Related papers: About Code Equivalence -- a Geometric Approach
We present simple, self-contained proofs of correctness for algorithms for linearity testing and program checking of linear functions on finite subsets of integers represented as n-bit numbers. In addition we explore a generalization of…
LLMs have been extensively used for the task of automated code generation. In this work, we examine the applicability of LLMs for the related but relatively unexplored task of code-equivalence checking, i.e., given two programs, whether…
Embedders play a central role in machine learning, projecting any object into numerical representations that can, in turn, be leveraged to perform various downstream tasks. The evaluation of embedding models typically depends on…
Mapping political party systems to metric policy spaces is one of the major methodological problems in political science. At present, in most political science project this task is performed by domain experts relying on purely qualitative…
AI-assisted coding has rapidly reshaped software practice and research workflows, yet today's models still struggle to produce correct code for complex 3D geometric vision. If models could reliably write such code, the research of our…
Quantum computing will change the way we tackle certain problems. It promises to dramatically speed-up many chemical, financial, and machine-learning applications. However, to capitalize on those promises, complex design flows composed of…
Let A, B, C, D be given finite sets of pairs of n-by-n complex matrices. We describe an algorithm to determine, with finitely many computations, whether there is a single unitary matrix U such that each pair of matrices in A is unitarily…
We investigate how to determine whether the states of a set of quantum systems are identical or not. This paper treats both error-free comparison, and comparison where errors in the result are allowed. Error-free comparison means that we…
We study the classification of ultrametric spaces based on their small scale geometry (uniform homeomorphism), large scale geometry (coarse equivalence) and both (all scale uniform equivalences). We prove that these equivalences can be…
The offset method for solving word analogies has become a standard evaluation tool for vector-space semantic models: it is considered desirable for a space to represent semantic relations as consistent vector offsets. We show that the…
We describe an approach to the question of finding real solutions to problems of enumerative geometry, in particular the question of whether a problem of enumerative geometry can have all of its solutions be real. We give some methods to…
We consider the popular and classical method of alternating projections for finding a point in the intersection of two closed sets. By situating the algorithm in a metric space, equipped only with well-behaved geodesics and angles (in the…
Analogs of Reed-Solomon codes are introduced within the framework of bottleneck poset metrics. These codes are proven to be maximum distance separable. Furthermore, the results are extended to the setting of Algebraic Geometry codes.
The quantum equivalence principle says that, for any given point, it is possible to find a quantum coordinate system with respect to which we have definite causal structure in the vicinity of that point. It is conjectured that this…
A personalized learning system needs a large pool of items for learners to solve. When working with a large pool of items, it is useful to measure the similarity of items. We outline a general approach to measuring the similarity of items…
Secure computation of equivalence has fundamental application in many different areas, including healthcare. We study this problem in the context of matching an individual identity to link medical records across systems. We develop an…
Testing whether a probability distribution is compatible with a given Bayesian network is a fundamental task in the field of causal inference, where Bayesian networks model causal relations. Here we consider the class of causal structures…
In most computer vision and image analysis problems, it is necessary to define a similarity measure between two or more different objects or images. Template matching is a classic and fundamental method used to score similarities between…
The selection of the best classification algorithm for a given dataset is a very widespread problem. It is also a complex one, in the sense it requires to make several important methodological choices. Among them, in this work we focus on…
We address the problem of finding harmonic colors, this problem has many applications, from fashion to industrial design. In order to solve this problem we consider that colors follow normal distributions in tone (chroma and lightness) and…