Related papers: Low coordinate degree algorithms I: Universality o…
In this letter, we develop an efficient linear programming (LP) decoding algorithm for low-density parity-check (LDPC) codes. We first relax the maximum likelihood (ML) decoding problem to a LP problem by using check-node decomposition.…
The universal approximation theorem, in one of its most general versions, says that if we consider only continuous activation functions $\sigma$, then a standard feedforward neural network with one hidden layer is able to approximate any…
We present a complete theoretical characterization of Latent Posterior Factors (LPF), a principled framework for aggregating multiple heterogeneous evidence items in probabilistic prediction tasks. Multi-evidence reasoning arises…
Quantum low-density parity-check (QLDPC) codes with asymptotically non-zero rates are prominent candidates for achieving fault-tolerant quantum computation, primarily due to their syndrome-measurement circuit's low operational depth.…
A distinctive representation of image patches in form of features is a key component of many computer vision and robotics tasks, such as image matching, image retrieval, and visual localization. State-of-the-art descriptors, from…
We consider neural networks with a single hidden layer and non-decreasing homogeneous activa-tion functions like the rectified linear units. By letting the number of hidden units grow unbounded and using classical non-Euclidean…
Future beyond-5G and 6G systems demand ultra-reliable, low-latency communication with short blocklengths, motivating the development of universal decoding algorithms. Guessing decoding, which infers the noise or codeword candidate in order…
Federated learning (FL), as a type of collaborative machine learning framework, is capable of preserving private data from mobile terminals (MTs) while training the data into useful models. Nevertheless, from a viewpoint of information…
This paper addresses hypothesis testing for the mean of matrix-valued data in high-dimensional settings. We investigate the minimum discrepancy test, originally proposed by Cragg (1997), which serves as a rank test for lower-dimensional…
Multiphase ranking functions ($\mathit{M{\Phi}RFs}$) were proposed as a means to prove the termination of a loop in which the computation progresses through a number of "phases", and the progress of each phase is described by a different…
We investigate the use of Gallager's low-density parity-check (LDPC) codes in a broadcast channel, one of the fundamental models in network information theory. Combining linear codes is a standard technique in practical network…
We extend the method of Ghasemi and Marshall [SIAM. J. Opt. 22(2) (2012), pp 460-473], to obtain a lower bound $f_{{\rm gp},M}$ for a multivariate polynomial $f(x) \in \mathbb{R}[x]$ of degree $ \le 2d$ in $n$ variables $x = (x_1,...,x_n)$…
Low-density parity-check (LDPC) codes together with belief propagation (BP) decoding yield exceptional error correction capabilities in the large block length regime. Yet, there remains a gap between BP decoding and maximum likelihood…
Representations of Boolean functions by real polynomials play an important role in complexity theory. Typically, one is interested in the least degree of a polynomial p(x_1,...,x_n) that approximates or sign-represents a given Boolean…
Low Rank Approximation is among most fundamental subjects of numerical linear algebra having important applications to various areas of modern computing and %they range from machine learning theory and %neural networks to data mining and…
We design new polynomials for representing threshold functions in three different regimes: probabilistic polynomials of low degree, which need far less randomness than previous constructions, polynomial threshold functions (PTFs) with…
We propose a theoretical framework to analyze semi-supervised classification under the low density separation assumption in a high-dimensional regime. In particular, we introduce QLDS, a linear classification model, where the low density…
This paper provides the theoretical foundation for the construction of lattice algorithms for multivariate $L_2$ approximation in the worst case setting, for functions in a periodic space with general weight parameters. Our construction…
A fundamental component of neural network verification is the computation of bounds on the values their outputs can take. Previous methods have either used off-the-shelf solvers, discarding the problem structure, or relaxed the problem even…
In this work, inspired by the study of semidefinite programming for block-diagonalizing matrix *-algebras, we propose an algorithm that can find the algebraic structure of decoherence-free subspaces (DFS's) for a given noisy quantum…