Efficient Bayesian Inference for Learning in the Ising Linear Perceptron and Signal Detection in CDMA

Efficient new Bayesian inference technique is employed for studying critical properties of the Ising linear perceptron and for signal detection in Code Division Multiple Access (CDMA). The approach is based on a recently introduced message passing technique for densely connected systems. Here we study both critical and non-critical regimes. Results obtained in the non-critical regime give rise to a highly efficient signal detection algorithm in the context of CDMA; while in the critical regime one observes a first order transition line that ends in a continuous phase transition point. Finite size effects are also studied.Comment: 11 pages, 3 figure

Genetic algorithms for discovery of matrix multiplication methods

We present a parallel genetic algorithm for nding matrix multiplication algo-rithms. For 3 x 3 matrices our genetic algorithm successfully discovered algo-rithms requiring 23 multiplications, which are equivalent to the currently best known human-developed algorithms. We also studied the cases with less mul-tiplications and evaluated the suitability of the methods discovered. Although our evolutionary method did not reach the theoretical lower bound it led to an approximate solution for 22 multiplications

Compression by replication

A recently introduced inference method based on system replication and an online message passing algorithm is employed to complete a previously suggested compression scheme based on a nonlinear perceptron. The algorithm is shown to approach the information theoretical bounds for compression as the number of replicated systems increases, offering superior performance compared to basic message passing algorithms. In addition, the suggested method does not require fine-tuning of parameters or other complementing heuristic techniques, such as the introduction of inertia terms, to improve convergence rates to nontrivial results

Inference by replication in densely connected systems

An efficient Bayesian inference method for problems that can be mapped onto dense graphs is presented. The approach is based on message passing where messages are averaged over a large number of replicated variable systems exposed to the same evidential nodes. An assumption about the symmetry of the solutions is required for carrying out the averages; here we extend the previous derivation based on a replica symmetric (RS) like structure to include a more complex one-step replica symmetry breaking (1RSB)-like ansatz. To demonstrate the potential of the approach it is employed for studying critical properties of the Ising linear perceptron and for multiuser detection in Code Division Multiple Access (CDMA) under different noise models. Results obtained under the RS assumption in the non-critical regime give rise to a highly efficient signal detection algorithm in the context of CDMA; while in the critical regime one observes a first order transition line that ends in a continuous phase transition point. Finite size effects are also observed. While the 1RSB ansatz is not required for the original problems, it was applied to the CDMA signal detection problem with a more complex noise model that exhibits RSB behaviour, resulting in an improvement in performance.Comment: 47 pages, 7 figure

Replication-based inference algorithms for hard computational problems

Inference algorithms based on evolving interactions between replicated solutions are introduced and analyzed on a prototypical NP-hard problem: the capacity of the binary Ising perceptron. The efficiency of the algorithm is examined numerically against that of the parallel tempering algorithm, showing improved performance in terms of the results obtained, computing requirements and simplicity of implementation. © 2013 American Physical Society