Related papers: Constituent automorphism decoding of Reed-Muller c…
We give an algorithm that learns a representation of data through compression. The algorithm 1) predicts bits sequentially from those previously seen and 2) has a structure and a number of computations similar to an autoencoder. The…
Decoding stimulus images from fMRI signals has advanced with pre-trained generative models. However, existing methods struggle with cross-subject mappings due to cognitive variability and subject-specific differences. This challenge arises…
Recursive projection aggregation (RPA) decoding as introduced in [1] is a novel decoding algorithm which performs close to the maximum likelihood decoder for short-length Reed-Muller codes. Recently, an extension to RPA decoding, called…
Autoencoding is a popular method in representation learning. Conventional autoencoders employ symmetric encoding-decoding procedures and a simple Euclidean latent space to detect hidden low-dimensional structures in an unsupervised way.…
Decoding cognitive states from functional magnetic resonance imaging is central to understanding the functional organization of the brain. Within-subject decoding avoids between-subject correspondence problems but requires large sample…
Interleaved Reed-Solomon codes admit efficient decoding algorithms which correct burst errors far beyond half the minimum distance in the random errors regime, e.g., by computing a common solution to the Key Equation for each Reed-Solomon…
Last years a number of papers were devoted to describing automorphisms of semigroups of endomorphisms of free finitely generated universal algebras of some varieties: groups, semigroups, associative commutative algebras, inverse semigroups,…
We introduce FAEclust, a novel functional autoencoder framework for cluster analysis of multi-dimensional functional data, data that are random realizations of vector-valued random functions. Our framework features a universal-approximator…
Machine learning on trees has been mostly focused on trees as input to algorithms. Much less research has investigated trees as output, which has many applications, such as molecule optimization for drug discovery, or hint generation for…
A rapidly growing area of research is the use of machine learning approaches such as autoencoders for dimensionality reduction of data and models in scientific applications. We show that the canonical formulation of autoencoders suffers…
We study the subfield subcodes of projective Reed-Solomon codes and their duals: we provide bases for these codes and estimate their parameters. With this knowledge, we can construct symmetric and asymmetric entanglement-assisted quantum…
In the present work we propose an unsupervised ensemble method consisting of oblique trees that can address the task of auto-encoding, namely Oblique Forest AutoEncoders (briefly OF-AE). Our method is a natural extension of the eForest…
The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a…
A combinatorial code $\mathcal{C}$ is a collection of subsets of $[n]$, or equivalently a set of points in $\{0,1\}^n$. A morphism of codes is a map from one combinatorial code to another such that the coordinates of points in the image can…
We decode Reed-Solomon codes using soft information provided at the receiver. The Extended Euclidean Algorithm (EEA) is considered as an initial step to obtain an intermediate result. The final decoding result is obtained by interpolating…
Learning in the latent variable model is challenging in the presence of the complex data structure or the intractable latent variable. Previous variational autoencoders can be low effective due to the straightforward encoder-decoder…
Cooperative constraint solving is an area of constraint programming that studies the interaction between constraint solvers with the aim of discovering the interaction patterns that amplify the positive qualities of individual solvers.…
Interpretable machine learning is rapidly becoming a crucial tool for scientific discovery. Among existing approaches, variational autoencoders (VAEs) have shown promise in extracting the hidden physical features of some input data, with no…
We design algorithms for Robust Principal Component Analysis (RPCA) which consists in decomposing a matrix into the sum of a low rank matrix and a sparse matrix. We propose a deep unrolled algorithm based on an accelerated alternating…
Soft materials play an integral part in many aspects of modern life including autonomy, sustainability, and human health, and their accurate modeling is critical to understand their unique properties and functions. Today's finite element…