Neural network parametrization of deep-inelastic structure functions

Abstract

We construct a parametrization of deep-inelastic structure functions which retains information on experimental errors and correlations, and which does not introduce any theoretical bias while interpolating between existing data points. We generate a Monte Carlo sample of pseudo-data configurations and we train an ensemble of neural networks on them. This effectively provides us with a probability measure in the space of structure functions, within the whole kinematic region where data are available. This measure can then be used to determine the value of the structure function, its error, point-to-point correlations and generally the value and uncertainty of any function of the structure function itself. We apply this technique to the determination of the structure function F 2 of the proton and deuteron, and a precision determination of the isotriplet combination F 2 [p-d]. We discuss in detail these results, check their stability and accuracy, and make them available in various formats for applications.April 2002

Neural network determination of parton distributions: the nonsinglet case

“…[9]. The basic idea is to combine a Monte Carlo sampling of the probability measure on the space of functions that one is trying to determine (as in the approach of ref.…”

“…[9,10] this strategy was tried off on a somewhat simpler problem, namely, the construction of a parametrization of existing data on the deep-inelastic structure function F 2 (x, Q 2 ) of the proton and neutron. In such case, one is only testing that the method can be used to construct a faithful representation of the probability density in a space of functions, based on the measurement of the function at a finite discrete number of points.…”

“…In section 2 we review the approach of refs. [9,10] to the construction of a neural network parametrization of a function based on its experimental sampling at a finite set of points, we describe its application to the construction of a parton set, thereby outlining the general strategy of the method, and we summarize the main features of our approach and thus of our results. In section 3 we construct a Monte Carlo representation of the information contained in the data, and test for its statistical accuracy.…”

“…[9] provides a general framework for the parametrization of physical observables by means of neural networks. This method has since then been…”

“…[9], it involves two distinct stages in order to go from the data to the parton parametrization. In the first stage, a Monte Carlo sample of replicas of the data ("artificial data") is generated.…”