<title>Dynamic perceptron: some theorems about the possibility of parallel pattern recognition with an application to high-energy physics</title>

Abstract

In the context of M.Minsky's and S.Papert's theorems on the impossibility of evaluating simple linear predicates by parallel architectures we want to show how these limitations can be avoided by introducing a generalized input-dependent preprocessing technique that does not suppose any a priori knowledge of input like in classical input filtering procedures. This technique can be formalized in a very general way and can be also deduced by meta-mathernatical arguments. A further development of the same technique can be applied at level of learning procedure to introduce in such a way the complete notion of " dynamic perceptron". From the experimental standpoint, we show two applications of the "dynamic perceptron" in particle track recognition in high-energy accelerators. Firstly, we show the amazing improvement of performances that can be obtained in a perceptron architecture with classical learning by adding our "dynamic" pre-processing technique, already introduced last year in another paper presented at this Conference. Secondly, we show the first results of this technique extended also at the level of learning procedure always applied to the problem of particle track recognition. This work is a part of "Fenice" international collaboration supported by INFN (National Institute for Nuclear Physics) devoted to the study of the time-like electromagnetic form factor of neutrons obtained by electron-positron high energy collisions in ADONE (Frascati, Rome) storage ring.1 The problem: parallel computation in the "geometrical" perceptron.Let us consider a classical perceptron computing on a lattice R a linear function 111(X) of a generic input X C R. The problem we want to discuss is whether there exists a predicate 4 able to assume the input characteristic function, given a fixed topology according to which the perceptron "reads" the input. In other terms, given some partition {A} of the retina R, our aim is to ascertain whether there exists a predicate 11' able to decide whether a generic input X has at least one point in each cell A.Formally, Definition 1 Let the retina R be an arbitrary set of points (it can be also finite).Definition 2 We define as the input X a generic subset of R: X C R. We indicate by bold letters the collections of subsets of I? 540 / SPIE Vol. 2243 0-8194-1547-2/94/$6.00 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/17/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx

Direct ultrashort-pulse intensity and phase retrieval by frequency-resolved optical gating and a computational neural network

“…5 -7 It has been shown that neural nets can accurately simulate any function. 6,7 Success has been attained in such diverse applications as handwriting recognition, high-energy physics, 8 and stockmarket prediction. In its simplest form a neural net (see Fig.…”