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We prove a precise formula for the minimal number K(n) such that every binary word of length $n$ can be divided into K(n) palindromes. Also we estimate the average number $\ol K(n)$ of palindromes composing a random binary word of the…
For classification tasks, dictionary learning based methods have attracted lots of attention in recent years. One popular way to achieve this purpose is to introduce label information to generate a discriminative dictionary to represent…
This paper introduces a Bayesian framework for image inversion by deriving a probabilistic counterpart to the regularization-by-denoising (RED) paradigm. It additionally implements a Monte Carlo algorithm specifically tailored for sampling…
We present an unsupervised word segmentation model, in which the learning objective is to maximize the generation probability of a sentence given its all possible segmentation. Such generation probability can be factorized into the…
We present a type system that combines, in a controlled way, first-order polymorphism with intersectiontypes, union types, and subtyping, and prove its safety. We then define a type reconstruction algorithm that issound and terminating.…
In this paper, we investigate the combinatorial and density properties of infinite words generated by Fibonacci-type morphisms, focusing on their subword structure, palindrome density, and extremal statistical behaviors. Using the morphism…
In this paper, we propose a coupled tensor norm regularization that could enable the model output feature and the data input to lie in a low-dimensional manifold, which helps us to reduce overfitting. We show this regularization term is…
This paper is concerned with the affine-invariant ternary codes which are defined by Hermitian functions. We compute the incidence matrices of 2-designs that are supported by the minimum weight codewords of these ternary codes. The linear…
A De Bruijn cycle is a cyclic sequence in which every word of length $n$ over an alphabet $\mathcal{A}$ appears exactly once. De Bruijn tori are a two-dimensional analogue. Motivated by recent progress on universal partial cycles and words,…
In this paper, we propose an algebraic formalization of the two important classes of dynamic programming algorithms called forward and forward-backward algorithms. They are generalized extensively in this study so that a wide range of other…
In this work we explore the connections between (linear) nested sequent calculi and ordinary sequent calculi for normal and non-normal modal logics. By proposing local versions to ordinary sequent rules we obtain linear nested sequent…
We introduce a method of obtaining a higher order extension problem, \'a la Caffarelli-Silvestre, utilizing ideas from renormalization. Moreover, we give an alternative perspective of the recently developed extension problem for the…
We describe a generalization of the group testing problem termed symmetric group testing. Unlike in classical binary group testing, the roles played by the input symbols zero and one are "symmetric" while the outputs are drawn from a…
Most recent approaches to bilingual dictionary induction find a linear alignment between the word vector spaces of two languages. We show that projecting the two languages onto a third, latent space, rather than directly onto each other,…
Higher-order unification has been shown to be undecidable. Miller discovered the pattern fragment and subsequently showed that higher-order pattern unification is decidable and has most general unifiers. We extend the algorithm to…
We present a technique to study normalizing strategies when termination is asymptotic, that is, it appears as a limit, as opposite to reaching a normal form in a finite number of steps. Asymptotic termination occurs in several settings,…
Discovering a lexicon from unlabeled audio is a longstanding challenge for zero-resource speech processing. One approach is to search for frequently occurring patterns in speech. We revisit this idea with DUSTED: Discrete Unit Spoken-TErm…
Building tools for code-mixed data is rapidly gaining popularity in the NLP research community as such data is exponentially rising on social media. Working with code-mixed data contains several challenges, especially due to grammatical…
We consider a class of systems over finite alphabets, namely discrete-time systems with linear dynamics and a finite input alphabet. We formulate a notion of finite uniform bisimulation, and motivate and propose a notion of regular finite…
In this paper we present a novel Neural Network algorithm for conducting semi-supervised learning for sequence labeling tasks arranged in a linguistically motivated hierarchy. This relationship is exploited to regularise the representations…