Related papers: Low Correlation Sequences from Linear Combinations…
Embedding models for entities and relations are extremely useful for recovering missing facts in a knowledge base. Intuitively, a relation can be modeled by a matrix mapping entity vectors. However, relations reside on low dimension…
Motivated by the constructions of binary sequences by utilizing the cyclic elliptic function fields over the finite field $\mathbb{F}_{2^{n}}$ by Jin \textit{et al.} in [IEEE Trans. Inf. Theory 71(8), 2025], we extend the construction to…
We calculate within a semiclassical approximation the autocorrelation function of cross sections. The starting point is the semiclassical expression for the diagonal matrix elements of an operator. For general operators with a smooth…
We compute the auto-correlations functions of order $m\ge 1$ for the characteristic polynomials of random matrices from certain subgroups of the unitary groups $\U(2)$ and $\U(3)$ by applying branching rules. These subgroups can be…
Asymptotic concentration behaviors of linear combinations of weight distributions on the random linear code ensemble are presented. Many important properties of a binary linear code can be expressed as the form of a linear combination of…
Causal representation learning seeks to uncover causal relationships among high-level latent variables from low-level, entangled, and noisy observations. Existing approaches often either rely on deep neural networks, which lack…
Using the construction by Bencs and T\'{o}th of invariant random subgroups on weakly branch groups acting on regular rooted trees we produce uncountably many indecomposable characters on these groups. In fact, we study three types of…
A pseudorandom number generator is widely used in cryptography. A cryptographic pseudorandom number generator is required to generate pseudorandom numbers which have good statistical properties as well as unpredictability. An m-sequence is…
A generic uniformly distributed random sequence on the unit interval has Poissonian pair correlations. At the same time, there are only very few explicitly known examples of sequences with this property. Moreover, many types of…
We study sets of recurrence, in both measurable and topological settings, for actions of $(\mathbb{N},\times)$ and $(\mathbb{Q}^{>0},\times)$. In particular, we show that autocorrelation sequences of positive functions arising from…
This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error…
In this article, $q$-regular sequences in the sense of Allouche and Shallit are analysed asymptotically. It is shown that the summatory function of a regular sequence can asymptotically be decomposed as a finite sum of periodic fluctuations…
Sequence generation applications require satisfying semantic constraints, such as ensuring that programs are correct, using certain keywords, or avoiding undesirable content. Language models, whether fine-tuned or prompted with few-shot…
We analyze the signum-generation method for creating random dichotomic sequences with prescribed correlation properties. The method is based on a binary mapping of the convolution of continuous random numbers with some function originated…
Correlation measure of order $k$ is an important measure of randomness in binary sequences. This measure tries to look for dependence between several shifted version of a sequence. We study the relation between the correlation measure of…
In recent years, complementary sequence sets have found many important applications in multi-carrier code-division multiple-access (MC-CDMA) systems for their good correlation properties. In this paper, we propose a construction, which can…
By controlling synaptic and neural correlations, deep learning has achieved empirical successes in improving classification performances. How synaptic correlations affect neural correlations to produce disentangled hidden representations…
A repetition free Longest Common Subsequence (LCS) of two sequences x and y is an LCS of x and y where each symbol may appear at most once. Let R denote the length of a repetition free LCS of two sequences of n symbols each one chosen…
We study the structure of multiple correlation sequences defined by measure preserving actions of commuting transformations. When the iterates of the transformations are integer polynomials we prove that any such correlation sequence is the…
Recent research has revealed that machine learning models have a tendency to leverage spurious correlations that exist in the training set but may not hold true in general circumstances. For instance, a sentiment classifier may erroneously…