Training with noise is equivalent to Tikhonov regularization

It is well known that the addition of noise to the input data of a neural network during training can, in some circumstances, lead to significant improvements in generalization performance. Previous work has shown that such training with noise is equivalent to a form of regularization in which an extra term is added to the error function. However, the regularization term, which involves second derivatives of the error function, is not bounded below, and so can lead to difficulties if used directly in a learning algorithm based on error minimization. In this paper we show that, for the purposes of network training, the regularization term can be reduced to a positive definite form which involves only first derivatives of the network mapping. For a sum-of-squares error function, the regularization term belongs to the class of generalized Tikhonov regularizers. Direct minimization of the regularized error function provides a practical alternative to training with noise.

Social sustainability initiatives in cocoa supply chains in Africa:an analysis of sustainability reporting of world's major chocolatiers

This research paper focuses on the self-declared initiatives of the four largest chocolate companies to tackle social problems within the context of establishing a sustainable supply chain. After the literature review of sustainability, supply chain management, and cocoa farming, this paper gives an assessment of the extant practices of the chocolatiers and makes a comparative analysis based on Corporate Social Responsibility (CSR) and Sustainability Reports. This paper uses a case study approach based on secondary-data. A roadmap and benchmarking of social sustainability initiatives were conducted for the supply chain management activities of the world's four largest chocolatiers. This paper analyses the extant sustainability practices of the chocolatiers and offers a model framework for comparison of the measures taken. This paper is based on self-declared secondary data. There is a chance that some practices were not documented by the case companies; or that companies claim what they don't actually do. This paper provides a framework for agricultural businesses to compare their sustainability efforts and improve the performance of their supply chains. Originality and value of this research reside in terms of both literature and methodology. The framework for analysing the social sustainability aspects of agricultural supply chains is original and gives an up-to-date view of sustainability practices. The use of secondary data to compare self-declared initiatives is also a novel approach to business sustainability research.