相关论文: Standard Lattices of Compatibly Embedded Finite Fi…

We prove a characterization of profinite algebras, i.e., topological algebras that are isomorphic to a projective limit of finite discrete algebras. In general profiniteness concerns both the topological and algebraic characteristics of a…

We present a class of photonic lattices with an underlying symmetry given by a finite-dimensional representation of the 2+1D Lorentz group. In order to construct such a finite-dimensional representation of a non-compact group, we have to…

Foundation models have established unified representations for natural language processing, yet this paradigm remains largely unexplored for tabular data. Existing methods face fundamental limitations: LLM-based approaches lack…

A representation of finite fields that has proved useful when implementing finite field arithmetic in hardware is based on an isomorphism between subrings and fields. In this paper, we present an unified formulation for multiplication in…

Polynomial reconstruction on Cartesian grids is fundamental in many scientific and engineering applications, yet it is still an open problem how to construct for a finite subset $K$ of $\mathbb{Z}^{\textsf{D}}$ a lattice $\mathcal{T}\subset…

The logarithmic number system (LNS) is arguably not broadly used due to exponential circuit overheads for summation tables relative to arithmetic precision. Methods to reduce this overhead have been proposed, yet still yield designs with…

Lattice reduction is a NP-hard problem well known in computer science and cryptography. The Lenstra-Lenstra-Lovasz (LLL) algorithm based on the calculation of orthogonal Gram-Schmidt (GS) bases is efficient and gives a good solution in…

Embedding tables are usually huge in click-through rate (CTR) prediction models. To train and deploy the CTR models efficiently and economically, it is necessary to compress their embedding tables at the training stage. To this end, we…

Despite their success, Large-Language Models (LLMs) still face criticism due to their lack of interpretability. Traditional post-hoc interpretation methods, based on attention and gradient-based analysis, offer limited insights as they only…

Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforward, this approach results in integration spaces larger than…

This paper describes substantial advances in the analysis (parsing) of diagrams using constraint grammars. The addition of set types to the grammar and spatial indexing of the data make it possible to efficiently parse real diagrams of…

This report investigates enhancing semantic caching effectiveness by employing specialized, fine-tuned embedding models. Semantic caching relies on embedding similarity rather than exact key matching, presenting unique challenges in…

We study classical hard-core dimer models on three-dimensional lattices using analytical approaches and Monte Carlo simulations. On the bipartite cubic lattice, a local gauge field generalization of the height representation used on the…

Embeddings serve as condensed vector representations for real-world entities, finding applications in Natural Language Processing (NLP), Computer Vision, and Data Management across diverse downstream tasks. Here, we introduce novel…

Interpolation is a fundamental technique in scientific computing and is at the heart of many scientific visualization techniques. There is usually a trade-off between the approximation capabilities of an interpolation scheme and its…

We use the embedding formalism to construct conformal fields in $D$ dimensions, by restricting Lorentz-invariant ensembles of homogeneous neural networks in $(D+2)$ dimensions to the projective null cone. Conformal correlators may be…

The use of high-dimensional features has become a normal practice in many computer vision applications. The large dimension of these features is a limiting factor upon the number of data points which may be effectively stored and processed,…

This paper explores applications of the so-called Freese's technique, a classical approach to study the congruence variety of a given algebra. We leverage this tool to investigate lattices that are admissible as congruence sublattice of a…

The standard in LLM-based prediction is to use the final-layer representation as the input to a downstream predictor. However, intermediate layers may encode complementary task-relevant signals. Existing approaches therefore either search…

For a closure space (P,f) with f(\emptyset)=\emptyset, the closures of open subsets of P, called the regular closed subsets, form an ortholattice Reg(P,f), extending the poset Clop(P,f) of all clopen subsets. If (P,f) is a finite convex…