Related papers: Fully Lattice-Linear Algorithms
This paper provides the theoretical foundation for the construction of lattice algorithms for multivariate $L_2$ approximation in the worst case setting, for functions in a periodic space with general weight parameters. Our construction…
In a multi-task learning (MTL) setting, a single model is trained to tackle a diverse set of tasks jointly. Despite rapid progress in the field, MTL remains challenging due to optimization issues such as conflicting and dominating…
We consider the classical Minimum Balanced Cut problem: given a graph $G$, compute a partition of its vertices into two subsets of roughly equal volume, while minimizing the number of edges connecting the subsets. We present the first {\em…
In the era of big data, one of the key challenges is the development of novel optimization algorithms that can accommodate vast amounts of data while at the same time satisfying constraints and limitations of the problem under study. The…
Vector clock algorithms are basic wait-free building blocks that facilitate causal ordering of events. As wait-free algorithms, they are guaranteed to complete their operations within a finite number of steps. Stabilizing algorithms allow…
As software systems become more complex, there is an increasing need for new static analyses. Thanks to the declarative style, logic programming is an attractive formalism for specifying them. However, prior work on using logic programming…
Defect-adaptive surface-code methods have substantially advanced the construction of valid logical patches on imperfect hardware, but fault-tolerant computation also requires executable logical oper ations on the resulting irregular…
In the context of formal verification in general and model checking in particular, parity games serve as a mighty vehicle: many problems are encoded as parity games, which are then solved by the seminal algorithm by Jurdzinski. In this…
Sparse linear regression (SLR) is a well-studied problem in statistics where one is given a design matrix $X\in\mathbb{R}^{m\times n}$ and a response vector $y=X\theta^*+w$ for a $k$-sparse vector $\theta^*$ (that is, $\|\theta^*\|_0\leq…
The paper investigates the problem of estimating the state of a time-varying system with a linear measurement model; in particular, the paper considers the case where the number of measurements available can be smaller than the number of…
Model merging offers an effective strategy to combine the strengths of multiple finetuned models into a unified model that preserves the specialized capabilities of each. Existing methods merge models in a global manner, performing…
Since the invention of the famous LLL algorithm, lattice reduction has been an extremely useful tool in computational number theory. By construction, the LLL algorithm deals with lattices living in a vector space endowed with a positive…
Randomized algorithms for very large matrix problems have received a great deal of attention in recent years. Much of this work was motivated by problems in large-scale data analysis, and this work was performed by individuals from many…
This survey article is concerned with the application of lattice rules to Deep Neural Networks (DNNs), lattice rules being a family of quasi-Monte Carlo methods. They have demonstrated effectiveness in various contexts for high-dimensional…
We describe algorithms which address two classical problems in lattice geometry: the lattice covering and the simultaneous lattice packing-covering problem. Theoretically our algorithms solve the two problems in any fixed dimension d in the…
This paper investigates two issues on identification of switched linear systems: persistence of excitation and numerical algorithms. The main contribution is a much weaker condition on the regressor to be persistently exciting that…
Lattice Boltzmann schemes rely on the enlargement of the size of the target problem in order to solve PDEs in a highly parallelizable and efficient kinetic-like fashion, split into a collision and a stream phase. This structure, despite the…
We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors are boundably short. For…
This study presents a novel deterministic optimization algorithm based on a special variant of the Linear Congruential Generator (LCG). While conventional algorithms generally operate within the search space, the introduced technique…
Large language models (LLMs) deployed on edge servers are increasingly used in latency-sensitive applications such as personalized assistants, recommendation, and content moderation. However, the non-stationary nature of user data…