Sensitivity analysis of neocognitron

Fukushima's (1988; 1989; 1992; 1993) neocognitron model is well-known for its performance in visual pattern recognition. Through a training process, the visual pattern information is stored in a form of numerical weights in memory. When the model is actually implemented in hardware, weight errors and input noises caused by hardware imprecision and imperfect input devices respectively cannot be avoided and consequently the recognition performance usually degrades substantially from the theoretical result. In this paper, the effects of weight imprecision and input noise to the recognition performance of neocognitron are studied through a sensitivity analysis of the model. The sensitivity of an S-cell to weight and input perturbations is first derived, as a function of the weight and input perturbation ratios. An algorithm is proposed to combine the sensitivities of the S-cells in different layers to form the overall sensitivity of the model. The established sensitivity measure is then demonstrated to be a useful tool for hardware design. In addition, it has been found that the decision (recognition) error of neocognitron increases with the weight perturbation, the input perturbation, and the number of weights per neuron. This is similar to the result obtained for the Madaline model. Another important result is that decision error increases with the threshold/selectivity parameter. This supports the functional description of the threshold reported by Fukushina.