Related papers: A linear transformation to accelerate the converge…
We consider the problem of sequencing a set of positive numbers. We try to find the optimal sequence to maximize the variance of its partial sums. The optimal sequence is shown to have a beautiful structure. It is interesting to note that…
Convolutional neural networks (CNNs) have enabled the state-of-the-art performance in many computer vision tasks. However, little effort has been devoted to establishing convolution in non-linear space. Existing works mainly leverage on the…
This paper is devoted to investigating the sequence of some linear functionals in the space $BV$ of finite variation functions. We prove that under certain conditions this sequence is bounded. We also prove that this result is sharp. In…
Sequence classification is the task of predicting a class label given a sequence of observations. In many applications such as healthcare monitoring or intrusion detection, early classification is crucial to prompt intervention. In this…
The kernel estimator is known not to be adequate for estimating the density of a positive random variable X. The main reason is the well-known boundary bias problems that it suffers from, but also its poor behaviour in the long right tail…
Transfer learning seeks to improve the generalization performance of a target task by exploiting the knowledge learned from a related source task. Central questions include deciding what information one should transfer and when transfer can…
The transformer is a powerful data modelling framework responsible for remarkable performance on a wide range of tasks. However, they are limited in terms of scalability as it is suboptimal and inefficient to process long-sequence data. To…
We give an explicit formula for the Hankel transform of a regular sequence in terms of the coefficients of the associated orthogonal polynomials and the sequence itself. We apply this formula to some sequences of combinatorial interest,…
A classical theorem of Kempner states that the sum of the reciprocals of positive integers with missing decimal digits converges. This result is extended to much larger families of "missing digits" sets of positive integers with convergent…
We consider the problem of directly optimizing a non-linear function of an outcome, where this outcome itself is the sum of many small contributions. The non-linearity of the function means that the problem is not equivalent to the…
Since its introduction, the transformer has shifted the development trajectory away from traditional models (e.g., RNN, MLP) in time series forecasting, which is attributed to its ability to capture global dependencies within temporal…
Domain adaptation refers to the process of learning prediction models in a target domain by making use of data from a source domain. Many classic methods solve the domain adaptation problem by establishing a common latent space, which may…
A classification algorithm, called the Linear Centralization Classifier (LCC), is introduced. The algorithm seeks to find a transformation that best maps instances from the feature space to a space where they concentrate towards the center…
Sequence rotation consists of a circular shift of the sequence's elements by a given number of positions. We present the four classic algorithms to rotate a sequence; the loop invariants underlying their correctness; detailed correctness…
The differential transform method is used to find numerical approximation of solution to a class of certain nonlinear differential algebraic equations. The method is based on Taylor's theorem. Coefficients of the Taylor series are…
The task of linearization is to find a grammatical order given a set of words. Traditional models use statistical methods. Syntactic linearization systems, which generate a sentence along with its syntactic tree, have shown state-of-the-art…
Transformers have become the dominant architecture for sequence modeling tasks such as natural language processing or audio processing, and they are now even considered for tasks that are not naturally sequential such as image…
In this paper, we introduce a new class of positive linear operators that generalize the classical Bernstein operators. Specifically, we construct a sequence of operators that reproduce the logarithmic function $\ln(1+\mu+x)$, with $\mu >…
In this paper, the compact linearization approach originally proposed for binary quadratic programs with assignment constraints is generalized to such programs with arbitrary linear equations and inequalities that have positive coefficients…
Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL…