Related papers: A Correction Note: Attractive Nearest Neighbor Spi…

Probabilistic Inference Modulo Theories (PIMT) is a recent framework that expands exact inference on graphical models to use richer languages that include arithmetic, equalities, and inequalities on both integers and real numbers. In this…

We propose a general proximal algorithm for the inversion of ill-conditioned matrices. This algorithm is based on a variational characterization of pseudo-inverses. We show that a particular instance of it (with constant regularization…

An integrable Heisenberg spin chain with nearest-neighbour couplings, next-nearest-neighbour couplings and Dzyaloshinski-Moriya interacton is constructed. The integrability of the model is proven. Based on the Bethe Ansatz solutions, the…

We explore an algorithm for approximating roots of integers, discuss its motivation and derivation, and analyze its convergence rates with varying parameters and inputs. We also perform comparisons with established methods for approximating…

Some unfortunate errors from our paper math/0505591 are corrected.

We introduce $k$-nearest-neighbor machine translation ($k$NN-MT), which predicts tokens with a nearest neighbor classifier over a large datastore of cached examples, using representations from a neural translation model for similarity…

We study S=1/2 quantum spin chains with shift-invariant and inversion-symmetric next-nearest-neighbor interaction, also known as zigzag spin chains. We completely classify the integrability and non-integrability of the above class of spin…

We study the propagation of gauge fields with arbitrary integer spins in the symmetrical Einstein space of any dimensionality. We reduce the problem of obtaining a gauge-invariant Lagrangian of integer spin fields in such background to an…

Neural machine translation has achieved promising results on many translation tasks. However, previous studies have shown that neural models induce a non-smooth representation space, which harms its generalization results. Recently, kNN-MT…

In this paper we consider four competing interactions (external field, nearest neighbor, second neighbors and triples of neighbors) of models with uncountable (i.e. $[0,1]$) set of spin values on the Cayley tree of order two. We reduce the…

The aim of this paper is to correct a mistake in earlier work on the conformal invariance of Rarita-Schwinger operators and use the method of correction to develop properties of some conformally invariant operators in the Rarita-Schwinger…

The emergence of similar representations between independently trained neural models has sparked significant interest in the representation learning community, leading to the development of various methods to obtain communication between…

Let M be an oriented compact 3-manifold and let T be a (loose) triangulation of M, with ideal vertices at the components of the boundary of M and possibly internal vertices. We show that any spin structure s on M can be encoded by extra…

We compare the continuous and discrete truncated Wigner approximations of various spin models' dynamics to exact analytical and numerical solutions. We account for all components of spin-spin correlations on equal footing, facilitated by a…

While different neural models often exhibit latent spaces that are alike when exposed to semantically related data, this intrinsic similarity is not always immediately discernible. Towards a better understanding of this phenomenon, our work…

We prove a result in the area of twisted Diophantine approximation related to the theory of Schmidt games. In particular, under certain restrictions we give a affirmative answer to the analogue in this setting of a famous conjecture of…

We introduce a class of nearest-neighbor integer random walks in random and non-random media, which includes excited random walks considered in the literature. At each site the random walker has a drift to the right, the strength of which…

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

We review some recent results on quasi-exactly solvable spin models presenting near-neighbors interactions. These systems can be understood as cyclic generalizations of the usual Calogero-Sutherland models. A nontrivial modification of the…

In this contribution we briefly review recent developments in the theory of long-range integrable spin chains. These spin chains constitute a natural generalisation of the well-studied integrable nearest-neighbour chains and are of…