The possibility of improving the generalization capability of a neural network by introducing additive noise to the training samples is discussed. The network considered is a feedforward layered neural network trained with the back-propagation algorithm. Back-propagation training is viewed as nonlinear least-squares regression and the additive noise is interpreted as generating a kernel estimate of the probability density that describes the training vector distribution. Two specific application types are considered: pattern classifier networks and estimation of a nonstochastic mapping from data corrupted by measurement errors. It is not proved that the introduction of additive noise to the training vectors always improves network generalization. However, the analysis suggests mathematically justified rules for choosing the characteristics of noise if additive noise is used in training. Results of mathematical statistics are used to establish various asymptotic consistency results for the proposed method. Numerical simulations support the applicability of the training method.

A diatom-based calibration model for predicting summer temperatures was developed using climatically sensitive subarctic lakes in northern Fennoscandia. The model was applied to a sediment core from a treeline lake to infer trends in Holocene climate. The record exhibits long-term variations, as well as a series of shorter-term fluctuations on a time scale of centuries. Summers were warmest in the area about 6200 cal yr B.P. and featured distinct cooling episodes around 8300, 7200, 4200, 3000, and 400 cal yr B.P., most of these coinciding with some known climate events (e.g., the 8200 cal yr B.P. event and the Little Ice Age). The similarity of the observed shifts with the pacings of climate events from marine and ice-core records represents evidence for coupled ocean–atmosphere forcing of the regional climate.

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