees. To this end, we derive new complexity bounds for…
Globally accurate full-dimensional ground state potential energy surface (PES) for the Cl($^2$P) + XCl $\to$ HCl + Cl($^2$P) reaction, a prototypical heavy-light-heavy abstract reaction, is developed using permutation invariant polynomial…
Continual learning (CL) is an approach to address catastrophic forgetting, which refers to forgetting previously learned knowledge by neural networks when trained on new tasks or data distributions. The adversarial robustness has decomposed…
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…
In a recent, strongly emergent literature on few-shot CLIP adaptation, Linear Probe (LP) has been often reported as a weak baseline. This has motivated intensive research building convoluted prompt learning or feature adaptation strategies.…
Machine learning potentials (MLPs) have become indispensable for conducting accurate large-scale atomistic simulations and for the efficient prediction of crystal structures. Polynomial MLPs, defined by polynomial rotational invariants,…
This paper studies the relations among system parameters, uniqueness, and stability of equilibria, for kinetic systems given in the form of polynomial ODEs. Such models are commonly used to describe the dynamics of nonnegative systems, with…
Computing equilibrium concentrations of molecular complexes is generally analytically intractable and requires numerical approaches. In this work we focus on the polymer-monomer level, where indivisible molecules (monomers) combine to form…
In [SIAM J. Optim., 2022], the authors introduced a new linear programming (LP) relaxation for K-means clustering. In this paper, we further investigate both theoretical and computational properties of this relaxation. As evident from our…
Bilevel linear programs (BLPs) form a class of hierarchical decision-making problems in which both the upper-level and the lower-level decision-makers, known as the leader and the follower, respectively, solve linear optimization problems.…
The Super Learner (SL) is a widely used ensemble method that combines predictions from a library of learners based on their predictive performance. Interval predictions are of considerable practical interest because they allow uncertainty…
Though deep neural networks have achieved the state of the art performance in visual classification, recent studies have shown that they are all vulnerable to the attack of adversarial examples. In this paper, we develop improved techniques…
We consider the general polynomial optimization problem $P: f^*=\min \{f(x)\,:\,x\in K\}$ where $K$ is a compact basic semi-algebraic set. We first show that the standard Lagrangian relaxation yields a lower bound as close as desired to the…
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…
Polynomial machine learning potentials (MLPs) based on polynomial rotational invariants have been systematically developed for various systems and applied to efficiently predict crystal structures. In this study, we propose a robust…
A novel numerical scheme to solve coupled systems of conservation laws is introduced. The scheme is derived based on a relaxation approach and does not require information on the Lax curves of the coupled systems, which simplifies the…
A linear programming (LP) based framework is presented for obtaining converses for finite blocklength lossy joint source-channel coding problems. The framework applies for any loss criterion, generalizes certain previously known converses,…
Deployment of neural networks on resource-constrained devices demands models that are both compact and robust to adversarial inputs. However, compression and adversarial robustness often conflict. In this work, we introduce a dynamical…
A full equilibrium treatment of molecular aggregation is presented for prototypes of 1D and 3D aggregates, with and without nucleation. By skipping complex kinetic parameters like aggregate size-dependent diffusion, the equilibrium…