Regularization is a well studied problem in the context of neural networks. It is usually used to improve the generalization performance when the number of input samples is relatively small or heavily contaminated with noise. The regularization of a parametric model can be achieved in different manners some of which are early stopping (Morgan and Bourlard, 1990), weight decay, output smoothing that are used to avoid overfitting during the training of the considered model. From a Bayesian point of view, many regularization techniques correspond to imposing certain prior distributions on model parameters (Krogh and Hertz, 1991). Using Bishop's approximation (Bishop, 1995) of the objective function when a restricted type of noise is added to the input of a parametric function, we derive the higher order terms of the Taylor expansion and analyze the coefficients of the regularization terms induced by the noisy input. In particular we study the effect of penalizing the Hessian of the mapping function with respect to the input in terms of generalization performance. We also show how we can control independently this coefficient by explicitly penalizing the Jacobian of the mapping function on corrupted inputs.

研究如何通过加入噪声对神经网络进行正则化及对其泛化性能的影响进行分析，并探讨不同类型的正则化技术对模型参数影响的先验分布。

对受正则化目标训练的模型输入添加噪音