Related papers: Constituent automorphism decoding of Reed-Muller c…
Recurrence plots were introduced to help aid the detection of signals in complicated data series. This effort was furthered by the quantification of recurrence plot elements. We now demonstrate the utility of combining recurrence…
The paper has been withdrawn since more effective experiments should be completed. Auto-encoders (AE) has been widely applied in different fields of machine learning. However, as a deep model, there are a large amount of learnable…
We present and evaluate a technique for computing path-sensitive interference conditions during abstract interpretation of concurrent programs. In lieu of fixed point computation, we use prime event structures to compactly represent causal…
This paper presents a novel and efficient method for characteristic mode decomposition in multi-structure systems. By leveraging the translation and rotation matrices of vector spherical wavefunctions, our approach enables the synthesis of…
Algebraic decoding algorithms are commonly applied for the decoding of Reed-Solomon codes. Their main advantages are low computational complexity and predictable decoding capabilities. Many algorithms can be extended for correction of both…
In developing data-driven modeling methodologies, there is an ongoing need to reconcile the strong predictive performance of opaque black-box models with the transparency required for critical applications. This work introduces an…
We study the interaction between two structures on the group of polynomial automorphisms of the affine plane: its structure as an amalgamated free product and as an infinite-dimensional algebraic variety. We introduce a new conjecture, and…
Dictionary learning and component analysis models are fundamental for learning compact representations that are relevant to a given task (feature extraction, dimensionality reduction, denoising, etc.). The model complexity is encoded by…
The main computational steps in algebraic soft-decoding, as well as Sudan-type list-decoding, of Reed-Solomon codes are bivariate polynomial interpolation and factorization. We introduce a computational technique, based upon re-encoding and…
We propose Recognition as Part Composition (RPC), an image encoding approach inspired by human cognition. It is based on the cognitive theory that humans recognize complex objects by components, and that they build a small compact…
Though modern neural networks have achieved impressive performance in both vision and language tasks, we know little about the functions that they implement. One possibility is that neural networks implicitly break down complex tasks into…
The DEDICOM algorithm provides a uniquely interpretable matrix factorization method for symmetric and asymmetric square matrices. We employ a new row-stochastic variation of DEDICOM on the pointwise mutual information matrices of text…
A new look on the principal component analysis has been presented. Firstly, a geometric interpretation of determination coefficient was shown. In turn, the ability to represent the analyzed data and their interdependencies in the form of…
Analyzing and visualizing scientific ensemble datasets with high dimensionality and complexity poses significant challenges. Dimensionality reduction techniques and autoencoders are powerful tools for extracting features, but they often…
Simulations of large-scale dynamical systems require expensive computations. Low-dimensional parametrization of high-dimensional states such as Proper Orthogonal Decomposition (POD) can be a solution to lessen the burdens by providing a…
We discuss an autoencoder model in which the encoding and decoding functions are implemented by decision trees. We use the soft decision tree where internal nodes realize soft multivariate splits given by a gating function and the overall…
Ensemble of predictions is known to perform better than individual predictions taken separately. However, for tasks that require heavy computational resources, e.g. semantic segmentation, creating an ensemble of learners that needs to be…
We provide a comprehensive overview of the fundamental structural properties of weighted projective Reed-Muller codes. We give a recursive construction for these codes, under some conditions for the weights, and we use it to derive bounds…
We propose an easy-to-implement hard-decision majority-logic decoding algorithm for Reed-Muller codes RM(r,m) with m >= 3, m/2 >= r >= 1. The presented algorithm outperforms the best known majority-logic decoding algorithms and offers…
Modeling and controlling complex spatiotemporal dynamical systems driven by partial differential equations (PDEs) often necessitate dimensionality reduction techniques to construct lower-order models for computational efficiency. This paper…