Antonio Luigi Perrone

Chaotic neural nets, computability, and undecidability: Toward a computational dynamics

In this article we intend to analyze a chaotic system from the standpoint of its computation capability. to pursue this aim, we refer to a complex chaotic dynamics that we characterize via its symbolic dynamics. We show that these dynamic systems are subjected to some typical undecidable problems. Particularly, we stress the impossibility of deciding on a unique invariant measure. This depends essentially on the supposition of the existence of a fixed universal grammar. the suggestion is thus of justifying a contextual redefinition of the grammar as a function of the same evolution of the system. We propose on this basis a general theorem for avoiding undecidable problems in computability theory by introducing a new class of recursive functions on different axiomatizations of numbers. From it a series expansion on n algebraic fields can be defined. In such a way, we are able to obtain a very fast extraction procedure of unstable periodic orbits from a generic chaotic dynamics. the computational efficiency of this algorithm allows us to characterize a chaotic system by the complete statistics of its unstable cycles. Some examples of these two techniques are discussed. Finally, we introduce the possibility of an application of this same class of recursive functions to the calculus of the absolute minimum of energy in neural nets, as far as it is equivalent to a well‐formed formula of a first‐order predicate calculus.

A fast hybrid block-sorting algorithm for lossless interferometric data compression

In this paper, we present an evolution of the classical Barrow-Wheeler Transform (BWT) algorithm applied to the sorting procedure of interferometric data, in view of their lossless compression: the Dynamic Segmentation and Sorting (DSS) algorithm. This algorithm is based on the application of the Dynamic Perceptron (DP) neural algorithm. It allows a fast and computationally efficient dynamic segmentation into homogeneous blocks of the coefficients of the Fourier transform. In this way, a limited order sorting procedure of such coefficients can be allowed, optimizing the BWT sorting procedure, characterized as such by an unlimited order. This new method has been specifically studied in order to its hardware implementation for integrating, as a fast compression module, the Micro-Electro-Optical-Mach Zender-Sensor (MEOMS) -- a integrated optical micro-sensor of the MEOS class, based on an array of Mach-Zender type interferometers. This device has been recently designed and constructed in Italy, at the IMM and ISAC Institutes of the Italian National Research Council (CNR) in Bologna. Because of its characteristics, the complete system is suitable for being installed onboard on satellites, for the continuous monitoring of the earth atmosphere. Some encouraging previous results of our lossless compression module of the interferograms outputted by the MEOMS are presented at the end of this paper.

Offline analysis of HEP events by “dynamic perceptron” neural network

In this paper we start from a critical analysis of the fundamental problems of the parallel calculus in linear structures and of their extension to the partial solutions obtained with non-linear architectures. Then, we present shortly a new dynamic architecture able to solve the limitations of the previous architectures through an automatic redefinition of the topology. This architecture is applied to real-time recognition of particle tracks in high-energy accelerators.

Neural module for real-time simultaneous discrimination and locking on different temporal series in noisy environment

After a short discussion on the problems related to the higher order correlations treatment in Hopfield neural net, we propose a modified architecture able to rearrange dynamically its topology in function of the input representation. The relations of this problem with computability problems are briefly considered, particularly in view of avoiding exponential time in computation. Some experimental results are shown for the recognition of particle traces in high energy accelerators and in speaker independent speed recognition.

A dynamic approach to invariant extraction from time-varying inputs by using chaos in neural nets

The authors briefly summarize the main lines of the convergent and chaotic-bifurcative approaches in neural networks, and present a general model founded on an informational use of a chaotic dynamics. It exploits the inner fine structure of unstable periodic orbits of a chaotic dynamics to perform invariant extractions and reconstruction tasks in a dynamic way from a complex time-varying (at least chaotic) input. The neurophysiological background (i.e. synchronization behavior and functional segregation in the sensory cortex) is discussed. The proposed approach suggests that there exists a strict relationship in chaotic systems between dynamic reconstruction, optimization, and stabilization intended as a relaxation process in as much as they are all functions of an inner self-correlation process. This may depend on the fact that chaos, owing to its ultimate deterministic nature, is an intelligent noise. In the fine structure of its invariants, it retains a memory of its evolution

Lossy plus lossless residual encoding with dynamic preprocessing for Hubble Space Telescope fits images

In this paper we present an innovative lossy plus lossless residual encoding scheme consisting of the following steps: (A) Dynamic pre-processing applied either to the original image in order to separate homogeneous parts of it; or to the histogram of the pixel values in order to generate three images each with the same size of the original one that superposed reconstruct exactly the source image. (B) Use of an efficient lossy compression scheme to pre-processed data in order to generate low bit rate images

Principles of computational dynamics: applications to parallel and neural computations

In this paper, starting from a general discussion on neural network dynamics from the standpoint of statistical mechanics, we discuss three different strategies to deal with the problem of pattern recognition in neural nets. Particularly we emphasized the role of matching the intrinsic correlations within the input patterns, to solve the problem of the optimal pattern recognition. In this context, the first two strategies, we applied to different problems and we discuss in this paper, consist essentially in adding either white noise or colored noise (deterministic chaos) on the input pattern pre-processing, to make easier for a classical backpropagation algorithm the class separation, respectively because the input patterns are too correlated among themselves or, on the contrary, are too noisy. The third more radical strategy, we applied to very hard pattern recognition problems in HEP experiments, consists in an automatic (dynamic) redefinition of the same net topology on the inner correlations of the inputs.

Using chaotic neural nets to compress, store, and transmit information

In order to find a very efficient technique to compress, store, and transmit to earth information from a satellite we developed a scheme of chaotic neural net using a new technique of extraction of unstable orbits within a chaotic attractor without applying classical embedding dimensions. We illustrate this technique both from the theoretical and the experimental standpoint. From the theoretical standpoint we show that by this extraction technique it is possible to perform a series expansion of a chaotic dynamics directly through all its composing cycles. Finally, we show how to apply these new possibilities deriving from our new technique of chaos detection, characterization, and stabilization to design a chaotic neural net. Because it is possible to profit by all the skeleton of unstable periodic orbits (i.e., all the inner frequencies) characterizing a chaotic attractor to store information, this net can in principle display an exponential increasing of memory capacity with respect to classical attractor nets.

Automatic redefinition of the fuzzy membership function to deal with high fluctuating phenomena in neural nets

Usually, to discriminate among particle tracks in high energy physics a set of discriminating parameters is used. To cope with the different particle behaviors these parameters are connected by the human observer with boolean operators. We tested successfully an automatic method for particle recognition using a stochastic method to pre-process the input to a back propagation algorithm. The test was made using raw experimental data of electrons and negative pions taken at CERN laboratories (Geneva). From the theoretical standpoint, the stochastic pre-processing of a back propagation algorithm can be interpreted as finding the optimal fuzzy membership function notwithstanding high fluctuating (noisy) input data.

A non-linear neural net to extract symmetries from input f(t)

A model of neural net activation dynamics with fixed random weights and a threshold on each site self-adjusting in function of the inner and unknown invariant of an input f(t) in noisy environments is proposed. This net is devoted to a real-time discrimination between different moving objects to furnish the net, by such preprocessing, with a coherent output for further processing. The main characteristic of the net is its ability to extract without a teacher an invariant of the input by a self-redefinition of the right covariance of the net dynamics forced by the outer input. An algebraic group formalization is proposed as well as a simulation application of the algorithm to the classical T-C in context discrimination problems.<<ETX>>