As neural networks are trained to be deeper and larger, the scalability of neural network analyzers is urgently required. The main technical insight of our method is modularly analyzing neural networks by segmenting a network into blocks and conduct the analysis for each block. In particular, we propose the network block summarization technique to capture the behaviors within a network block using a block summary and leverage the summary to speed up the analysis process. We instantiate our method in the context of a CPU-version of the state-of-the-art analyzer DeepPoly and name our system as Bounded-Block Poly (BBPoly). We evaluate BBPoly extensively on various experiment settings. The experimental result indicates that our method yields comparable precision as DeepPoly but runs faster and requires less computational resources. For example, BBPoly can analyze really large neural networks like SkipNet or ResNet which contain up to one million neurons in less than around 1 hour per input image, while DeepPoly needs to spend even 40 hours to analyze one image.
Recently regression analysis becomes a popular tool for face recognition. The existing regression methods all use the one-dimensional pixel-based error model, which characterizes the representation error pixel by pixel individually and thus neglects the whole structure of the error image. We observe that occlusion and illumination changes generally lead to a low-rank error image. To make use of this low-rank structural information, this paper presents a two-dimensional image matrix based error model, i.e. matrix regression, for face representation and classification. Our model uses the minimal nuclear norm of representation error image as a criterion, and the alternating direction method of multipliers method to calculate the regression coefficients. Compared with the current regression methods, the proposed Nuclear Norm based Matrix Regression (NMR) model is more robust for alleviating the effect of illumination, and more intuitive and powerful for removing the structural noise caused by occlusion. We experiment using four popular face image databases, the Extended Yale B database, the AR database, the Multi-PIE and the FRGC database. Experimental results demonstrate the performance advantage of NMR over the state-of-the-art regression based face recognition methods.