Related papers: Renormalization Group Approach To Error-Correcting…
Group zero-attracting LMS and its reweighted form have been proposed for addressing system identification problems with structural group sparsity in the parameters to estimate. Both algorithms however suffer from a trade-off between…
A Monte Carlo Renormalization Group algorithm is used on the Ising model to derive critical exponents and the critical temperature. The algorithm is based on a minimum relative entropy iteration developed previously to derive potentials…
Batch Normalization (BN) is a milestone technique in the development of deep learning, enabling various networks to train. However, normalizing along the batch dimension introduces problems --- BN's error increases rapidly when the batch…
We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena…
We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of pQCD predictions, exposes the general pattern of…
Quantum low-density parity-check codes are promising candidates for low-overhead fault-tolerant quantum computing, but degeneracy is known to impair the convergence of belief-propagation (BP) decoding of these codes. In this work, we show…
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…
An exact solution to a family of parity check error-correcting codes is provided by mapping the problem onto a Husimi cactus. The solution obtained in the thermodynamic limit recovers the replica symmetric theory results and provides a very…
This paper provides a block coordinate descent algorithm to solve unconstrained optimization problems. In our algorithm, computation of function values or gradients is not required. Instead, pairwise comparison of function values is used.…
The performance of an error correcting code is evaluated by its error probability, rate, and en/decoding complexity. The performance of a series of codes is evaluated by, as the block lengths approach infinity, whether their error…
Property testing has been a major area of research in computer science in the last three decades. By property testing we refer to an ensemble of problems, results and algorithms which enable to deduce global information about some data by…
We propose a renormalization group (RG) approach to compare and collapse eigenvalue densities of random matrix models of complex systems across different system sizes. The approach is to fix a natural spectral scale by letting the model…
We present sparse graph codes appropriate for use in quantum error-correction. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based…
The normalized min-sum algorithm can achieve near-optimal performance at decoding LDPC codes. However, it is a critical question to understand the mathematical principle underlying the algorithm. Traditionally, people thought that the…
In this paper we have considered a finite unitary matrix group with exact elements being unknown and only approximate elements available. Such a group becomes inconsistent with its own multiplication table. We found simple correction…
We present a numerical implementation of the renormalization group (RG) for partial differential equations, constructing similarity solutions and travelling waves. We show that for a large class of well-localized initial conditions,…
Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical…
We present a renormalization group (RG) procedure which works naturally on a wide class of interacting one-dimension models based on perturbed (possibly strongly) continuum conformal and integrable models. This procedure integrates Kenneth…
The bit-wise unequal error protection problem, for the case when the number of groups of bits $\ell$ is fixed, is considered for variable length block codes with feedback. An encoding scheme based on fixed length block codes with erasures…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…