Statistical mechanics of lossy compression for non-monotonic multilayer perceptrons

A lossy data compression scheme for uniformly biased Boolean messages is investigated via statistical mechanics techniques. We utilize tree-like committee machine (committee tree) and tree-like parity machine (parity tree) whose transfer functions are non-monotonic. The scheme performance at the infinite code length limit is analyzed using the replica method. Both committee and parity treelike networks are shown to saturate the Shannon bound. The AT stability of the Replica Symmetric solution is analyzed, and the tuning of the non-monotonic transfer function is also discussed.Comment: 29 pages, 7 figure

Error correcting code using tree-like multilayer perceptron

An error correcting code using a tree-like multilayer perceptron is proposed. An original message \mbi{s}^0 is encoded into a codeword \boldmath{y}_0 using a tree-like committee machine (committee tree) or a tree-like parity machine (parity tree). Based on these architectures, several schemes featuring monotonic or non-monotonic units are introduced. The codeword \mbi{y}_0 is then transmitted via a Binary Asymmetric Channel (BAC) where it is corrupted by noise. The analytical performance of these schemes is investigated using the replica method of statistical mechanics. Under some specific conditions, some of the proposed schemes are shown to saturate the Shannon bound at the infinite codeword length limit. The influence of the monotonicity of the units on the performance is also discussed.Comment: 23 pages, 3 figures, Content has been extended and revise

Statistical mechanics of lossy compression using multilayer perceptrons

Statistical mechanics is applied to lossy compression using multilayer perceptrons for unbiased Boolean messages. We utilize a tree-like committee machine (committee tree) and tree-like parity machine (parity tree) whose transfer functions are monotonic. For compression using committee tree, a lower bound of achievable distortion becomes small as the number of hidden units K increases. However, it cannot reach the Shannon bound even where K -> infty. For a compression using a parity tree with K >= 2 hidden units, the rate distortion function, which is known as the theoretical limit for compression, is derived where the code length becomes infinity.Comment: 12 pages, 5 figure

Belief Propagation for Error Correcting Codes and Lossy Compression Using Multilayer Perceptrons

The belief propagation (BP) based algorithm is investigated as a potential decoder for both of error correcting codes and lossy compression, which are based on non-monotonic tree-like multilayer perceptron encoders. We discuss that whether the BP can give practical algorithms or not in these schemes. The BP implementations in those kind of fully connected networks unfortunately shows strong limitation, while the theoretical results seems a bit promising. Instead, it reveals it might have a rich and complex structure of the solution space via the BP-based algorithms.Comment: 18 pages, 18 figure

Computational capabilities of multilayer committee machines

We obtained an analytical expression for the computational complexity of many layered committee machines with a finite number of hidden layers (L < 8) using the generalization complexity measure introduced by Franco et al (2006) IEEE Trans. Neural Netw. 17 578. Although our result is valid in the large-size limit and for an overlap synaptic matrix that is ultrametric, it provides a useful tool for inferring the appropriate architecture a network must have to reproduce an arbitrary realizable Boolean function

Analysis of Mismatched Estimation Errors Using Gradients of Partition Functions

We consider the problem of signal estimation (denoising) from a statistical-mechanical perspective, in continuation to a recent work on the analysis of mean-square error (MSE) estimation using a direct relationship between optimum estimation and certain partition functions. The paper consists of essentially two parts. In the first part, using the aforementioned relationship, we derive single-letter expressions of the mismatched MSE of a codeword (from a randomly selected code), corrupted by a Gaussian vector channel. In the second part, we provide several examples to demonstrate phase transitions in the behavior of the MSE. These examples enable us to understand more deeply and to gather intuition regarding the roles of the real and the mismatched probability measures in creating these phase transitions.Comment: 58 pages;Submitted to IEEE Trans. on Information Theor

Technology Directions for the 21st Century

The Office of Space Communications (OSC) is tasked by NASA to conduct a planning process to meet NASA's science mission and other communications and data processing requirements. A set of technology trend studies was undertaken by Science Applications International Corporation (SAIC) for OSC to identify quantitative data that can be used to predict performance of electronic equipment in the future to assist in the planning process. Only commercially available, off-the-shelf technology was included. For each technology area considered, the current state of the technology is discussed, future applications that could benefit from use of the technology are identified, and likely future developments of the technology are described. The impact of each technology area on NASA operations is presented together with a discussion of the feasibility and risk associated with its development. An approximate timeline is given for the next 15 to 25 years to indicate the anticipated evolution of capabilities within each of the technology areas considered. This volume contains four chapters: one each on technology trends for database systems, computer software, neural and fuzzy systems, and artificial intelligence. The principal study results are summarized at the beginning of each chapter

Self-organising maps : statistical analysis, treatment and applications.

This thesis presents some substantial theoretical analyses and optimal treatments of Kohonen's self-organising map (SOM) algorithm, and explores the practical application potential of the algorithm for vector quantisation, pattern classification, and image processing. It consists of two major parts. In the first part, the SOM algorithm is investigated and analysed from a statistical viewpoint. The proof of its universal convergence for any dimensionality is obtained using a novel and extended form of the Central Limit Theorem. Its feature space is shown to be an approximate multivariate Gaussian process, which will eventually converge and form a mapping, which minimises the mean-square distortion between the feature and input spaces. The diminishing effect of the initial states and implicit effects of the learning rate and neighbourhood function on its convergence and ordering are analysed and discussed. Distinct and meaningful definitions, and associated measures, of its ordering are presented in relation to map's fault-tolerance. The SOM algorithm is further enhanced by incorporating a proposed constraint, or Bayesian modification, in order to achieve optimal vector quantisation or pattern classification. The second part of this thesis addresses the task of unsupervised texture-image segmentation by means of SOM networks and model-based descriptions. A brief review of texture analysis in terms of definitions, perceptions, and approaches is given. Markov random field model-based approaches are discussed in detail. Arising from this a hierarchical self-organised segmentation structure, which consists of a local MRF parameter estimator, a SOM network, and a simple voting layer, is proposed and is shown, by theoretical analysis and practical experiment, to achieve a maximum likelihood or maximum a posteriori segmentation. A fast, simple, but efficient boundary relaxation algorithm is proposed as a post-processor to further refine the resulting segmentation. The class number validation problem in a fully unsupervised segmentation is approached by a classical, simple, and on-line minimum mean-square-error method. Experimental results indicate that this method is very efficient for texture segmentation problems. The thesis concludes with some suggestions for further work on SOM neural networks